From 2f94cfb14f621bf2a32bfb2ded9f95bd572836d9 Mon Sep 17 00:00:00 2001 From: agc Date: Sat, 12 Jul 2014 15:45:52 +0000 Subject: Update netpgpverify package to 20140712 + bring the bignum implementation up to the latest version + radix conversion routines added + bitwise operations added + whitespace cleanups --- security/netpgpverify/Makefile | 4 +- security/netpgpverify/files/bignum.c | 8671 +++++++++++++++++----------------- security/netpgpverify/files/bn.h | 6 + 3 files changed, 4362 insertions(+), 4319 deletions(-) diff --git a/security/netpgpverify/Makefile b/security/netpgpverify/Makefile index 70428eede59..a5a1b610aec 100644 --- a/security/netpgpverify/Makefile +++ b/security/netpgpverify/Makefile @@ -1,6 +1,6 @@ -# $NetBSD: Makefile,v 1.7 2014/03/05 04:51:37 agc Exp $ +# $NetBSD: Makefile,v 1.8 2014/07/12 15:45:52 agc Exp $ -DISTNAME= netpgpverify-20140304 +DISTNAME= netpgpverify-20140712 CATEGORIES= security MASTER_SITES= # empty DISTFILES= # empty diff --git a/security/netpgpverify/files/bignum.c b/security/netpgpverify/files/bignum.c index c825b30c501..f02b512d0fe 100644 --- a/security/netpgpverify/files/bignum.c +++ b/security/netpgpverify/files/bignum.c @@ -39,26 +39,20 @@ #include "config.h" #include -#include #include #ifdef _KERNEL # include #else # include -# include -# include # include # include # include # include -# include # include #endif -#include "misc.h" #include "bn.h" -#include "digest.h" /**************************************************************************/ @@ -94,116 +88,108 @@ #define __arraycount(__x) (sizeof(__x) / sizeof(__x[0])) #endif -#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO) - -#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1) +#define MP_ISZERO(a) (((a)->used == 0) ? MP_YES : MP_NO) typedef int mp_err; -static int mp_mul(mp_int * a, mp_int * b, mp_int * c); -static int mp_sqr(mp_int * a, mp_int * b); +static int signed_multiply(mp_int * a, mp_int * b, mp_int * c); +static int square(mp_int * a, mp_int * b); -static int mp_sub_d(mp_int *a, mp_digit b, mp_int *c); +static int signed_subtract_word(mp_int *a, mp_digit b, mp_int *c); -/* set to zero */ -static void -mp_zero(mp_int *a) +static inline void * +allocate(size_t n, size_t m) { - int n; - mp_digit *tmp; + return calloc(n, m); +} - a->sign = MP_ZPOS; - a->used = 0; +static inline void +deallocate(void *v, size_t sz) +{ + USE_ARG(sz); + free(v); +} - tmp = a->dp; - /* XXX - memset */ - for (n = 0; n < a->alloc; n++) { - *tmp++ = 0; - } +/* set to zero */ +static inline void +mp_zero(mp_int *a) +{ + a->sign = MP_ZPOS; + a->used = 0; + memset(a->dp, 0x0, a->alloc * sizeof(*a->dp)); } /* grow as required */ static int mp_grow(mp_int *a, int size) { - int i; - mp_digit *tmp; - - /* if the alloc size is smaller alloc more ram */ - if (a->alloc < size) { - /* ensure there are always at least MP_PREC digits extra on top */ - size += (MP_PREC * 2) - (size % MP_PREC); - - /* reallocate the array a->dp - * - * We store the return in a temporary variable - * in case the operation failed we don't want - * to overwrite the dp member of a. - */ - tmp = realloc(a->dp, sizeof(*tmp) * size); - if (tmp == NULL) { - /* reallocation failed but "a" is still valid [can be freed] */ - return MP_MEM; - } - - /* reallocation succeeded so set a->dp */ - a->dp = tmp; - - /* zero excess digits */ - i = a->alloc; - a->alloc = size; - for (; i < a->alloc; i++) { - a->dp[i] = 0; - } - } - return MP_OKAY; + mp_digit *tmp; + + /* if the alloc size is smaller alloc more ram */ + if (a->alloc < size) { + /* ensure there are always at least MP_PREC digits extra on top */ + size += (MP_PREC * 2) - (size % MP_PREC); + + /* reallocate the array a->dp + * + * We store the return in a temporary variable + * in case the operation failed we don't want + * to overwrite the dp member of a. + */ + tmp = realloc(a->dp, sizeof(*tmp) * size); + if (tmp == NULL) { + /* reallocation failed but "a" is still valid [can be freed] */ + return MP_MEM; + } + + /* reallocation succeeded so set a->dp */ + a->dp = tmp; + /* zero excess digits */ + memset(&a->dp[a->alloc], 0x0, (size - a->alloc) * sizeof(*a->dp)); + a->alloc = size; + } + return MP_OKAY; } /* shift left a certain amount of digits */ static int -mp_lshd (mp_int * a, int b) +lshift_digits(mp_int * a, int b) { - int x, res; - - /* if its less than zero return */ - if (b <= 0) { - return MP_OKAY; - } + mp_digit *top, *bottom; + int x, res; - /* grow to fit the new digits */ - if (a->alloc < a->used + b) { - if ((res = mp_grow (a, a->used + b)) != MP_OKAY) { - return res; - } - } + /* if its less than zero return */ + if (b <= 0) { + return MP_OKAY; + } - { - mp_digit *top, *bottom; + /* grow to fit the new digits */ + if (a->alloc < a->used + b) { + if ((res = mp_grow(a, a->used + b)) != MP_OKAY) { + return res; + } + } - /* increment the used by the shift amount then copy upwards */ - a->used += b; + /* increment the used by the shift amount then copy upwards */ + a->used += b; - /* top */ - top = a->dp + a->used - 1; + /* top */ + top = a->dp + a->used - 1; - /* base */ - bottom = a->dp + a->used - 1 - b; + /* base */ + bottom = a->dp + a->used - 1 - b; - /* much like mp_rshd this is implemented using a sliding window - * except the window goes the otherway around. Copying from - * the bottom to the top. see bn_mp_rshd.c for more info. - */ - for (x = a->used - 1; x >= b; x--) { - *top-- = *bottom--; - } + /* much like rshift_digits this is implemented using a sliding window + * except the window goes the otherway around. Copying from + * the bottom to the top. + */ + for (x = a->used - 1; x >= b; x--) { + *top-- = *bottom--; + } - /* zero the lower digits */ - top = a->dp; - for (x = 0; x < b; x++) { - *top++ = 0; - } - } - return MP_OKAY; + /* zero the lower digits */ + memset(a->dp, 0x0, b * sizeof(*a->dp)); + return MP_OKAY; } /* trim unused digits @@ -214,710 +200,646 @@ mp_lshd (mp_int * a, int b) * are no more leading digits */ static void -mp_clamp (mp_int * a) +trim_unused_digits(mp_int * a) { - /* decrease used while the most significant digit is - * zero. - */ - while (a->used > 0 && a->dp[a->used - 1] == 0) { - --(a->used); - } - - /* reset the sign flag if used == 0 */ - if (a->used == 0) { - a->sign = MP_ZPOS; - } + /* decrease used while the most significant digit is + * zero. + */ + while (a->used > 0 && a->dp[a->used - 1] == 0) { + a->used -= 1; + } + /* reset the sign flag if used == 0 */ + if (a->used == 0) { + a->sign = MP_ZPOS; + } } /* copy, b = a */ static int mp_copy(BIGNUM *a, BIGNUM *b) { - int res, n; + int res; + + /* if dst == src do nothing */ + if (a == b) { + return MP_OKAY; + } + if (a == NULL || b == NULL) { + return MP_VAL; + } + + /* grow dest */ + if (b->alloc < a->used) { + if ((res = mp_grow(b, a->used)) != MP_OKAY) { + return res; + } + } + + memcpy(b->dp, a->dp, a->used * sizeof(*b->dp)); + if (b->used > a->used) { + memset(&b->dp[a->used], 0x0, (b->used - a->used) * sizeof(*b->dp)); + } + + /* copy used count and sign */ + b->used = a->used; + b->sign = a->sign; + return MP_OKAY; +} + +/* shift left by a certain bit count */ +static int +lshift_bits(mp_int *a, int b, mp_int *c) +{ + mp_digit d; + int res; + + /* copy */ + if (a != c) { + if ((res = mp_copy(a, c)) != MP_OKAY) { + return res; + } + } - /* if dst == src do nothing */ - if (a == b) { - return MP_OKAY; - } - if (a == NULL || b == NULL) { - return MP_VAL; - } + if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) { + if ((res = mp_grow(c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) { + return res; + } + } - /* grow dest */ - if (b->alloc < a->used) { - if ((res = mp_grow (b, a->used)) != MP_OKAY) { - return res; - } - } + /* shift by as many digits in the bit count */ + if (b >= (int)DIGIT_BIT) { + if ((res = lshift_digits(c, b / DIGIT_BIT)) != MP_OKAY) { + return res; + } + } - /* zero b and copy the parameters over */ - { - mp_digit *tmpa, *tmpb; + /* shift any bit count < DIGIT_BIT */ + d = (mp_digit) (b % DIGIT_BIT); + if (d != 0) { + mp_digit *tmpc, shift, mask, carry, rr; + int x; - /* pointer aliases */ + /* bitmask for carries */ + mask = (((mp_digit)1) << d) - 1; - /* source */ - tmpa = a->dp; + /* shift for msbs */ + shift = DIGIT_BIT - d; - /* destination */ - tmpb = b->dp; + /* alias */ + tmpc = c->dp; - /* copy all the digits */ - for (n = 0; n < a->used; n++) { - *tmpb++ = *tmpa++; - } + /* carry */ + carry = 0; + for (x = 0; x < c->used; x++) { + /* get the higher bits of the current word */ + rr = (*tmpc >> shift) & mask; - /* clear high digits */ - for (; n < b->used; n++) { - *tmpb++ = 0; - } - } + /* shift the current word and OR in the carry */ + *tmpc = ((*tmpc << d) | carry) & MP_MASK; + ++tmpc; - /* copy used count and sign */ - b->used = a->used; - b->sign = a->sign; - return MP_OKAY; -} + /* set the carry to the carry bits of the current word */ + carry = rr; + } -/* shift left by a certain bit count */ -static int -mp_mul_2d(mp_int *a, int b, mp_int *c) -{ - mp_digit d; - int res; - - /* copy */ - if (a != c) { - if ((res = mp_copy (a, c)) != MP_OKAY) { - return res; - } - } - - if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) { - if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) { - return res; - } - } - - /* shift by as many digits in the bit count */ - if (b >= (int)DIGIT_BIT) { - if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) { - return res; - } - } - - /* shift any bit count < DIGIT_BIT */ - d = (mp_digit) (b % DIGIT_BIT); - if (d != 0) { - mp_digit *tmpc, shift, mask, r, rr; - int x; - - /* bitmask for carries */ - mask = (((mp_digit)1) << d) - 1; - - /* shift for msbs */ - shift = DIGIT_BIT - d; - - /* alias */ - tmpc = c->dp; - - /* carry */ - r = 0; - for (x = 0; x < c->used; x++) { - /* get the higher bits of the current word */ - rr = (*tmpc >> shift) & mask; - - /* shift the current word and OR in the carry */ - *tmpc = ((*tmpc << d) | r) & MP_MASK; - ++tmpc; - - /* set the carry to the carry bits of the current word */ - r = rr; - } - - /* set final carry */ - if (r != 0) { - c->dp[(c->used)++] = r; - } - } - mp_clamp (c); - return MP_OKAY; + /* set final carry */ + if (carry != 0) { + c->dp[c->used++] = carry; + } + } + trim_unused_digits(c); + return MP_OKAY; } /* reads a unsigned char array, assumes the msb is stored first [big endian] */ static int mp_read_unsigned_bin(mp_int *a, const uint8_t *b, int c) { - int res; + int res; - /* make sure there are at least two digits */ - if (a->alloc < 2) { - if ((res = mp_grow(a, 2)) != MP_OKAY) { - return res; - } - } + /* make sure there are at least two digits */ + if (a->alloc < 2) { + if ((res = mp_grow(a, 2)) != MP_OKAY) { + return res; + } + } - /* zero the int */ - mp_zero (a); + /* zero the int */ + mp_zero(a); - /* read the bytes in */ - while (c-- > 0) { - if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) { - return res; - } + /* read the bytes in */ + while (c-- > 0) { + if ((res = lshift_bits(a, 8, a)) != MP_OKAY) { + return res; + } - a->dp[0] |= *b++; - a->used += 1; - } - mp_clamp (a); - return MP_OKAY; + a->dp[0] |= *b++; + a->used += 1; + } + trim_unused_digits(a); + return MP_OKAY; } -/* returns the number of bits in an int */ +/* returns the number of bits in an mpi */ static int mp_count_bits(const mp_int *a) { - int r; - mp_digit q; + int r; + mp_digit q; + + /* shortcut */ + if (a->used == 0) { + return 0; + } - /* shortcut */ - if (a->used == 0) { - return 0; - } + /* get number of digits and add that */ + r = (a->used - 1) * DIGIT_BIT; - /* get number of digits and add that */ - r = (a->used - 1) * DIGIT_BIT; - - /* take the last digit and count the bits in it */ - q = a->dp[a->used - 1]; - while (q > ((mp_digit) 0)) { - ++r; - q >>= ((mp_digit) 1); - } - return r; + /* take the last digit and count the bits in it */ + for (q = a->dp[a->used - 1]; q > ((mp_digit) 0) ; r++) { + q >>= ((mp_digit) 1); + } + return r; } /* compare maginitude of two ints (unsigned) */ static int -mp_cmp_mag (mp_int * a, mp_int * b) +compare_magnitude(mp_int * a, mp_int * b) { - int n; - mp_digit *tmpa, *tmpb; + int n; + mp_digit *tmpa, *tmpb; + + /* compare based on # of non-zero digits */ + if (a->used > b->used) { + return MP_GT; + } - /* compare based on # of non-zero digits */ - if (a->used > b->used) { - return MP_GT; - } - - if (a->used < b->used) { - return MP_LT; - } + if (a->used < b->used) { + return MP_LT; + } - /* alias for a */ - tmpa = a->dp + (a->used - 1); + /* alias for a */ + tmpa = a->dp + (a->used - 1); - /* alias for b */ - tmpb = b->dp + (a->used - 1); + /* alias for b */ + tmpb = b->dp + (a->used - 1); - /* compare based on digits */ - for (n = 0; n < a->used; ++n, --tmpa, --tmpb) { - if (*tmpa > *tmpb) { - return MP_GT; - } + /* compare based on digits */ + for (n = 0; n < a->used; ++n, --tmpa, --tmpb) { + if (*tmpa > *tmpb) { + return MP_GT; + } - if (*tmpa < *tmpb) { - return MP_LT; - } - } - return MP_EQ; + if (*tmpa < *tmpb) { + return MP_LT; + } + } + return MP_EQ; } /* compare two ints (signed)*/ static int -mp_cmp (mp_int * a, mp_int * b) -{ - /* compare based on sign */ - if (a->sign != b->sign) { - if (a->sign == MP_NEG) { - return MP_LT; - } else { - return MP_GT; - } - } - - /* compare digits */ - if (a->sign == MP_NEG) { - /* if negative compare opposite direction */ - return mp_cmp_mag(b, a); - } else { - return mp_cmp_mag(a, b); - } +signed_compare(mp_int * a, mp_int * b) +{ + /* compare based on sign */ + if (a->sign != b->sign) { + return (a->sign == MP_NEG) ? MP_LT : MP_GT; + } + return (a->sign == MP_NEG) ? compare_magnitude(b, a) : compare_magnitude(a, b); } /* get the size for an unsigned equivalent */ static int -mp_unsigned_bin_size (mp_int * a) +mp_unsigned_bin_size(mp_int * a) { - int size = mp_count_bits (a); - return (size / 8 + ((size & 7) != 0 ? 1 : 0)); + int size = mp_count_bits(a); + + return (size / 8 + ((size & 7) != 0 ? 1 : 0)); } /* init a new mp_int */ static int -mp_init (mp_int * a) +mp_init(mp_int * a) { - int i; - - /* allocate memory required and clear it */ - a->dp = netpgp_allocate(1, sizeof (*a->dp) * MP_PREC); - if (a->dp == NULL) { - return MP_MEM; - } + /* allocate memory required and clear it */ + a->dp = allocate(1, sizeof(*a->dp) * MP_PREC); + if (a->dp == NULL) { + return MP_MEM; + } - /* set the digits to zero */ - for (i = 0; i < MP_PREC; i++) { - a->dp[i] = 0; - } + /* set the digits to zero */ + memset(a->dp, 0x0, MP_PREC * sizeof(*a->dp)); - /* set the used to zero, allocated digits to the default precision - * and sign to positive */ - a->used = 0; - a->alloc = MP_PREC; - a->sign = MP_ZPOS; + /* set the used to zero, allocated digits to the default precision + * and sign to positive */ + a->used = 0; + a->alloc = MP_PREC; + a->sign = MP_ZPOS; - return MP_OKAY; + return MP_OKAY; } /* clear one (frees) */ static void -mp_clear (mp_int * a) +mp_clear(mp_int * a) { - int i; - - /* only do anything if a hasn't been freed previously */ - if (a->dp != NULL) { - /* first zero the digits */ - for (i = 0; i < a->used; i++) { - a->dp[i] = 0; - } + /* only do anything if a hasn't been freed previously */ + if (a->dp != NULL) { + memset(a->dp, 0x0, a->used * sizeof(*a->dp)); - /* free ram */ - netpgp_deallocate(a->dp, (size_t)a->alloc); + /* free ram */ + deallocate(a->dp, (size_t)a->alloc); - /* reset members to make debugging easier */ - a->dp = NULL; - a->alloc = a->used = 0; - a->sign = MP_ZPOS; - } + /* reset members to make debugging easier */ + a->dp = NULL; + a->alloc = a->used = 0; + a->sign = MP_ZPOS; + } } static int mp_init_multi(mp_int *mp, ...) { - mp_err res = MP_OKAY; /* Assume ok until proven otherwise */ - int n = 0; /* Number of ok inits */ - mp_int* cur_arg = mp; - va_list args; - - va_start(args, mp); /* init args to next argument from caller */ - while (cur_arg != NULL) { - if (mp_init(cur_arg) != MP_OKAY) { - /* Oops - error! Back-track and mp_clear what we already - succeeded in init-ing, then return error. - */ - va_list clean_args; - - /* end the current list */ - va_end(args); - - /* now start cleaning up */ - cur_arg = mp; - va_start(clean_args, mp); - while (n--) { - mp_clear(cur_arg); - cur_arg = va_arg(clean_args, mp_int*); - } - va_end(clean_args); - res = MP_MEM; - break; - } - n++; - cur_arg = va_arg(args, mp_int*); - } - va_end(args); - return res; /* Assumed ok, if error flagged above. */ + mp_err res = MP_OKAY; /* Assume ok until proven otherwise */ + int n = 0; /* Number of ok inits */ + mp_int* cur_arg = mp; + va_list args; + + va_start(args, mp); /* init args to next argument from caller */ + while (cur_arg != NULL) { + if (mp_init(cur_arg) != MP_OKAY) { + /* Oops - error! Back-track and mp_clear what we already + succeeded in init-ing, then return error. + */ + va_list clean_args; + + /* end the current list */ + va_end(args); + + /* now start cleaning up */ + cur_arg = mp; + va_start(clean_args, mp); + while (n--) { + mp_clear(cur_arg); + cur_arg = va_arg(clean_args, mp_int*); + } + va_end(clean_args); + res = MP_MEM; + break; + } + n++; + cur_arg = va_arg(args, mp_int*); + } + va_end(args); + return res; /* Assumed ok, if error flagged above. */ } /* init an mp_init for a given size */ static int -mp_init_size (mp_int * a, int size) +mp_init_size(mp_int * a, int size) { - int x; - - /* pad size so there are always extra digits */ - size += (MP_PREC * 2) - (size % MP_PREC); - - /* alloc mem */ - a->dp = netpgp_allocate (1, sizeof (*a->dp) * size); - if (a->dp == NULL) { - return MP_MEM; - } + /* pad size so there are always extra digits */ + size += (MP_PREC * 2) - (size % MP_PREC); - /* set the members */ - a->used = 0; - a->alloc = size; - a->sign = MP_ZPOS; + /* alloc mem */ + a->dp = allocate(1, sizeof(*a->dp) * size); + if (a->dp == NULL) { + return MP_MEM; + } - /* zero the digits */ - for (x = 0; x < size; x++) { - a->dp[x] = 0; - } + /* set the members */ + a->used = 0; + a->alloc = size; + a->sign = MP_ZPOS; - return MP_OKAY; + /* zero the digits */ + memset(a->dp, 0x0, size * sizeof(*a->dp)); + return MP_OKAY; } /* creates "a" then copies b into it */ -static int mp_init_copy (mp_int * a, mp_int * b) +static int +mp_init_copy(mp_int * a, mp_int * b) { - int res; + int res; - if ((res = mp_init (a)) != MP_OKAY) { - return res; - } - return mp_copy (b, a); + if ((res = mp_init(a)) != MP_OKAY) { + return res; + } + return mp_copy(b, a); } /* low level addition, based on HAC pp.594, Algorithm 14.7 */ static int -s_mp_add (mp_int * a, mp_int * b, mp_int * c) -{ - mp_int *x; - int olduse, res, min, max; - - /* find sizes, we let |a| <= |b| which means we have to sort - * them. "x" will point to the input with the most digits - */ - if (a->used > b->used) { - min = b->used; - max = a->used; - x = a; - } else { - min = a->used; - max = b->used; - x = b; - } - - /* init result */ - if (c->alloc < max + 1) { - if ((res = mp_grow (c, max + 1)) != MP_OKAY) { - return res; - } - } - - /* get old used digit count and set new one */ - olduse = c->used; - c->used = max + 1; - - { - mp_digit u, *tmpa, *tmpb, *tmpc; - int i; - - /* alias for digit pointers */ - - /* first input */ - tmpa = a->dp; - - /* second input */ - tmpb = b->dp; - - /* destination */ - tmpc = c->dp; - - /* zero the carry */ - u = 0; - for (i = 0; i < min; i++) { - /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */ - *tmpc = *tmpa++ + *tmpb++ + u; - - /* U = carry bit of T[i] */ - u = *tmpc >> ((mp_digit)DIGIT_BIT); - - /* take away carry bit from T[i] */ - *tmpc++ &= MP_MASK; - } - - /* now copy higher words if any, that is in A+B - * if A or B has more digits add those in - */ - if (min != max) { - for (; i < max; i++) { - /* T[i] = X[i] + U */ - *tmpc = x->dp[i] + u; - - /* U = carry bit of T[i] */ - u = *tmpc >> ((mp_digit)DIGIT_BIT); - - /* take away carry bit from T[i] */ - *tmpc++ &= MP_MASK; - } - } - - /* add carry */ - *tmpc++ = u; - - /* clear digits above oldused */ - for (i = c->used; i < olduse; i++) { - *tmpc++ = 0; - } - } - - mp_clamp (c); - return MP_OKAY; +basic_add(mp_int * a, mp_int * b, mp_int * c) +{ + mp_int *x; + int olduse, res, min, max; + + /* find sizes, we let |a| <= |b| which means we have to sort + * them. "x" will point to the input with the most digits + */ + if (a->used > b->used) { + min = b->used; + max = a->used; + x = a; + } else { + min = a->used; + max = b->used; + x = b; + } + + /* init result */ + if (c->alloc < max + 1) { + if ((res = mp_grow(c, max + 1)) != MP_OKAY) { + return res; + } + } + + /* get old used digit count and set new one */ + olduse = c->used; + c->used = max + 1; + + { + mp_digit carry, *tmpa, *tmpb, *tmpc; + int i; + + /* alias for digit pointers */ + + /* first input */ + tmpa = a->dp; + + /* second input */ + tmpb = b->dp; + + /* destination */ + tmpc = c->dp; + + /* zero the carry */ + carry = 0; + for (i = 0; i < min; i++) { + /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */ + *tmpc = *tmpa++ + *tmpb++ + carry; + + /* U = carry bit of T[i] */ + carry = *tmpc >> ((mp_digit)DIGIT_BIT); + + /* take away carry bit from T[i] */ + *tmpc++ &= MP_MASK; + } + + /* now copy higher words if any, that is in A+B + * if A or B has more digits add those in + */ + if (min != max) { + for (; i < max; i++) { + /* T[i] = X[i] + U */ + *tmpc = x->dp[i] + carry; + + /* U = carry bit of T[i] */ + carry = *tmpc >> ((mp_digit)DIGIT_BIT); + + /* take away carry bit from T[i] */ + *tmpc++ &= MP_MASK; + } + } + + /* add carry */ + *tmpc++ = carry; + + /* clear digits above oldused */ + if (olduse > c->used) { + memset(tmpc, 0x0, (olduse - c->used) * sizeof(*c->dp)); + } + } + + trim_unused_digits(c); + return MP_OKAY; } /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */ static int -s_mp_sub (mp_int * a, mp_int * b, mp_int * c) -{ - int olduse, res, min, max; - - /* find sizes */ - min = b->used; - max = a->used; - - /* init result */ - if (c->alloc < max) { - if ((res = mp_grow (c, max)) != MP_OKAY) { - return res; - } - } - olduse = c->used; - c->used = max; - - { - mp_digit u, *tmpa, *tmpb, *tmpc; - int i; - - /* alias for digit pointers */ - tmpa = a->dp; - tmpb = b->dp; - tmpc = c->dp; - - /* set carry to zero */ - u = 0; - for (i = 0; i < min; i++) { - /* T[i] = A[i] - B[i] - U */ - *tmpc = *tmpa++ - *tmpb++ - u; - - /* U = carry bit of T[i] - * Note this saves performing an AND operation since - * if a carry does occur it will propagate all the way to the - * MSB. As a result a single shift is enough to get the carry - */ - u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1)); - - /* Clear carry from T[i] */ - *tmpc++ &= MP_MASK; - } - - /* now copy higher words if any, e.g. if A has more digits than B */ - for (; i < max; i++) { - /* T[i] = A[i] - U */ - *tmpc = *tmpa++ - u; - - /* U = carry bit of T[i] */ - u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1)); - - /* Clear carry from T[i] */ - *tmpc++ &= MP_MASK; - } - - /* clear digits above used (since we may not have grown result above) */ - for (i = c->used; i < olduse; i++) { - *tmpc++ = 0; - } - } - - mp_clamp (c); - return MP_OKAY; -} +basic_subtract(mp_int * a, mp_int * b, mp_int * c) +{ + int olduse, res, min, max; -/* high level subtraction (handles signs) */ -static int -mp_sub (mp_int * a, mp_int * b, mp_int * c) -{ - int sa, sb, res; - - sa = a->sign; - sb = b->sign; - - if (sa != sb) { - /* subtract a negative from a positive, OR */ - /* subtract a positive from a negative. */ - /* In either case, ADD their magnitudes, */ - /* and use the sign of the first number. */ - c->sign = sa; - res = s_mp_add (a, b, c); - } else { - /* subtract a positive from a positive, OR */ - /* subtract a negative from a negative. */ - /* First, take the difference between their */ - /* magnitudes, then... */ - if (mp_cmp_mag (a, b) != MP_LT) { - /* Copy the sign from the first */ - c->sign = sa; - /* The first has a larger or equal magnitude */ - res = s_mp_sub (a, b, c); - } else { - /* The result has the *opposite* sign from */ - /* the first number. */ - c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS; - /* The second has a larger magnitude */ - res = s_mp_sub (b, a, c); - } - } - return res; -} + /* find sizes */ + min = b->used; + max = a->used; -/* shift right a certain amount of digits */ -static int mp_rshd (mp_int * a, int b) -{ - int x; + /* init result */ + if (c->alloc < max) { + if ((res = mp_grow(c, max)) != MP_OKAY) { + return res; + } + } + olduse = c->used; + c->used = max; + + { + mp_digit carry, *tmpa, *tmpb, *tmpc; + int i; + + /* alias for digit pointers */ + tmpa = a->dp; + tmpb = b->dp; + tmpc = c->dp; + + /* set carry to zero */ + carry = 0; + for (i = 0; i < min; i++) { + /* T[i] = A[i] - B[i] - U */ + *tmpc = *tmpa++ - *tmpb++ - carry; + + /* U = carry bit of T[i] + * Note this saves performing an AND operation since + * if a carry does occur it will propagate all the way to the + * MSB. As a result a single shift is enough to get the carry + */ + carry = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof(mp_digit) - 1)); + + /* Clear carry from T[i] */ + *tmpc++ &= MP_MASK; + } - /* if b <= 0 then ignore it */ - if (b <= 0) { - return 0; - } + /* now copy higher words if any, e.g. if A has more digits than B */ + for (; i < max; i++) { + /* T[i] = A[i] - U */ + *tmpc = *tmpa++ - carry; - /* if b > used then simply zero it and return */ - if (a->used <= b) { - mp_zero (a); - return 0; - } + /* U = carry bit of T[i] */ + carry = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof(mp_digit) - 1)); - { - mp_digit *bottom, *top; + /* Clear carry from T[i] */ + *tmpc++ &= MP_MASK; + } - /* shift the digits down */ + /* clear digits above used (since we may not have grown result above) */ + if (olduse > c->used) { + memset(tmpc, 0x0, (olduse - c->used) * sizeof(*a->dp)); + } + } - /* bottom */ - bottom = a->dp; + trim_unused_digits(c); + return MP_OKAY; +} - /* top [offset into digits] */ - top = a->dp + b; +/* high level subtraction (handles signs) */ +static int +signed_subtract(mp_int * a, mp_int * b, mp_int * c) +{ + int sa, sb, res; + + sa = a->sign; + sb = b->sign; + + if (sa != sb) { + /* subtract a negative from a positive, OR */ + /* subtract a positive from a negative. */ + /* In either case, ADD their magnitudes, */ + /* and use the sign of the first number. */ + c->sign = sa; + res = basic_add(a, b, c); + } else { + /* subtract a positive from a positive, OR */ + /* subtract a negative from a negative. */ + /* First, take the difference between their */ + /* magnitudes, then... */ + if (compare_magnitude(a, b) != MP_LT) { + /* Copy the sign from the first */ + c->sign = sa; + /* The first has a larger or equal magnitude */ + res = basic_subtract(a, b, c); + } else { + /* The result has the *opposite* sign from */ + /* the first number. */ + c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS; + /* The second has a larger magnitude */ + res = basic_subtract(b, a, c); + } + } + return res; +} - /* this is implemented as a sliding window where - * the window is b-digits long and digits from - * the top of the window are copied to the bottom - * - * e.g. +/* shift right a certain amount of digits */ +static int +rshift_digits(mp_int * a, int b) +{ + /* if b <= 0 then ignore it */ + if (b <= 0) { + return 0; + } - b-2 | b-1 | b0 | b1 | b2 | ... | bb | ----> - /\ | ----> - \-------------------/ ----> - */ - for (x = 0; x < (a->used - b); x++) { - *bottom++ = *top++; - } + /* if b > used then simply zero it and return */ + if (a->used <= b) { + mp_zero(a); + return 0; + } - /* zero the top digits */ - for (; x < a->used; x++) { - *bottom++ = 0; - } - } - - /* remove excess digits */ - a->used -= b; - return 1; + /* this is implemented as a sliding window where + * the window is b-digits long and digits from + * the top of the window are copied to the bottom + * + * e.g. + + b-2 | b-1 | b0 | b1 | b2 | ... | bb | ----> + /\ | ----> + \-------------------/ ----> + */ + memmove(a->dp, &a->dp[b], (a->used - b) * sizeof(*a->dp)); + memset(&a->dp[a->used - b], 0x0, b * sizeof(*a->dp)); + + /* remove excess digits */ + a->used -= b; + return 1; } /* multiply by a digit */ static int -mp_mul_d (mp_int * a, mp_digit b, mp_int * c) +multiply_digit(mp_int * a, mp_digit b, mp_int * c) { - mp_digit u, *tmpa, *tmpc; - mp_word r; - int ix, res, olduse; - - /* make sure c is big enough to hold a*b */ - if (c->alloc < a->used + 1) { - if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) { - return res; - } - } + mp_digit carry, *tmpa, *tmpc; + mp_word r; + int ix, res, olduse; - /* get the original destinations used count */ - olduse = c->used; + /* make sure c is big enough to hold a*b */ + if (c->alloc < a->used + 1) { + if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) { + return res; + } + } - /* set the sign */ - c->sign = a->sign; + /* get the original destinations used count */ + olduse = c->used; - /* alias for a->dp [source] */ - tmpa = a->dp; + /* set the sign */ + c->sign = a->sign; - /* alias for c->dp [dest] */ - tmpc = c->dp; + /* alias for a->dp [source] */ + tmpa = a->dp; - /* zero carry */ - u = 0; + /* alias for c->dp [dest] */ + tmpc = c->dp; - /* compute columns */ - for (ix = 0; ix < a->used; ix++) { - /* compute product and carry sum for this term */ - r = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b); + /* zero carry */ + carry = 0; - /* mask off higher bits to get a single digit */ - *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK)); + /* compute columns */ + for (ix = 0; ix < a->used; ix++) { + /* compute product and carry sum for this term */ + r = ((mp_word) carry) + ((mp_word)*tmpa++) * ((mp_word)b); - /* send carry into next iteration */ - u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); - } + /* mask off higher bits to get a single digit */ + *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK)); - /* store final carry [if any] and increment ix offset */ - *tmpc++ = u; - ++ix; + /* send carry into next iteration */ + carry = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); + } - /* now zero digits above the top */ - while (ix++ < olduse) { - *tmpc++ = 0; - } + /* store final carry [if any] and increment ix offset */ + *tmpc++ = carry; + ++ix; + if (olduse > ix) { + memset(tmpc, 0x0, (olduse - ix) * sizeof(*tmpc)); + } - /* set used count */ - c->used = a->used + 1; - mp_clamp(c); + /* set used count */ + c->used = a->used + 1; + trim_unused_digits(c); - return MP_OKAY; + return MP_OKAY; } /* high level addition (handles signs) */ -static int mp_add (mp_int * a, mp_int * b, mp_int * c) -{ - int sa, sb, res; - - /* get sign of both inputs */ - sa = a->sign; - sb = b->sign; - - /* handle two cases, not four */ - if (sa == sb) { - /* both positive or both negative */ - /* add their magnitudes, copy the sign */ - c->sign = sa; - res = s_mp_add (a, b, c); - } else { - /* one positive, the other negative */ - /* subtract the one with the greater magnitude from */ - /* the one of the lesser magnitude. The result gets */ - /* the sign of the one with the greater magnitude. */ - if (mp_cmp_mag (a, b) == MP_LT) { - c->sign = sb; - res = s_mp_sub (b, a, c); - } else { - c->sign = sa; - res = s_mp_sub (a, b, c); - } - } - return res; +static int +signed_add(mp_int * a, mp_int * b, mp_int * c) +{ + int asign, bsign, res; + + /* get sign of both inputs */ + asign = a->sign; + bsign = b->sign; + + /* handle two cases, not four */ + if (asign == bsign) { + /* both positive or both negative */ + /* add their magnitudes, copy the sign */ + c->sign = asign; + res = basic_add(a, b, c); + } else { + /* one positive, the other negative */ + /* subtract the one with the greater magnitude from */ + /* the one of the lesser magnitude. The result gets */ + /* the sign of the one with the greater magnitude. */ + if (compare_magnitude(a, b) == MP_LT) { + c->sign = bsign; + res = basic_subtract(b, a, c); + } else { + c->sign = asign; + res = basic_subtract(a, b, c); + } + } + return res; } /* swap the elements of two integers, for cases where you can't simply swap the @@ -926,121 +848,122 @@ static int mp_add (mp_int * a, mp_int * b, mp_int * c) static void mp_exch(mp_int *a, mp_int *b) { - mp_int t; + mp_int t; - t = *a; - *a = *b; - *b = t; + t = *a; + *a = *b; + *b = t; } /* calc a value mod 2**b */ static int -mp_mod_2d (mp_int * a, int b, mp_int * c) -{ - int x, res; - - /* if b is <= 0 then zero the int */ - if (b <= 0) { - mp_zero (c); - return MP_OKAY; - } - - /* if the modulus is larger than the value than return */ - if (b >= (int) (a->used * DIGIT_BIT)) { - res = mp_copy (a, c); - return res; - } - - /* copy */ - if ((res = mp_copy (a, c)) != MP_OKAY) { - return res; - } - - /* zero digits above the last digit of the modulus */ - for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) { - c->dp[x] = 0; - } - /* clear the digit that is not completely outside/inside the modulus */ - c->dp[b / DIGIT_BIT] &= - (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1)); - mp_clamp (c); - return MP_OKAY; +modulo_2_to_power(mp_int * a, int b, mp_int * c) +{ + int x, res; + + /* if b is <= 0 then zero the int */ + if (b <= 0) { + mp_zero(c); + return MP_OKAY; + } + + /* if the modulus is larger than the value than return */ + if (b >= (int) (a->used * DIGIT_BIT)) { + res = mp_copy(a, c); + return res; + } + + /* copy */ + if ((res = mp_copy(a, c)) != MP_OKAY) { + return res; + } + + /* zero digits above the last digit of the modulus */ + for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) { + c->dp[x] = 0; + } + /* clear the digit that is not completely outside/inside the modulus */ + c->dp[b / DIGIT_BIT] &= + (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1)); + trim_unused_digits(c); + return MP_OKAY; } /* shift right by a certain bit count (store quotient in c, optional remainder in d) */ -static int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d) -{ - mp_digit D, r, rr; - int x, res; - mp_int t; - - - /* if the shift count is <= 0 then we do no work */ - if (b <= 0) { - res = mp_copy (a, c); - if (d != NULL) { - mp_zero (d); - } - return res; - } - - if ((res = mp_init (&t)) != MP_OKAY) { - return res; - } - - /* get the remainder */ - if (d != NULL) { - if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) { - mp_clear (&t); - return res; - } - } - - /* copy */ - if ((res = mp_copy (a, c)) != MP_OKAY) { - mp_clear (&t); - return res; - } - - /* shift by as many digits in the bit count */ - if (b >= (int)DIGIT_BIT) { - mp_rshd (c, b / DIGIT_BIT); - } - - /* shift any bit count < DIGIT_BIT */ - D = (mp_digit) (b % DIGIT_BIT); - if (D != 0) { - mp_digit *tmpc, mask, shift; - - /* mask */ - mask = (((mp_digit)1) << D) - 1; - - /* shift for lsb */ - shift = DIGIT_BIT - D; - - /* alias */ - tmpc = c->dp + (c->used - 1); - - /* carry */ - r = 0; - for (x = c->used - 1; x >= 0; x--) { - /* get the lower bits of this word in a temp */ - rr = *tmpc & mask; - - /* shift the current word and mix in the carry bits from the previous word */ - *tmpc = (*tmpc >> D) | (r << shift); - --tmpc; - - /* set the carry to the carry bits of the current word found above */ - r = rr; - } - } - mp_clamp (c); - if (d != NULL) { - mp_exch (&t, d); - } - mp_clear (&t); - return MP_OKAY; +static int +rshift_bits(mp_int * a, int b, mp_int * c, mp_int * d) +{ + mp_digit D, r, rr; + int x, res; + mp_int t; + + + /* if the shift count is <= 0 then we do no work */ + if (b <= 0) { + res = mp_copy(a, c); + if (d != NULL) { + mp_zero(d); + } + return res; + } + + if ((res = mp_init(&t)) != MP_OKAY) { + return res; + } + + /* get the remainder */ + if (d != NULL) { + if ((res = modulo_2_to_power(a, b, &t)) != MP_OKAY) { + mp_clear(&t); + return res; + } + } + + /* copy */ + if ((res = mp_copy(a, c)) != MP_OKAY) { + mp_clear(&t); + return res; + } + + /* shift by as many digits in the bit count */ + if (b >= (int)DIGIT_BIT) { + rshift_digits(c, b / DIGIT_BIT); + } + + /* shift any bit count < DIGIT_BIT */ + D = (mp_digit) (b % DIGIT_BIT); + if (D != 0) { + mp_digit *tmpc, mask, shift; + + /* mask */ + mask = (((mp_digit)1) << D) - 1; + + /* shift for lsb */ + shift = DIGIT_BIT - D; + + /* alias */ + tmpc = c->dp + (c->used - 1); + + /* carry */ + r = 0; + for (x = c->used - 1; x >= 0; x--) { + /* get the lower bits of this word in a temp */ + rr = *tmpc & mask; + + /* shift the current word and mix in the carry bits from the previous word */ + *tmpc = (*tmpc >> D) | (r << shift); + --tmpc; + + /* set the carry to the carry bits of the current word found above */ + r = rr; + } + } + trim_unused_digits(c); + if (d != NULL) { + mp_exch(&t, d); + } + mp_clear(&t); + return MP_OKAY; } /* integer signed division. @@ -1057,304 +980,314 @@ static int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d) * 14.20 from HAC but fixed to treat these cases. */ static int -mp_div(mp_int *c, mp_int *d, mp_int *a, mp_int *b) -{ - mp_int q, x, y, t1, t2; - int res, n, t, i, norm, neg; - - /* is divisor zero ? */ - if (BN_is_zero (b) == 1) { - return MP_VAL; - } - - /* if a < b then q=0, r = a */ - if (mp_cmp_mag (a, b) == MP_LT) { - if (d != NULL) { - res = mp_copy (a, d); - } else { - res = MP_OKAY; - } - if (c != NULL) { - mp_zero (c); - } - return res; - } - - if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) { - return res; - } - q.used = a->used + 2; - - if ((res = mp_init (&t1)) != MP_OKAY) { - goto LBL_Q; - } - - if ((res = mp_init (&t2)) != MP_OKAY) { - goto LBL_T1; - } - - if ((res = mp_init_copy (&x, a)) != MP_OKAY) { - goto LBL_T2; - } - - if ((res = mp_init_copy (&y, b)) != MP_OKAY) { - goto LBL_X; - } - - /* fix the sign */ - neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; - x.sign = y.sign = MP_ZPOS; - - /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */ - norm = mp_count_bits(&y) % DIGIT_BIT; - if (norm < (int)(DIGIT_BIT-1)) { - norm = (DIGIT_BIT-1) - norm; - if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) { - goto LBL_Y; - } - if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) { - goto LBL_Y; - } - } else { - norm = 0; - } - - /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */ - n = x.used - 1; - t = y.used - 1; - - /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */ - if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */ - goto LBL_Y; - } - - while (mp_cmp (&x, &y) != MP_LT) { - ++(q.dp[n - t]); - if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) { - goto LBL_Y; - } - } - - /* reset y by shifting it back down */ - mp_rshd (&y, n - t); - - /* step 3. for i from n down to (t + 1) */ - for (i = n; i >= (t + 1); i--) { - if (i > x.used) { - continue; - } - - /* step 3.1 if xi == yt then set q{i-t-1} to b-1, - * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */ - if (x.dp[i] == y.dp[t]) { - q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1); - } else { - mp_word tmp; - tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT); - tmp |= ((mp_word) x.dp[i - 1]); - tmp /= ((mp_word) y.dp[t]); - if (tmp > (mp_word) MP_MASK) - tmp = MP_MASK; - q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK)); - } - - /* while (q{i-t-1} * (yt * b + y{t-1})) > - xi * b**2 + xi-1 * b + xi-2 - - do q{i-t-1} -= 1; - */ - q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK; - do { - q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK; - - /* find left hand */ - mp_zero (&t1); - t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1]; - t1.dp[1] = y.dp[t]; - t1.used = 2; - if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) { - goto LBL_Y; - } - - /* find right hand */ - t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2]; - t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1]; - t2.dp[2] = x.dp[i]; - t2.used = 3; - } while (mp_cmp_mag(&t1, &t2) == MP_GT); - - /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */ - if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) { - goto LBL_Y; - } - - if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) { - goto LBL_Y; - } - - if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) { - goto LBL_Y; - } - - /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */ - if (x.sign == MP_NEG) { - if ((res = mp_copy (&y, &t1)) != MP_OKAY) { - goto LBL_Y; - } - if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) { - goto LBL_Y; - } - if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) { - goto LBL_Y; - } - - q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK; - } - } - - /* now q is the quotient and x is the remainder - * [which we have to normalize] - */ - - /* get sign before writing to c */ - x.sign = x.used == 0 ? MP_ZPOS : a->sign; - - if (c != NULL) { - mp_clamp (&q); - mp_exch (&q, c); - c->sign = neg; - } - - if (d != NULL) { - mp_div_2d (&x, norm, &x, NULL); - mp_exch (&x, d); - } - - res = MP_OKAY; - -LBL_Y:mp_clear (&y); -LBL_X:mp_clear (&x); -LBL_T2:mp_clear (&t2); -LBL_T1:mp_clear (&t1); -LBL_Q:mp_clear (&q); - return res; +signed_divide(mp_int *c, mp_int *d, mp_int *a, mp_int *b) +{ + mp_int q, x, y, t1, t2; + int res, n, t, i, norm, neg; + + /* is divisor zero ? */ + if (MP_ISZERO(b) == MP_YES) { + return MP_VAL; + } + + /* if a < b then q=0, r = a */ + if (compare_magnitude(a, b) == MP_LT) { + if (d != NULL) { + res = mp_copy(a, d); + } else { + res = MP_OKAY; + } + if (c != NULL) { + mp_zero(c); + } + return res; + } + + if ((res = mp_init_size(&q, a->used + 2)) != MP_OKAY) { + return res; + } + q.used = a->used + 2; + + if ((res = mp_init(&t1)) != MP_OKAY) { + goto LBL_Q; + } + + if ((res = mp_init(&t2)) != MP_OKAY) { + goto LBL_T1; + } + + if ((res = mp_init_copy(&x, a)) != MP_OKAY) { + goto LBL_T2; + } + + if ((res = mp_init_copy(&y, b)) != MP_OKAY) { + goto LBL_X; + } + + /* fix the sign */ + neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; + x.sign = y.sign = MP_ZPOS; + + /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */ + norm = mp_count_bits(&y) % DIGIT_BIT; + if (norm < (int)(DIGIT_BIT-1)) { + norm = (DIGIT_BIT-1) - norm; + if ((res = lshift_bits(&x, norm, &x)) != MP_OKAY) { + goto LBL_Y; + } + if ((res = lshift_bits(&y, norm, &y)) != MP_OKAY) { + goto LBL_Y; + } + } else { + norm = 0; + } + + /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */ + n = x.used - 1; + t = y.used - 1; + + /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */ + if ((res = lshift_digits(&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */ + goto LBL_Y; + } + + while (signed_compare(&x, &y) != MP_LT) { + ++(q.dp[n - t]); + if ((res = signed_subtract(&x, &y, &x)) != MP_OKAY) { + goto LBL_Y; + } + } + + /* reset y by shifting it back down */ + rshift_digits(&y, n - t); + + /* step 3. for i from n down to (t + 1) */ + for (i = n; i >= (t + 1); i--) { + if (i > x.used) { + continue; + } + + /* step 3.1 if xi == yt then set q{i-t-1} to b-1, + * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */ + if (x.dp[i] == y.dp[t]) { + q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1); + } else { + mp_word tmp; + tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT); + tmp |= ((mp_word) x.dp[i - 1]); + tmp /= ((mp_word) y.dp[t]); + if (tmp > (mp_word) MP_MASK) { + tmp = MP_MASK; + } + q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK)); + } + + /* while (q{i-t-1} * (yt * b + y{t-1})) > + xi * b**2 + xi-1 * b + xi-2 + do q{i-t-1} -= 1; + */ + q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK; + do { + q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK; + + /* find left hand */ + mp_zero(&t1); + t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1]; + t1.dp[1] = y.dp[t]; + t1.used = 2; + if ((res = multiply_digit(&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) { + goto LBL_Y; + } + + /* find right hand */ + t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2]; + t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1]; + t2.dp[2] = x.dp[i]; + t2.used = 3; + } while (compare_magnitude(&t1, &t2) == MP_GT); + + /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */ + if ((res = multiply_digit(&y, q.dp[i - t - 1], &t1)) != MP_OKAY) { + goto LBL_Y; + } + + if ((res = lshift_digits(&t1, i - t - 1)) != MP_OKAY) { + goto LBL_Y; + } + + if ((res = signed_subtract(&x, &t1, &x)) != MP_OKAY) { + goto LBL_Y; + } + + /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */ + if (x.sign == MP_NEG) { + if ((res = mp_copy(&y, &t1)) != MP_OKAY) { + goto LBL_Y; + } + if ((res = lshift_digits(&t1, i - t - 1)) != MP_OKAY) { + goto LBL_Y; + } + if ((res = signed_add(&x, &t1, &x)) != MP_OKAY) { + goto LBL_Y; + } + + q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK; + } + } + + /* now q is the quotient and x is the remainder + * [which we have to normalize] + */ + + /* get sign before writing to c */ + x.sign = x.used == 0 ? MP_ZPOS : a->sign; + + if (c != NULL) { + trim_unused_digits(&q); + mp_exch(&q, c); + c->sign = neg; + } + + if (d != NULL) { + rshift_bits(&x, norm, &x, NULL); + mp_exch(&x, d); + } + + res = MP_OKAY; + +LBL_Y: + mp_clear(&y); +LBL_X: + mp_clear(&x); +LBL_T2: + mp_clear(&t2); +LBL_T1: + mp_clear(&t1); +LBL_Q: + mp_clear(&q); + return res; } /* c = a mod b, 0 <= c < b */ static int -mp_mod (mp_int * a, mp_int * b, mp_int * c) +modulo(mp_int * a, mp_int * b, mp_int * c) { - mp_int t; - int res; + mp_int t; + int res; - if ((res = mp_init (&t)) != MP_OKAY) { - return res; - } + if ((res = mp_init(&t)) != MP_OKAY) { + return res; + } - if ((res = mp_div (NULL, &t, a, b)) != MP_OKAY) { - mp_clear (&t); - return res; - } + if ((res = signed_divide(NULL, &t, a, b)) != MP_OKAY) { + mp_clear(&t); + return res; + } - if (t.sign != b->sign) { - res = mp_add (b, &t, c); - } else { - res = MP_OKAY; - mp_exch (&t, c); - } + if (t.sign != b->sign) { + res = signed_add(b, &t, c); + } else { + res = MP_OKAY; + mp_exch(&t, c); + } - mp_clear (&t); - return res; + mp_clear(&t); + return res; } /* set to a digit */ -static void mp_set (mp_int * a, mp_digit b) +static void +set_word(mp_int * a, mp_digit b) { - mp_zero (a); - a->dp[0] = b & MP_MASK; - a->used = (a->dp[0] != 0) ? 1 : 0; + mp_zero(a); + a->dp[0] = b & MP_MASK; + a->used = (a->dp[0] != 0) ? 1 : 0; } /* b = a/2 */ -static int mp_div_2(mp_int * a, mp_int * b) +static int +half(mp_int * a, mp_int * b) { - int x, res, oldused; + int x, res, oldused; - /* copy */ - if (b->alloc < a->used) { - if ((res = mp_grow (b, a->used)) != MP_OKAY) { - return res; - } - } + /* copy */ + if (b->alloc < a->used) { + if ((res = mp_grow(b, a->used)) != MP_OKAY) { + return res; + } + } - oldused = b->used; - b->used = a->used; - { - mp_digit r, rr, *tmpa, *tmpb; + oldused = b->used; + b->used = a->used; + { + mp_digit r, rr, *tmpa, *tmpb; - /* source alias */ - tmpa = a->dp + b->used - 1; + /* source alias */ + tmpa = a->dp + b->used - 1; - /* dest alias */ - tmpb = b->dp + b->used - 1; + /* dest alias */ + tmpb = b->dp + b->used - 1; - /* carry */ - r = 0; - for (x = b->used - 1; x >= 0; x--) { - /* get the carry for the next iteration */ - rr = *tmpa & 1; + /* carry */ + r = 0; + for (x = b->used - 1; x >= 0; x--) { + /* get the carry for the next iteration */ + rr = *tmpa & 1; - /* shift the current digit, add in carry and store */ - *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1)); + /* shift the current digit, add in carry and store */ + *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1)); - /* forward carry to next iteration */ - r = rr; - } + /* forward carry to next iteration */ + r = rr; + } - /* zero excess digits */ - tmpb = b->dp + b->used; - for (x = b->used; x < oldused; x++) { - *tmpb++ = 0; - } - } - b->sign = a->sign; - mp_clamp (b); - return MP_OKAY; + /* zero excess digits */ + tmpb = b->dp + b->used; + for (x = b->used; x < oldused; x++) { + *tmpb++ = 0; + } + } + b->sign = a->sign; + trim_unused_digits(b); + return MP_OKAY; } /* compare a digit */ -static int mp_cmp_d(mp_int * a, mp_digit b) +static int +compare_digit(mp_int * a, mp_digit b) { - /* compare based on sign */ - if (a->sign == MP_NEG) { - return MP_LT; - } + /* compare based on sign */ + if (a->sign == MP_NEG) { + return MP_LT; + } - /* compare based on magnitude */ - if (a->used > 1) { - return MP_GT; - } + /* compare based on magnitude */ + if (a->used > 1) { + return MP_GT; + } - /* compare the only digit of a to b */ - if (a->dp[0] > b) { - return MP_GT; - } else if (a->dp[0] < b) { - return MP_LT; - } else { - return MP_EQ; - } + /* compare the only digit of a to b */ + if (a->dp[0] > b) { + return MP_GT; + } else if (a->dp[0] < b) { + return MP_LT; + } else { + return MP_EQ; + } } -static void mp_clear_multi(mp_int *mp, ...) +static void +mp_clear_multi(mp_int *mp, ...) { - mp_int* next_mp = mp; - va_list args; - va_start(args, mp); - while (next_mp != NULL) { - mp_clear(next_mp); - next_mp = va_arg(args, mp_int*); - } - va_end(args); + mp_int* next_mp = mp; + va_list args; + + va_start(args, mp); + while (next_mp != NULL) { + mp_clear(next_mp); + next_mp = va_arg(args, mp_int*); + } + va_end(args); } /* computes the modular inverse via binary extended euclidean algorithm, @@ -1364,299 +1297,297 @@ static void mp_clear_multi(mp_int *mp, ...) * odd as per HAC Note 14.64 on pp. 610 */ static int -fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c) -{ - mp_int x, y, u, v, B, D; - int res, neg; - - /* 2. [modified] b must be odd */ - if (BN_is_even (b) == 1) { - return MP_VAL; - } - - /* init all our temps */ - if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) { - return res; - } - - /* x == modulus, y == value to invert */ - if ((res = mp_copy (b, &x)) != MP_OKAY) { - goto LBL_ERR; - } - - /* we need y = |a| */ - if ((res = mp_mod (a, b, &y)) != MP_OKAY) { - goto LBL_ERR; - } - - /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ - if ((res = mp_copy (&x, &u)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_copy (&y, &v)) != MP_OKAY) { - goto LBL_ERR; - } - mp_set (&D, 1); +fast_modular_inverse(mp_int * a, mp_int * b, mp_int * c) +{ + mp_int x, y, u, v, B, D; + int res, neg; -top: - /* 4. while u is even do */ - while (BN_is_even (&u) == 1) { - /* 4.1 u = u/2 */ - if ((res = mp_div_2 (&u, &u)) != MP_OKAY) { - goto LBL_ERR; - } - /* 4.2 if B is odd then */ - if (BN_is_odd (&B) == 1) { - if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } - /* B = B/2 */ - if ((res = mp_div_2 (&B, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* 5. while v is even do */ - while (BN_is_even (&v) == 1) { - /* 5.1 v = v/2 */ - if ((res = mp_div_2 (&v, &v)) != MP_OKAY) { - goto LBL_ERR; - } - /* 5.2 if D is odd then */ - if (BN_is_odd (&D) == 1) { - /* D = (D-x)/2 */ - if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - /* D = D/2 */ - if ((res = mp_div_2 (&D, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* 6. if u >= v then */ - if (mp_cmp (&u, &v) != MP_LT) { - /* u = u - v, B = B - D */ - if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } else { - /* v - v - u, D = D - B */ - if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* if not zero goto step 4 */ - if (BN_is_zero (&u) == 0) { - goto top; - } - - /* now a = C, b = D, gcd == g*v */ - - /* if v != 1 then there is no inverse */ - if (mp_cmp_d (&v, 1) != MP_EQ) { - res = MP_VAL; - goto LBL_ERR; - } - - /* b is now the inverse */ - neg = a->sign; - while (D.sign == MP_NEG) { - if ((res = mp_add (&D, b, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - mp_exch (&D, c); - c->sign = neg; - res = MP_OKAY; - -LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); - return res; -} + /* 2. [modified] b must be odd */ + if (MP_ISZERO(b) == MP_YES) { + return MP_VAL; + } -/* hac 14.61, pp608 */ -static int -mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c) -{ - mp_int x, y, u, v, A, B, C, D; - int res; - - /* b cannot be negative */ - if (b->sign == MP_NEG || BN_is_zero(b) == 1) { - return MP_VAL; - } - - /* init temps */ - if ((res = mp_init_multi(&x, &y, &u, &v, - &A, &B, &C, &D, NULL)) != MP_OKAY) { - return res; - } - - /* x = a, y = b */ - if ((res = mp_mod(a, b, &x)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_copy (b, &y)) != MP_OKAY) { - goto LBL_ERR; - } - - /* 2. [modified] if x,y are both even then return an error! */ - if (BN_is_even (&x) == 1 && BN_is_even (&y) == 1) { - res = MP_VAL; - goto LBL_ERR; - } - - /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ - if ((res = mp_copy (&x, &u)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_copy (&y, &v)) != MP_OKAY) { - goto LBL_ERR; - } - mp_set (&A, 1); - mp_set (&D, 1); + /* init all our temps */ + if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) { + return res; + } -top: - /* 4. while u is even do */ - while (BN_is_even (&u) == 1) { - /* 4.1 u = u/2 */ - if ((res = mp_div_2 (&u, &u)) != MP_OKAY) { - goto LBL_ERR; - } - /* 4.2 if A or B is odd then */ - if (BN_is_odd (&A) == 1 || BN_is_odd (&B) == 1) { - /* A = (A+y)/2, B = (B-x)/2 */ - if ((res = mp_add (&A, &y, &A)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } - /* A = A/2, B = B/2 */ - if ((res = mp_div_2 (&A, &A)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_div_2 (&B, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* 5. while v is even do */ - while (BN_is_even (&v) == 1) { - /* 5.1 v = v/2 */ - if ((res = mp_div_2 (&v, &v)) != MP_OKAY) { - goto LBL_ERR; - } - /* 5.2 if C or D is odd then */ - if (BN_is_odd (&C) == 1 || BN_is_odd (&D) == 1) { - /* C = (C+y)/2, D = (D-x)/2 */ - if ((res = mp_add (&C, &y, &C)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - /* C = C/2, D = D/2 */ - if ((res = mp_div_2 (&C, &C)) != MP_OKAY) { - goto LBL_ERR; - } - if ((res = mp_div_2 (&D, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* 6. if u >= v then */ - if (mp_cmp (&u, &v) != MP_LT) { - /* u = u - v, A = A - C, B = B - D */ - if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) { - goto LBL_ERR; - } - } else { - /* v - v - u, C = C - A, D = D - B */ - if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) { - goto LBL_ERR; - } - - if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* if not zero goto step 4 */ - if (BN_is_zero (&u) == 0) - goto top; - - /* now a = C, b = D, gcd == g*v */ - - /* if v != 1 then there is no inverse */ - if (mp_cmp_d (&v, 1) != MP_EQ) { - res = MP_VAL; - goto LBL_ERR; - } - - /* if its too low */ - while (mp_cmp_d(&C, 0) == MP_LT) { - if ((res = mp_add(&C, b, &C)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* too big */ - while (mp_cmp_mag(&C, b) != MP_LT) { - if ((res = mp_sub(&C, b, &C)) != MP_OKAY) { - goto LBL_ERR; - } - } - - /* C is now the inverse */ - mp_exch (&C, c); - res = MP_OKAY; -LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); - return res; -} + /* x == modulus, y == value to invert */ + if ((res = mp_copy(b, &x)) != MP_OKAY) { + goto LBL_ERR; + } -static int -mp_invmod(mp_int *c, mp_int *a, mp_int *b) -{ - /* b cannot be negative */ - if (b->sign == MP_NEG || BN_is_zero(b) == 1) { - return MP_VAL; - } + /* we need y = |a| */ + if ((res = modulo(a, b, &y)) != MP_OKAY) { + goto LBL_ERR; + } - /* if the modulus is odd we can use a faster routine instead */ - if (BN_is_odd (b) == 1) { - return fast_mp_invmod(a, b, c); - } + /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ + if ((res = mp_copy(&x, &u)) != MP_OKAY) { + goto LBL_ERR; + } + if ((res = mp_copy(&y, &v)) != MP_OKAY) { + goto LBL_ERR; + } + set_word(&D, 1); + +top: + /* 4. while u is even do */ + while (BN_is_even(&u) == 1) { + /* 4.1 u = u/2 */ + if ((res = half(&u, &u)) != MP_OKAY) { + goto LBL_ERR; + } + /* 4.2 if B is odd then */ + if (BN_is_odd(&B) == 1) { + if ((res = signed_subtract(&B, &x, &B)) != MP_OKAY) { + goto LBL_ERR; + } + } + /* B = B/2 */ + if ((res = half(&B, &B)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* 5. while v is even do */ + while (BN_is_even(&v) == 1) { + /* 5.1 v = v/2 */ + if ((res = half(&v, &v)) != MP_OKAY) { + goto LBL_ERR; + } + /* 5.2 if D is odd then */ + if (BN_is_odd(&D) == 1) { + /* D = (D-x)/2 */ + if ((res = signed_subtract(&D, &x, &D)) != MP_OKAY) { + goto LBL_ERR; + } + } + /* D = D/2 */ + if ((res = half(&D, &D)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* 6. if u >= v then */ + if (signed_compare(&u, &v) != MP_LT) { + /* u = u - v, B = B - D */ + if ((res = signed_subtract(&u, &v, &u)) != MP_OKAY) { + goto LBL_ERR; + } + + if ((res = signed_subtract(&B, &D, &B)) != MP_OKAY) { + goto LBL_ERR; + } + } else { + /* v - v - u, D = D - B */ + if ((res = signed_subtract(&v, &u, &v)) != MP_OKAY) { + goto LBL_ERR; + } + + if ((res = signed_subtract(&D, &B, &D)) != MP_OKAY) { + goto LBL_ERR; + } + } - return mp_invmod_slow(a, b, c); + /* if not zero goto step 4 */ + if (MP_ISZERO(&u) == MP_NO) { + goto top; + } + + /* now a = C, b = D, gcd == g*v */ + + /* if v != 1 then there is no inverse */ + if (compare_digit(&v, 1) != MP_EQ) { + res = MP_VAL; + goto LBL_ERR; + } + + /* b is now the inverse */ + neg = a->sign; + while (D.sign == MP_NEG) { + if ((res = signed_add(&D, b, &D)) != MP_OKAY) { + goto LBL_ERR; + } + } + mp_exch(&D, c); + c->sign = neg; + res = MP_OKAY; - /*NOTREACHED*/ - return MP_VAL; +LBL_ERR: + mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); + return res; +} + +/* hac 14.61, pp608 */ +static int +slow_modular_inverse(mp_int * a, mp_int * b, mp_int * c) +{ + mp_int x, y, u, v, A, B, C, D; + int res; + + /* b cannot be negative */ + if (b->sign == MP_NEG || MP_ISZERO(b) == MP_YES) { + return MP_VAL; + } + + /* init temps */ + if ((res = mp_init_multi(&x, &y, &u, &v, + &A, &B, &C, &D, NULL)) != MP_OKAY) { + return res; + } + + /* x = a, y = b */ + if ((res = modulo(a, b, &x)) != MP_OKAY) { + goto LBL_ERR; + } + if ((res = mp_copy(b, &y)) != MP_OKAY) { + goto LBL_ERR; + } + + /* 2. [modified] if x,y are both even then return an error! */ + if (BN_is_even(&x) == 1 && BN_is_even(&y) == 1) { + res = MP_VAL; + goto LBL_ERR; + } + + /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ + if ((res = mp_copy(&x, &u)) != MP_OKAY) { + goto LBL_ERR; + } + if ((res = mp_copy(&y, &v)) != MP_OKAY) { + goto LBL_ERR; + } + set_word(&A, 1); + set_word(&D, 1); + +top: + /* 4. while u is even do */ + while (BN_is_even(&u) == 1) { + /* 4.1 u = u/2 */ + if ((res = half(&u, &u)) != MP_OKAY) { + goto LBL_ERR; + } + /* 4.2 if A or B is odd then */ + if (BN_is_odd(&A) == 1 || BN_is_odd(&B) == 1) { + /* A = (A+y)/2, B = (B-x)/2 */ + if ((res = signed_add(&A, &y, &A)) != MP_OKAY) { + goto LBL_ERR; + } + if ((res = signed_subtract(&B, &x, &B)) != MP_OKAY) { + goto LBL_ERR; + } + } + /* A = A/2, B = B/2 */ + if ((res = half(&A, &A)) != MP_OKAY) { + goto LBL_ERR; + } + if ((res = half(&B, &B)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* 5. while v is even do */ + while (BN_is_even(&v) == 1) { + /* 5.1 v = v/2 */ + if ((res = half(&v, &v)) != MP_OKAY) { + goto LBL_ERR; + } + /* 5.2 if C or D is odd then */ + if (BN_is_odd(&C) == 1 || BN_is_odd(&D) == 1) { + /* C = (C+y)/2, D = (D-x)/2 */ + if ((res = signed_add(&C, &y, &C)) != MP_OKAY) { + goto LBL_ERR; + } + if ((res = signed_subtract(&D, &x, &D)) != MP_OKAY) { + goto LBL_ERR; + } + } + /* C = C/2, D = D/2 */ + if ((res = half(&C, &C)) != MP_OKAY) { + goto LBL_ERR; + } + if ((res = half(&D, &D)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* 6. if u >= v then */ + if (signed_compare(&u, &v) != MP_LT) { + /* u = u - v, A = A - C, B = B - D */ + if ((res = signed_subtract(&u, &v, &u)) != MP_OKAY) { + goto LBL_ERR; + } + + if ((res = signed_subtract(&A, &C, &A)) != MP_OKAY) { + goto LBL_ERR; + } + + if ((res = signed_subtract(&B, &D, &B)) != MP_OKAY) { + goto LBL_ERR; + } + } else { + /* v - v - u, C = C - A, D = D - B */ + if ((res = signed_subtract(&v, &u, &v)) != MP_OKAY) { + goto LBL_ERR; + } + + if ((res = signed_subtract(&C, &A, &C)) != MP_OKAY) { + goto LBL_ERR; + } + + if ((res = signed_subtract(&D, &B, &D)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* if not zero goto step 4 */ + if (BN_is_zero(&u) == 0) { + goto top; + } + /* now a = C, b = D, gcd == g*v */ + + /* if v != 1 then there is no inverse */ + if (compare_digit(&v, 1) != MP_EQ) { + res = MP_VAL; + goto LBL_ERR; + } + + /* if its too low */ + while (compare_digit(&C, 0) == MP_LT) { + if ((res = signed_add(&C, b, &C)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* too big */ + while (compare_magnitude(&C, b) != MP_LT) { + if ((res = signed_subtract(&C, b, &C)) != MP_OKAY) { + goto LBL_ERR; + } + } + + /* C is now the inverse */ + mp_exch(&C, c); + res = MP_OKAY; +LBL_ERR: + mp_clear_multi(&x, &y, &u, &v, &A, &B, &C, &D, NULL); + return res; +} + +static int +modular_inverse(mp_int *c, mp_int *a, mp_int *b) +{ + /* b cannot be negative */ + if (b->sign == MP_NEG || MP_ISZERO(b) == MP_YES) { + return MP_VAL; + } + + /* if the modulus is odd we can use a faster routine instead */ + if (BN_is_odd(b) == 1) { + return fast_modular_inverse(a, b, c); + } + return slow_modular_inverse(a, b, c); } /* b = |a| @@ -1664,43 +1595,44 @@ mp_invmod(mp_int *c, mp_int *a, mp_int *b) * Simple function copies the input and fixes the sign to positive */ static int -mp_abs (mp_int * a, mp_int * b) +absolute(mp_int * a, mp_int * b) { - int res; + int res; - /* copy a to b */ - if (a != b) { - if ((res = mp_copy (a, b)) != MP_OKAY) { - return res; - } - } + /* copy a to b */ + if (a != b) { + if ((res = mp_copy(a, b)) != MP_OKAY) { + return res; + } + } - /* force the sign of b to positive */ - b->sign = MP_ZPOS; + /* force the sign of b to positive */ + b->sign = MP_ZPOS; - return MP_OKAY; + return MP_OKAY; } /* determines if reduce_2k_l can be used */ -static int mp_reduce_is_2k_l(mp_int *a) -{ - int ix, iy; - - if (a->used == 0) { - return MP_NO; - } else if (a->used == 1) { - return MP_YES; - } else if (a->used > 1) { - /* if more than half of the digits are -1 we're sold */ - for (iy = ix = 0; ix < a->used; ix++) { - if (a->dp[ix] == MP_MASK) { - ++iy; - } - } - return (iy >= (a->used/2)) ? MP_YES : MP_NO; - - } - return MP_NO; +static int +mp_reduce_is_2k_l(mp_int *a) +{ + int ix, iy; + + if (a->used == 0) { + return MP_NO; + } else if (a->used == 1) { + return MP_YES; + } else if (a->used > 1) { + /* if more than half of the digits are -1 we're sold */ + for (iy = ix = 0; ix < a->used; ix++) { + if (a->dp[ix] == MP_MASK) { + ++iy; + } + } + return (iy >= (a->used/2)) ? MP_YES : MP_NO; + + } + return MP_NO; } /* computes a = 2**b @@ -1709,156 +1641,158 @@ static int mp_reduce_is_2k_l(mp_int *a) * as required. */ static int -mp_2expt (mp_int * a, int b) +mp_2expt(mp_int * a, int b) { - int res; + int res; - /* zero a as per default */ - mp_zero (a); + /* zero a as per default */ + mp_zero(a); - /* grow a to accomodate the single bit */ - if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) { - return res; - } + /* grow a to accomodate the single bit */ + if ((res = mp_grow(a, b / DIGIT_BIT + 1)) != MP_OKAY) { + return res; + } - /* set the used count of where the bit will go */ - a->used = b / DIGIT_BIT + 1; + /* set the used count of where the bit will go */ + a->used = b / DIGIT_BIT + 1; - /* put the single bit in its place */ - a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT); + /* put the single bit in its place */ + a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT); - return MP_OKAY; + return MP_OKAY; } /* pre-calculate the value required for Barrett reduction * For a given modulus "b" it calulates the value required in "a" */ -static int mp_reduce_setup (mp_int * a, mp_int * b) +static int +mp_reduce_setup(mp_int * a, mp_int * b) { - int res; - - if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) { - return res; - } - return mp_div (a, NULL, a, b); + int res; + + if ((res = mp_2expt(a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) { + return res; + } + return signed_divide(a, NULL, a, b); } /* b = a*2 */ -static int mp_mul_2(mp_int * a, mp_int * b) -{ - int x, res, oldused; - - /* grow to accomodate result */ - if (b->alloc < a->used + 1) { - if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) { - return res; - } - } - - oldused = b->used; - b->used = a->used; - - { - mp_digit r, rr, *tmpa, *tmpb; - - /* alias for source */ - tmpa = a->dp; - - /* alias for dest */ - tmpb = b->dp; - - /* carry */ - r = 0; - for (x = 0; x < a->used; x++) { - - /* get what will be the *next* carry bit from the - * MSB of the current digit - */ - rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1)); - - /* now shift up this digit, add in the carry [from the previous] */ - *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK; - - /* copy the carry that would be from the source - * digit into the next iteration - */ - r = rr; - } - - /* new leading digit? */ - if (r != 0) { - /* add a MSB which is always 1 at this point */ - *tmpb = 1; - ++(b->used); - } - - /* now zero any excess digits on the destination - * that we didn't write to - */ - tmpb = b->dp + b->used; - for (x = b->used; x < oldused; x++) { - *tmpb++ = 0; - } - } - b->sign = a->sign; - return MP_OKAY; +static int +doubled(mp_int * a, mp_int * b) +{ + int x, res, oldused; + + /* grow to accomodate result */ + if (b->alloc < a->used + 1) { + if ((res = mp_grow(b, a->used + 1)) != MP_OKAY) { + return res; + } + } + + oldused = b->used; + b->used = a->used; + + { + mp_digit r, rr, *tmpa, *tmpb; + + /* alias for source */ + tmpa = a->dp; + + /* alias for dest */ + tmpb = b->dp; + + /* carry */ + r = 0; + for (x = 0; x < a->used; x++) { + + /* get what will be the *next* carry bit from the + * MSB of the current digit + */ + rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1)); + + /* now shift up this digit, add in the carry [from the previous] */ + *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK; + + /* copy the carry that would be from the source + * digit into the next iteration + */ + r = rr; + } + + /* new leading digit? */ + if (r != 0) { + /* add a MSB which is always 1 at this point */ + *tmpb = 1; + ++(b->used); + } + + /* now zero any excess digits on the destination + * that we didn't write to + */ + tmpb = b->dp + b->used; + for (x = b->used; x < oldused; x++) { + *tmpb++ = 0; + } + } + b->sign = a->sign; + return MP_OKAY; } /* divide by three (based on routine from MPI and the GMP manual) */ static int -mp_div_3 (mp_int * a, mp_int *c, mp_digit * d) -{ - mp_int q; - mp_word w, t; - mp_digit b; - int res, ix; - - /* b = 2**DIGIT_BIT / 3 */ - b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3); - - if ((res = mp_init_size(&q, a->used)) != MP_OKAY) { - return res; - } - - q.used = a->used; - q.sign = a->sign; - w = 0; - for (ix = a->used - 1; ix >= 0; ix--) { - w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]); - - if (w >= 3) { - /* multiply w by [1/3] */ - t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT); - - /* now subtract 3 * [w/3] from w, to get the remainder */ - w -= t+t+t; - - /* fixup the remainder as required since - * the optimization is not exact. - */ - while (w >= 3) { - t += 1; - w -= 3; - } - } else { - t = 0; - } - q.dp[ix] = (mp_digit)t; - } - - /* [optional] store the remainder */ - if (d != NULL) { - *d = (mp_digit)w; - } - - /* [optional] store the quotient */ - if (c != NULL) { - mp_clamp(&q); - mp_exch(&q, c); - } - mp_clear(&q); - - return res; +third(mp_int * a, mp_int *c, mp_digit * d) +{ + mp_int q; + mp_word w, t; + mp_digit b; + int res, ix; + + /* b = 2**DIGIT_BIT / 3 */ + b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3); + + if ((res = mp_init_size(&q, a->used)) != MP_OKAY) { + return res; + } + + q.used = a->used; + q.sign = a->sign; + w = 0; + for (ix = a->used - 1; ix >= 0; ix--) { + w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]); + + if (w >= 3) { + /* multiply w by [1/3] */ + t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT); + + /* now subtract 3 * [w/3] from w, to get the remainder */ + w -= t+t+t; + + /* fixup the remainder as required since + * the optimization is not exact. + */ + while (w >= 3) { + t += 1; + w -= 3; + } + } else { + t = 0; + } + q.dp[ix] = (mp_digit)t; + } + + /* [optional] store the remainder */ + if (d != NULL) { + *d = (mp_digit)w; + } + + /* [optional] store the quotient */ + if (c != NULL) { + trim_unused_digits(&q); + mp_exch(&q, c); + } + mp_clear(&q); + + return res; } /* multiplication using the Toom-Cook 3-way algorithm @@ -1868,259 +1802,260 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d) * only particularly useful on VERY large inputs * (we're talking 1000s of digits here...). */ -static int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c) -{ - mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2; - int res, B; - - /* init temps */ - if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, - &a0, &a1, &a2, &b0, &b1, - &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) { - return res; - } - - /* B */ - B = MIN(a->used, b->used) / 3; - - /* a = a2 * B**2 + a1 * B + a0 */ - if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_copy(a, &a1)) != MP_OKAY) { - goto ERR; - } - mp_rshd(&a1, B); - mp_mod_2d(&a1, DIGIT_BIT * B, &a1); - - if ((res = mp_copy(a, &a2)) != MP_OKAY) { - goto ERR; - } - mp_rshd(&a2, B*2); - - /* b = b2 * B**2 + b1 * B + b0 */ - if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_copy(b, &b1)) != MP_OKAY) { - goto ERR; - } - mp_rshd(&b1, B); - mp_mod_2d(&b1, DIGIT_BIT * B, &b1); - - if ((res = mp_copy(b, &b2)) != MP_OKAY) { - goto ERR; - } - mp_rshd(&b2, B*2); - - /* w0 = a0*b0 */ - if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) { - goto ERR; - } - - /* w4 = a2 * b2 */ - if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) { - goto ERR; - } - - /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */ - if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) { - goto ERR; - } - - /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */ - if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) { - goto ERR; - } - - - /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */ - if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) { - goto ERR; - } - - /* now solve the matrix - - 0 0 0 0 1 - 1 2 4 8 16 - 1 1 1 1 1 - 16 8 4 2 1 - 1 0 0 0 0 - - using 12 subtractions, 4 shifts, - 2 small divisions and 1 small multiplication - */ - - /* r1 - r4 */ - if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - r0 */ - if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) { - goto ERR; - } - /* r1/2 */ - if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3/2 */ - if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) { - goto ERR; - } - /* r2 - r0 - r4 */ - if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) { - goto ERR; - } - /* r1 - r2 */ - if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - r2 */ - if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) { - goto ERR; - } - /* r1 - 8r0 */ - if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - 8r4 */ - if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) { - goto ERR; - } - /* 3r2 - r1 - r3 */ - if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) { - goto ERR; - } - /* r1 - r2 */ - if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - r2 */ - if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) { - goto ERR; - } - /* r1/3 */ - if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) { - goto ERR; - } - /* r3/3 */ - if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) { - goto ERR; - } - - /* at this point shift W[n] by B*n */ - if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) { - goto ERR; - } - +static int +toom_cook_multiply(mp_int *a, mp_int *b, mp_int *c) +{ + mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2; + int res, B; + + /* init temps */ + if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, + &a0, &a1, &a2, &b0, &b1, + &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) { + return res; + } + + /* B */ + B = MIN(a->used, b->used) / 3; + + /* a = a2 * B**2 + a1 * B + a0 */ + if ((res = modulo_2_to_power(a, DIGIT_BIT * B, &a0)) != MP_OKAY) { + goto ERR; + } + + if ((res = mp_copy(a, &a1)) != MP_OKAY) { + goto ERR; + } + rshift_digits(&a1, B); + modulo_2_to_power(&a1, DIGIT_BIT * B, &a1); + + if ((res = mp_copy(a, &a2)) != MP_OKAY) { + goto ERR; + } + rshift_digits(&a2, B*2); + + /* b = b2 * B**2 + b1 * B + b0 */ + if ((res = modulo_2_to_power(b, DIGIT_BIT * B, &b0)) != MP_OKAY) { + goto ERR; + } + + if ((res = mp_copy(b, &b1)) != MP_OKAY) { + goto ERR; + } + rshift_digits(&b1, B); + modulo_2_to_power(&b1, DIGIT_BIT * B, &b1); + + if ((res = mp_copy(b, &b2)) != MP_OKAY) { + goto ERR; + } + rshift_digits(&b2, B*2); + + /* w0 = a0*b0 */ + if ((res = signed_multiply(&a0, &b0, &w0)) != MP_OKAY) { + goto ERR; + } + + /* w4 = a2 * b2 */ + if ((res = signed_multiply(&a2, &b2, &w4)) != MP_OKAY) { + goto ERR; + } + + /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */ + if ((res = doubled(&a0, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = doubled(&tmp1, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp1, &a2, &tmp1)) != MP_OKAY) { + goto ERR; + } + + if ((res = doubled(&b0, &tmp2)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp2, &b1, &tmp2)) != MP_OKAY) { + goto ERR; + } + if ((res = doubled(&tmp2, &tmp2)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp2, &b2, &tmp2)) != MP_OKAY) { + goto ERR; + } + + if ((res = signed_multiply(&tmp1, &tmp2, &w1)) != MP_OKAY) { + goto ERR; + } + + /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */ + if ((res = doubled(&a2, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = doubled(&tmp1, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { + goto ERR; + } + + if ((res = doubled(&b2, &tmp2)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp2, &b1, &tmp2)) != MP_OKAY) { + goto ERR; + } + if ((res = doubled(&tmp2, &tmp2)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp2, &b0, &tmp2)) != MP_OKAY) { + goto ERR; + } + + if ((res = signed_multiply(&tmp1, &tmp2, &w3)) != MP_OKAY) { + goto ERR; + } + + + /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */ + if ((res = signed_add(&a2, &a1, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&b2, &b1, &tmp2)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp2, &b0, &tmp2)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_multiply(&tmp1, &tmp2, &w2)) != MP_OKAY) { + goto ERR; + } + + /* now solve the matrix + + 0 0 0 0 1 + 1 2 4 8 16 + 1 1 1 1 1 + 16 8 4 2 1 + 1 0 0 0 0 + + using 12 subtractions, 4 shifts, + 2 small divisions and 1 small multiplication + */ + + /* r1 - r4 */ + if ((res = signed_subtract(&w1, &w4, &w1)) != MP_OKAY) { + goto ERR; + } + /* r3 - r0 */ + if ((res = signed_subtract(&w3, &w0, &w3)) != MP_OKAY) { + goto ERR; + } + /* r1/2 */ + if ((res = half(&w1, &w1)) != MP_OKAY) { + goto ERR; + } + /* r3/2 */ + if ((res = half(&w3, &w3)) != MP_OKAY) { + goto ERR; + } + /* r2 - r0 - r4 */ + if ((res = signed_subtract(&w2, &w0, &w2)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_subtract(&w2, &w4, &w2)) != MP_OKAY) { + goto ERR; + } + /* r1 - r2 */ + if ((res = signed_subtract(&w1, &w2, &w1)) != MP_OKAY) { + goto ERR; + } + /* r3 - r2 */ + if ((res = signed_subtract(&w3, &w2, &w3)) != MP_OKAY) { + goto ERR; + } + /* r1 - 8r0 */ + if ((res = lshift_bits(&w0, 3, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_subtract(&w1, &tmp1, &w1)) != MP_OKAY) { + goto ERR; + } + /* r3 - 8r4 */ + if ((res = lshift_bits(&w4, 3, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_subtract(&w3, &tmp1, &w3)) != MP_OKAY) { + goto ERR; + } + /* 3r2 - r1 - r3 */ + if ((res = multiply_digit(&w2, 3, &w2)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_subtract(&w2, &w1, &w2)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_subtract(&w2, &w3, &w2)) != MP_OKAY) { + goto ERR; + } + /* r1 - r2 */ + if ((res = signed_subtract(&w1, &w2, &w1)) != MP_OKAY) { + goto ERR; + } + /* r3 - r2 */ + if ((res = signed_subtract(&w3, &w2, &w3)) != MP_OKAY) { + goto ERR; + } + /* r1/3 */ + if ((res = third(&w1, &w1, NULL)) != MP_OKAY) { + goto ERR; + } + /* r3/3 */ + if ((res = third(&w3, &w3, NULL)) != MP_OKAY) { + goto ERR; + } + + /* at this point shift W[n] by B*n */ + if ((res = lshift_digits(&w1, 1*B)) != MP_OKAY) { + goto ERR; + } + if ((res = lshift_digits(&w2, 2*B)) != MP_OKAY) { + goto ERR; + } + if ((res = lshift_digits(&w3, 3*B)) != MP_OKAY) { + goto ERR; + } + if ((res = lshift_digits(&w4, 4*B)) != MP_OKAY) { + goto ERR; + } + + if ((res = signed_add(&w0, &w1, c)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&w2, &w3, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&w4, &tmp1, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp1, c, c)) != MP_OKAY) { + goto ERR; + } + ERR: - mp_clear_multi(&w0, &w1, &w2, &w3, &w4, - &a0, &a1, &a2, &b0, &b1, - &b2, &tmp1, &tmp2, NULL); - return res; + mp_clear_multi(&w0, &w1, &w2, &w3, &w4, + &a0, &a1, &a2, &b0, &b1, + &b2, &tmp1, &tmp2, NULL); + return res; } #define TOOM_MUL_CUTOFF 350 @@ -2147,7 +2082,7 @@ ERR: * Note that a multiplication of half the digits requires * 1/4th the number of single precision multiplications so in * total after one call 25% of the single precision multiplications - * are saved. Note also that the call to mp_mul can end up back + * are saved. Note also that the call to signed_multiply can end up back * in this function if the a0, a1, b0, or b1 are above the threshold. * This is known as divide-and-conquer and leads to the famous * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than @@ -2155,122 +2090,141 @@ ERR: * Generally though the overhead of this method doesn't pay off * until a certain size (N ~ 80) is reached. */ -static int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c) -{ - mp_int x0, x1, y0, y1, t1, x0y0, x1y1; - int B; - int err; - - /* default the return code to an error */ - err = MP_MEM; - - /* min # of digits */ - B = MIN (a->used, b->used); - - /* now divide in two */ - B = (int)((unsigned)B >> 1); - - /* init copy all the temps */ - if (mp_init_size (&x0, B) != MP_OKAY) - goto ERR; - if (mp_init_size (&x1, a->used - B) != MP_OKAY) - goto X0; - if (mp_init_size (&y0, B) != MP_OKAY) - goto X1; - if (mp_init_size (&y1, b->used - B) != MP_OKAY) - goto Y0; - - /* init temps */ - if (mp_init_size (&t1, B * 2) != MP_OKAY) - goto Y1; - if (mp_init_size (&x0y0, B * 2) != MP_OKAY) - goto T1; - if (mp_init_size (&x1y1, B * 2) != MP_OKAY) - goto X0Y0; - - /* now shift the digits */ - x0.used = y0.used = B; - x1.used = a->used - B; - y1.used = b->used - B; - - { - int x; - mp_digit *tmpa, *tmpb, *tmpx, *tmpy; - - /* we copy the digits directly instead of using higher level functions - * since we also need to shift the digits - */ - tmpa = a->dp; - tmpb = b->dp; - - tmpx = x0.dp; - tmpy = y0.dp; - for (x = 0; x < B; x++) { - *tmpx++ = *tmpa++; - *tmpy++ = *tmpb++; - } - - tmpx = x1.dp; - for (x = B; x < a->used; x++) { - *tmpx++ = *tmpa++; - } - - tmpy = y1.dp; - for (x = B; x < b->used; x++) { - *tmpy++ = *tmpb++; - } - } - - /* only need to clamp the lower words since by definition the - * upper words x1/y1 must have a known number of digits - */ - mp_clamp (&x0); - mp_clamp (&y0); - - /* now calc the products x0y0 and x1y1 */ - /* after this x0 is no longer required, free temp [x0==t2]! */ - if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY) - goto X1Y1; /* x0y0 = x0*y0 */ - if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY) - goto X1Y1; /* x1y1 = x1*y1 */ - - /* now calc x1+x0 and y1+y0 */ - if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) - goto X1Y1; /* t1 = x1 - x0 */ - if (s_mp_add (&y1, &y0, &x0) != MP_OKAY) - goto X1Y1; /* t2 = y1 - y0 */ - if (mp_mul (&t1, &x0, &t1) != MP_OKAY) - goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */ - - /* add x0y0 */ - if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY) - goto X1Y1; /* t2 = x0y0 + x1y1 */ - if (s_mp_sub (&t1, &x0, &t1) != MP_OKAY) - goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */ - - /* shift by B */ - if (mp_lshd (&t1, B) != MP_OKAY) - goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<used, b->used); + + /* now divide in two */ + B = (int)((unsigned)B >> 1); + + /* init copy all the temps */ + if (mp_init_size(&x0, B) != MP_OKAY) { + goto ERR; + } + if (mp_init_size(&x1, a->used - B) != MP_OKAY) { + goto X0; + } + if (mp_init_size(&y0, B) != MP_OKAY) { + goto X1; + } + if (mp_init_size(&y1, b->used - B) != MP_OKAY) { + goto Y0; + } + /* init temps */ + if (mp_init_size(&t1, B * 2) != MP_OKAY) { + goto Y1; + } + if (mp_init_size(&x0y0, B * 2) != MP_OKAY) { + goto T1; + } + if (mp_init_size(&x1y1, B * 2) != MP_OKAY) { + goto X0Y0; + } + /* now shift the digits */ + x0.used = y0.used = B; + x1.used = a->used - B; + y1.used = b->used - B; + + { + int x; + mp_digit *tmpa, *tmpb, *tmpx, *tmpy; + + /* we copy the digits directly instead of using higher level functions + * since we also need to shift the digits + */ + tmpa = a->dp; + tmpb = b->dp; + + tmpx = x0.dp; + tmpy = y0.dp; + for (x = 0; x < B; x++) { + *tmpx++ = *tmpa++; + *tmpy++ = *tmpb++; + } + + tmpx = x1.dp; + for (x = B; x < a->used; x++) { + *tmpx++ = *tmpa++; + } + + tmpy = y1.dp; + for (x = B; x < b->used; x++) { + *tmpy++ = *tmpb++; + } + } + + /* only need to clamp the lower words since by definition the + * upper words x1/y1 must have a known number of digits + */ + trim_unused_digits(&x0); + trim_unused_digits(&y0); + + /* now calc the products x0y0 and x1y1 */ + /* after this x0 is no longer required, free temp [x0==t2]! */ + if (signed_multiply(&x0, &y0, &x0y0) != MP_OKAY) { + goto X1Y1; /* x0y0 = x0*y0 */ + } + if (signed_multiply(&x1, &y1, &x1y1) != MP_OKAY) { + goto X1Y1; /* x1y1 = x1*y1 */ + } + /* now calc x1+x0 and y1+y0 */ + if (basic_add(&x1, &x0, &t1) != MP_OKAY) { + goto X1Y1; /* t1 = x1 - x0 */ + } + if (basic_add(&y1, &y0, &x0) != MP_OKAY) { + goto X1Y1; /* t2 = y1 - y0 */ + } + if (signed_multiply(&t1, &x0, &t1) != MP_OKAY) { + goto X1Y1; /* t1 = (x1 + x0) * (y1 + y0) */ + } + /* add x0y0 */ + if (signed_add(&x0y0, &x1y1, &x0) != MP_OKAY) { + goto X1Y1; /* t2 = x0y0 + x1y1 */ + } + if (basic_subtract(&t1, &x0, &t1) != MP_OKAY) { + goto X1Y1; /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */ + } + /* shift by B */ + if (lshift_digits(&t1, B) != MP_OKAY) { + goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<alloc < digs) { - if ((res = mp_grow (c, digs)) != MP_OKAY) { - return res; - } - } - - /* number of output digits to produce */ - pa = MIN(digs, a->used + b->used); - - /* clear the carry */ - _W = 0; - for (ix = 0; ix < pa; ix++) { - int tx, ty; - int iy; - mp_digit *tmpx, *tmpy; - - /* get offsets into the two bignums */ - ty = MIN(b->used-1, ix); - tx = ix - ty; - - /* setup temp aliases */ - tmpx = a->dp + tx; - tmpy = b->dp + ty; - - /* this is the number of times the loop will iterrate, essentially - while (tx++ < a->used && ty-- >= 0) { ... } - */ - iy = MIN(a->used-tx, ty+1); - - /* execute loop */ - for (iz = 0; iz < iy; ++iz) { - _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); - - } - - /* store term */ - W[ix] = ((mp_digit)_W) & MP_MASK; - - /* make next carry */ - _W = _W >> ((mp_word)DIGIT_BIT); - } - - /* setup dest */ - olduse = c->used; - c->used = pa; - - { - mp_digit *tmpc; - tmpc = c->dp; - for (ix = 0; ix < pa+1; ix++) { - /* now extract the previous digit [below the carry] */ - *tmpc++ = W[ix]; - } - - /* clear unused digits [that existed in the old copy of c] */ - for (; ix < olduse; ix++) { - *tmpc++ = 0; - } - } - mp_clamp (c); - return MP_OKAY; +static int +fast_col_array_multiply(mp_int * a, mp_int * b, mp_int * c, int digs) +{ + int olduse, res, pa, ix, iz; + /*LINTED*/ + mp_digit W[MP_WARRAY]; + mp_word _W; + + /* grow the destination as required */ + if (c->alloc < digs) { + if ((res = mp_grow(c, digs)) != MP_OKAY) { + return res; + } + } + + /* number of output digits to produce */ + pa = MIN(digs, a->used + b->used); + + /* clear the carry */ + _W = 0; + for (ix = 0; ix < pa; ix++) { + int tx, ty; + int iy; + mp_digit *tmpx, *tmpy; + + /* get offsets into the two bignums */ + ty = MIN(b->used-1, ix); + tx = ix - ty; + + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = b->dp + ty; + + /* this is the number of times the loop will iterrate, essentially + while (tx++ < a->used && ty-- >= 0) { ... } + */ + iy = MIN(a->used-tx, ty+1); + + /* execute loop */ + for (iz = 0; iz < iy; ++iz) { + _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); + + } + + /* store term */ + W[ix] = ((mp_digit)_W) & MP_MASK; + + /* make next carry */ + _W = _W >> ((mp_word)DIGIT_BIT); + } + + /* setup dest */ + olduse = c->used; + c->used = pa; + + { + mp_digit *tmpc; + tmpc = c->dp; + for (ix = 0; ix < pa+1; ix++) { + /* now extract the previous digit [below the carry] */ + *tmpc++ = W[ix]; + } + + /* clear unused digits [that existed in the old copy of c] */ + for (; ix < olduse; ix++) { + *tmpc++ = 0; + } + } + trim_unused_digits(c); + return MP_OKAY; +} + +/* return 1 if we can use fast column array multiply */ +/* +* The fast multiplier can be used if the output will +* have less than MP_WARRAY digits and the number of +* digits won't affect carry propagation +*/ +static inline int +can_use_fast_column_array(int ndigits, int used) +{ + return (((unsigned)ndigits < MP_WARRAY) && + used < (1 << (unsigned)((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT)))); } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_s_mp_mul_digs.c,v $ */ @@ -2369,69 +2337,68 @@ static int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) * HAC pp. 595, Algorithm 14.12 Modified so you can control how * many digits of output are created. */ -static int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) -{ - mp_int t; - int res, pa, pb, ix, iy; - mp_digit u; - mp_word r; - mp_digit tmpx, *tmpt, *tmpy; - - /* can we use the fast multiplier? */ - if (((unsigned)(digs) < MP_WARRAY) && - MIN (a->used, b->used) < - (1 << (unsigned)((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { - return fast_s_mp_mul_digs (a, b, c, digs); - } - - if ((res = mp_init_size (&t, digs)) != MP_OKAY) { - return res; - } - t.used = digs; - - /* compute the digits of the product directly */ - pa = a->used; - for (ix = 0; ix < pa; ix++) { - /* set the carry to zero */ - u = 0; - - /* limit ourselves to making digs digits of output */ - pb = MIN (b->used, digs - ix); - - /* setup some aliases */ - /* copy of the digit from a used within the nested loop */ - tmpx = a->dp[ix]; - - /* an alias for the destination shifted ix places */ - tmpt = t.dp + ix; - - /* an alias for the digits of b */ - tmpy = b->dp; - - /* compute the columns of the output and propagate the carry */ - for (iy = 0; iy < pb; iy++) { - /* compute the column as a mp_word */ - r = ((mp_word)*tmpt) + - ((mp_word)tmpx) * ((mp_word)*tmpy++) + - ((mp_word) u); - - /* the new column is the lower part of the result */ - *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); - - /* get the carry word from the result */ - u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); - } - /* set carry if it is placed below digs */ - if (ix + iy < digs) { - *tmpt = u; - } - } - - mp_clamp (&t); - mp_exch (&t, c); - - mp_clear (&t); - return MP_OKAY; +static int +basic_multiply_partial_lower(mp_int * a, mp_int * b, mp_int * c, int digs) +{ + mp_int t; + int res, pa, pb, ix, iy; + mp_digit u; + mp_word r; + mp_digit tmpx, *tmpt, *tmpy; + + /* can we use the fast multiplier? */ + if (can_use_fast_column_array(digs, MIN(a->used, b->used))) { + return fast_col_array_multiply(a, b, c, digs); + } + + if ((res = mp_init_size(&t, digs)) != MP_OKAY) { + return res; + } + t.used = digs; + + /* compute the digits of the product directly */ + pa = a->used; + for (ix = 0; ix < pa; ix++) { + /* set the carry to zero */ + u = 0; + + /* limit ourselves to making digs digits of output */ + pb = MIN(b->used, digs - ix); + + /* setup some aliases */ + /* copy of the digit from a used within the nested loop */ + tmpx = a->dp[ix]; + + /* an alias for the destination shifted ix places */ + tmpt = t.dp + ix; + + /* an alias for the digits of b */ + tmpy = b->dp; + + /* compute the columns of the output and propagate the carry */ + for (iy = 0; iy < pb; iy++) { + /* compute the column as a mp_word */ + r = ((mp_word)*tmpt) + + ((mp_word)tmpx) * ((mp_word)*tmpy++) + + ((mp_word) u); + + /* the new column is the lower part of the result */ + *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); + + /* get the carry word from the result */ + u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); + } + /* set carry if it is placed below digs */ + if (ix + iy < digs) { + *tmpt = u; + } + } + + trim_unused_digits(&t); + mp_exch(&t, c); + + mp_clear(&t); + return MP_OKAY; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_s_mp_mul_digs.c,v $ */ @@ -2440,38 +2407,29 @@ static int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) /* high level multiplication (handles sign) */ static int -mp_mul(mp_int * a, mp_int * b, mp_int * c) -{ - int res, neg; - neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; - - /* use Toom-Cook? */ - if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) { - res = mp_toom_mul(a, b, c); - } else - /* use Karatsuba? */ - if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) { - res = mp_karatsuba_mul (a, b, c); - } else - { - /* can we use the fast multiplier? - * - * The fast multiplier can be used if the output will - * have less than MP_WARRAY digits and the number of - * digits won't affect carry propagation - */ - int digs = a->used + b->used + 1; - - if (((unsigned)digs < MP_WARRAY) && - MIN(a->used, b->used) <= - (1 << (unsigned)((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { - res = fast_s_mp_mul_digs (a, b, c, digs); - } else - res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */ - - } - c->sign = (c->used > 0) ? neg : MP_ZPOS; - return res; +signed_multiply(mp_int * a, mp_int * b, mp_int * c) +{ + int res, neg; + + neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; + /* use Toom-Cook? */ + if (MIN(a->used, b->used) >= TOOM_MUL_CUTOFF) { + res = toom_cook_multiply(a, b, c); + } else if (MIN(a->used, b->used) >= KARATSUBA_MUL_CUTOFF) { + /* use Karatsuba? */ + res = karatsuba_multiply(a, b, c); + } else { + /* can we use the fast multiplier? */ + int digs = a->used + b->used + 1; + + if (can_use_fast_column_array(digs, MIN(a->used, b->used))) { + res = fast_col_array_multiply(a, b, c, digs); + } else { + res = basic_multiply_partial_lower(a, b, c, (a)->used + (b)->used + 1); + } + } + c->sign = (c->used > 0) ? neg : MP_ZPOS; + return res; } /* this is a modified version of fast_s_mul_digs that only produces @@ -2484,72 +2442,72 @@ mp_mul(mp_int * a, mp_int * b, mp_int * c) * Based on Algorithm 14.12 on pp.595 of HAC. */ static int -fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) -{ - int olduse, res, pa, ix, iz; - mp_digit W[MP_WARRAY]; - mp_word _W; - - /* grow the destination as required */ - pa = a->used + b->used; - if (c->alloc < pa) { - if ((res = mp_grow (c, pa)) != MP_OKAY) { - return res; - } - } - - /* number of output digits to produce */ - pa = a->used + b->used; - _W = 0; - for (ix = digs; ix < pa; ix++) { - int tx, ty, iy; - mp_digit *tmpx, *tmpy; - - /* get offsets into the two bignums */ - ty = MIN(b->used-1, ix); - tx = ix - ty; - - /* setup temp aliases */ - tmpx = a->dp + tx; - tmpy = b->dp + ty; - - /* this is the number of times the loop will iterrate, essentially its - while (tx++ < a->used && ty-- >= 0) { ... } - */ - iy = MIN(a->used-tx, ty+1); - - /* execute loop */ - for (iz = 0; iz < iy; iz++) { - _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); - } - - /* store term */ - W[ix] = ((mp_digit)_W) & MP_MASK; - - /* make next carry */ - _W = _W >> ((mp_word)DIGIT_BIT); - } - - /* setup dest */ - olduse = c->used; - c->used = pa; - - { - mp_digit *tmpc; - - tmpc = c->dp + digs; - for (ix = digs; ix < pa; ix++) { - /* now extract the previous digit [below the carry] */ - *tmpc++ = W[ix]; - } - - /* clear unused digits [that existed in the old copy of c] */ - for (; ix < olduse; ix++) { - *tmpc++ = 0; - } - } - mp_clamp (c); - return MP_OKAY; +fast_basic_multiply_partial_upper(mp_int * a, mp_int * b, mp_int * c, int digs) +{ + int olduse, res, pa, ix, iz; + mp_digit W[MP_WARRAY]; + mp_word _W; + + /* grow the destination as required */ + pa = a->used + b->used; + if (c->alloc < pa) { + if ((res = mp_grow(c, pa)) != MP_OKAY) { + return res; + } + } + + /* number of output digits to produce */ + pa = a->used + b->used; + _W = 0; + for (ix = digs; ix < pa; ix++) { + int tx, ty, iy; + mp_digit *tmpx, *tmpy; + + /* get offsets into the two bignums */ + ty = MIN(b->used-1, ix); + tx = ix - ty; + + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = b->dp + ty; + + /* this is the number of times the loop will iterrate, essentially its + while (tx++ < a->used && ty-- >= 0) { ... } + */ + iy = MIN(a->used-tx, ty+1); + + /* execute loop */ + for (iz = 0; iz < iy; iz++) { + _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); + } + + /* store term */ + W[ix] = ((mp_digit)_W) & MP_MASK; + + /* make next carry */ + _W = _W >> ((mp_word)DIGIT_BIT); + } + + /* setup dest */ + olduse = c->used; + c->used = pa; + + { + mp_digit *tmpc; + + tmpc = c->dp + digs; + for (ix = digs; ix < pa; ix++) { + /* now extract the previous digit [below the carry] */ + *tmpc++ = W[ix]; + } + + /* clear unused digits [that existed in the old copy of c] */ + for (; ix < olduse; ix++) { + *tmpc++ = 0; + } + } + trim_unused_digits(c); + return MP_OKAY; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_s_mp_mul_high_digs.c,v $ */ @@ -2560,58 +2518,57 @@ fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) * [meant to get the higher part of the product] */ static int -s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) -{ - mp_int t; - int res, pa, pb, ix, iy; - mp_digit u; - mp_word r; - mp_digit tmpx, *tmpt, *tmpy; - - /* can we use the fast multiplier? */ - if (((unsigned)(a->used + b->used + 1) < MP_WARRAY) - && MIN (a->used, b->used) < (1 << (unsigned)((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { - return fast_s_mp_mul_high_digs (a, b, c, digs); - } - - if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) { - return res; - } - t.used = a->used + b->used + 1; - - pa = a->used; - pb = b->used; - for (ix = 0; ix < pa; ix++) { - /* clear the carry */ - u = 0; - - /* left hand side of A[ix] * B[iy] */ - tmpx = a->dp[ix]; - - /* alias to the address of where the digits will be stored */ - tmpt = &(t.dp[digs]); - - /* alias for where to read the right hand side from */ - tmpy = b->dp + (digs - ix); - - for (iy = digs - ix; iy < pb; iy++) { - /* calculate the double precision result */ - r = ((mp_word)*tmpt) + - ((mp_word)tmpx) * ((mp_word)*tmpy++) + - ((mp_word) u); - - /* get the lower part */ - *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); - - /* carry the carry */ - u = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); - } - *tmpt = u; - } - mp_clamp (&t); - mp_exch (&t, c); - mp_clear (&t); - return MP_OKAY; +basic_multiply_partial_upper(mp_int * a, mp_int * b, mp_int * c, int digs) +{ + mp_int t; + int res, pa, pb, ix, iy; + mp_digit carry; + mp_word r; + mp_digit tmpx, *tmpt, *tmpy; + + /* can we use the fast multiplier? */ + if (can_use_fast_column_array(a->used + b->used + 1, MIN(a->used, b->used))) { + return fast_basic_multiply_partial_upper(a, b, c, digs); + } + + if ((res = mp_init_size(&t, a->used + b->used + 1)) != MP_OKAY) { + return res; + } + t.used = a->used + b->used + 1; + + pa = a->used; + pb = b->used; + for (ix = 0; ix < pa; ix++) { + /* clear the carry */ + carry = 0; + + /* left hand side of A[ix] * B[iy] */ + tmpx = a->dp[ix]; + + /* alias to the address of where the digits will be stored */ + tmpt = &(t.dp[digs]); + + /* alias for where to read the right hand side from */ + tmpy = b->dp + (digs - ix); + + for (iy = digs - ix; iy < pb; iy++) { + /* calculate the double precision result */ + r = ((mp_word)*tmpt) + + ((mp_word)tmpx) * ((mp_word)*tmpy++) + + ((mp_word) carry); + + /* get the lower part */ + *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); + + /* carry the carry */ + carry = (mp_digit) (r >> ((mp_word) DIGIT_BIT)); + } + *tmpt = carry; + } + trim_unused_digits(&t); + mp_exch(&t, c); + mp_clear(&t); + return MP_OKAY; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_s_mp_mul_high_digs.c,v $ */ @@ -2623,91 +2580,94 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) * From HAC pp.604 Algorithm 14.42 */ static int -mp_reduce (mp_int * x, mp_int * m, mp_int * mu) -{ - mp_int q; - int res, um = m->used; - - /* q = x */ - if ((res = mp_init_copy (&q, x)) != MP_OKAY) { - return res; - } - - /* q1 = x / b**(k-1) */ - mp_rshd (&q, um - 1); - - /* according to HAC this optimization is ok */ - if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) { - if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) { - goto CLEANUP; - } - } else { - if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) { - goto CLEANUP; - } - } - - /* q3 = q2 / b**(k+1) */ - mp_rshd (&q, um + 1); - - /* x = x mod b**(k+1), quick (no division) */ - if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) { - goto CLEANUP; - } - - /* q = q * m mod b**(k+1), quick (no division) */ - if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) { - goto CLEANUP; - } - - /* x = x - q */ - if ((res = mp_sub (x, &q, x)) != MP_OKAY) { - goto CLEANUP; - } - - /* If x < 0, add b**(k+1) to it */ - if (mp_cmp_d (x, 0) == MP_LT) { - mp_set (&q, 1); - if ((res = mp_lshd (&q, um + 1)) != MP_OKAY) - goto CLEANUP; - if ((res = mp_add (x, &q, x)) != MP_OKAY) - goto CLEANUP; - } - - /* Back off if it's too big */ - while (mp_cmp (x, m) != MP_LT) { - if ((res = s_mp_sub (x, m, x)) != MP_OKAY) { - goto CLEANUP; - } - } - +mp_reduce(mp_int * x, mp_int * m, mp_int * mu) +{ + mp_int q; + int res, um = m->used; + + /* q = x */ + if ((res = mp_init_copy(&q, x)) != MP_OKAY) { + return res; + } + + /* q1 = x / b**(k-1) */ + rshift_digits(&q, um - 1); + + /* according to HAC this optimization is ok */ + if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) { + if ((res = signed_multiply(&q, mu, &q)) != MP_OKAY) { + goto CLEANUP; + } + } else { + if ((res = basic_multiply_partial_upper(&q, mu, &q, um)) != MP_OKAY) { + goto CLEANUP; + } + } + + /* q3 = q2 / b**(k+1) */ + rshift_digits(&q, um + 1); + + /* x = x mod b**(k+1), quick (no division) */ + if ((res = modulo_2_to_power(x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) { + goto CLEANUP; + } + + /* q = q * m mod b**(k+1), quick (no division) */ + if ((res = basic_multiply_partial_lower(&q, m, &q, um + 1)) != MP_OKAY) { + goto CLEANUP; + } + + /* x = x - q */ + if ((res = signed_subtract(x, &q, x)) != MP_OKAY) { + goto CLEANUP; + } + + /* If x < 0, add b**(k+1) to it */ + if (compare_digit(x, 0) == MP_LT) { + set_word(&q, 1); + if ((res = lshift_digits(&q, um + 1)) != MP_OKAY) { + goto CLEANUP; + } + if ((res = signed_add(x, &q, x)) != MP_OKAY) { + goto CLEANUP; + } + } + + /* Back off if it's too big */ + while (signed_compare(x, m) != MP_LT) { + if ((res = basic_subtract(x, m, x)) != MP_OKAY) { + goto CLEANUP; + } + } + CLEANUP: - mp_clear (&q); + mp_clear(&q); - return res; + return res; } /* determines the setup value */ -static int mp_reduce_2k_setup_l(mp_int *a, mp_int *d) -{ - int res; - mp_int tmp; - - if ((res = mp_init(&tmp)) != MP_OKAY) { - return res; - } - - if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) { - goto ERR; - } - - if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) { - goto ERR; - } - +static int +mp_reduce_2k_setup_l(mp_int *a, mp_int *d) +{ + int res; + mp_int tmp; + + if ((res = mp_init(&tmp)) != MP_OKAY) { + return res; + } + + if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) { + goto ERR; + } + + if ((res = basic_subtract(&tmp, a, d)) != MP_OKAY) { + goto ERR; + } + ERR: - mp_clear(&tmp); - return res; + mp_clear(&tmp); + return res; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_2k_setup_l.c,v $ */ @@ -2721,38 +2681,38 @@ ERR: static int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d) { - mp_int q; - int p, res; - - if ((res = mp_init(&q)) != MP_OKAY) { - return res; - } - - p = mp_count_bits(n); + mp_int q; + int p, res; + + if ((res = mp_init(&q)) != MP_OKAY) { + return res; + } + + p = mp_count_bits(n); top: - /* q = a/2**p, a = a mod 2**p */ - if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) { - goto ERR; - } - - /* q = q * d */ - if ((res = mp_mul(&q, d, &q)) != MP_OKAY) { - goto ERR; - } - - /* a = a + q */ - if ((res = s_mp_add(a, &q, a)) != MP_OKAY) { - goto ERR; - } - - if (mp_cmp_mag(a, n) != MP_LT) { - s_mp_sub(a, n, a); - goto top; - } - + /* q = a/2**p, a = a mod 2**p */ + if ((res = rshift_bits(a, p, &q, a)) != MP_OKAY) { + goto ERR; + } + + /* q = q * d */ + if ((res = signed_multiply(&q, d, &q)) != MP_OKAY) { + goto ERR; + } + + /* a = a + q */ + if ((res = basic_add(a, &q, a)) != MP_OKAY) { + goto ERR; + } + + if (compare_magnitude(a, n) != MP_LT) { + basic_subtract(a, n, a); + goto top; + } + ERR: - mp_clear(&q); - return res; + mp_clear(&q); + return res; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_2k_l.c,v $ */ @@ -2761,206 +2721,206 @@ ERR: /* squaring using Toom-Cook 3-way algorithm */ static int -mp_toom_sqr(mp_int *a, mp_int *b) -{ - mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2; - int res, B; - - /* init temps */ - if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) { - return res; - } - - /* B */ - B = a->used / 3; - - /* a = a2 * B**2 + a1 * B + a0 */ - if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_copy(a, &a1)) != MP_OKAY) { - goto ERR; - } - mp_rshd(&a1, B); - mp_mod_2d(&a1, DIGIT_BIT * B, &a1); - - if ((res = mp_copy(a, &a2)) != MP_OKAY) { - goto ERR; - } - mp_rshd(&a2, B*2); - - /* w0 = a0*a0 */ - if ((res = mp_sqr(&a0, &w0)) != MP_OKAY) { - goto ERR; - } - - /* w4 = a2 * a2 */ - if ((res = mp_sqr(&a2, &w4)) != MP_OKAY) { - goto ERR; - } - - /* w1 = (a2 + 2(a1 + 2a0))**2 */ - if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_sqr(&tmp1, &w1)) != MP_OKAY) { - goto ERR; - } - - /* w3 = (a0 + 2(a1 + 2a2))**2 */ - if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_sqr(&tmp1, &w3)) != MP_OKAY) { - goto ERR; - } - - - /* w2 = (a2 + a1 + a0)**2 */ - if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sqr(&tmp1, &w2)) != MP_OKAY) { - goto ERR; - } - - /* now solve the matrix - - 0 0 0 0 1 - 1 2 4 8 16 - 1 1 1 1 1 - 16 8 4 2 1 - 1 0 0 0 0 - - using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication. - */ - - /* r1 - r4 */ - if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - r0 */ - if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) { - goto ERR; - } - /* r1/2 */ - if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3/2 */ - if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) { - goto ERR; - } - /* r2 - r0 - r4 */ - if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) { - goto ERR; - } - /* r1 - r2 */ - if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - r2 */ - if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) { - goto ERR; - } - /* r1 - 8r0 */ - if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - 8r4 */ - if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) { - goto ERR; - } - /* 3r2 - r1 - r3 */ - if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) { - goto ERR; - } - /* r1 - r2 */ - if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) { - goto ERR; - } - /* r3 - r2 */ - if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) { - goto ERR; - } - /* r1/3 */ - if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) { - goto ERR; - } - /* r3/3 */ - if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) { - goto ERR; - } - - /* at this point shift W[n] by B*n */ - if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) { - goto ERR; - } - - if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) { - goto ERR; - } - if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) { - goto ERR; - } +toom_cook_square(mp_int *a, mp_int *b) +{ + mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2; + int res, B; + + /* init temps */ + if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) { + return res; + } + + /* B */ + B = a->used / 3; + + /* a = a2 * B**2 + a1 * B + a0 */ + if ((res = modulo_2_to_power(a, DIGIT_BIT * B, &a0)) != MP_OKAY) { + goto ERR; + } + + if ((res = mp_copy(a, &a1)) != MP_OKAY) { + goto ERR; + } + rshift_digits(&a1, B); + modulo_2_to_power(&a1, DIGIT_BIT * B, &a1); + + if ((res = mp_copy(a, &a2)) != MP_OKAY) { + goto ERR; + } + rshift_digits(&a2, B*2); + + /* w0 = a0*a0 */ + if ((res = square(&a0, &w0)) != MP_OKAY) { + goto ERR; + } + + /* w4 = a2 * a2 */ + if ((res = square(&a2, &w4)) != MP_OKAY) { + goto ERR; + } + + /* w1 = (a2 + 2(a1 + 2a0))**2 */ + if ((res = doubled(&a0, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = doubled(&tmp1, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp1, &a2, &tmp1)) != MP_OKAY) { + goto ERR; + } + + if ((res = square(&tmp1, &w1)) != MP_OKAY) { + goto ERR; + } + + /* w3 = (a0 + 2(a1 + 2a2))**2 */ + if ((res = doubled(&a2, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp1, &a1, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = doubled(&tmp1, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { + goto ERR; + } + + if ((res = square(&tmp1, &w3)) != MP_OKAY) { + goto ERR; + } + + + /* w2 = (a2 + a1 + a0)**2 */ + if ((res = signed_add(&a2, &a1, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp1, &a0, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = square(&tmp1, &w2)) != MP_OKAY) { + goto ERR; + } + + /* now solve the matrix + + 0 0 0 0 1 + 1 2 4 8 16 + 1 1 1 1 1 + 16 8 4 2 1 + 1 0 0 0 0 + + using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication. + */ + + /* r1 - r4 */ + if ((res = signed_subtract(&w1, &w4, &w1)) != MP_OKAY) { + goto ERR; + } + /* r3 - r0 */ + if ((res = signed_subtract(&w3, &w0, &w3)) != MP_OKAY) { + goto ERR; + } + /* r1/2 */ + if ((res = half(&w1, &w1)) != MP_OKAY) { + goto ERR; + } + /* r3/2 */ + if ((res = half(&w3, &w3)) != MP_OKAY) { + goto ERR; + } + /* r2 - r0 - r4 */ + if ((res = signed_subtract(&w2, &w0, &w2)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_subtract(&w2, &w4, &w2)) != MP_OKAY) { + goto ERR; + } + /* r1 - r2 */ + if ((res = signed_subtract(&w1, &w2, &w1)) != MP_OKAY) { + goto ERR; + } + /* r3 - r2 */ + if ((res = signed_subtract(&w3, &w2, &w3)) != MP_OKAY) { + goto ERR; + } + /* r1 - 8r0 */ + if ((res = lshift_bits(&w0, 3, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_subtract(&w1, &tmp1, &w1)) != MP_OKAY) { + goto ERR; + } + /* r3 - 8r4 */ + if ((res = lshift_bits(&w4, 3, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_subtract(&w3, &tmp1, &w3)) != MP_OKAY) { + goto ERR; + } + /* 3r2 - r1 - r3 */ + if ((res = multiply_digit(&w2, 3, &w2)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_subtract(&w2, &w1, &w2)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_subtract(&w2, &w3, &w2)) != MP_OKAY) { + goto ERR; + } + /* r1 - r2 */ + if ((res = signed_subtract(&w1, &w2, &w1)) != MP_OKAY) { + goto ERR; + } + /* r3 - r2 */ + if ((res = signed_subtract(&w3, &w2, &w3)) != MP_OKAY) { + goto ERR; + } + /* r1/3 */ + if ((res = third(&w1, &w1, NULL)) != MP_OKAY) { + goto ERR; + } + /* r3/3 */ + if ((res = third(&w3, &w3, NULL)) != MP_OKAY) { + goto ERR; + } + + /* at this point shift W[n] by B*n */ + if ((res = lshift_digits(&w1, 1*B)) != MP_OKAY) { + goto ERR; + } + if ((res = lshift_digits(&w2, 2*B)) != MP_OKAY) { + goto ERR; + } + if ((res = lshift_digits(&w3, 3*B)) != MP_OKAY) { + goto ERR; + } + if ((res = lshift_digits(&w4, 4*B)) != MP_OKAY) { + goto ERR; + } + + if ((res = signed_add(&w0, &w1, b)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&w2, &w3, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&w4, &tmp1, &tmp1)) != MP_OKAY) { + goto ERR; + } + if ((res = signed_add(&tmp1, b, b)) != MP_OKAY) { + goto ERR; + } ERR: - mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL); - return res; + mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL); + return res; } @@ -2975,97 +2935,99 @@ ERR: * is essentially the same algorithm but merely * tuned to perform recursive squarings. */ -static int mp_karatsuba_sqr (mp_int * a, mp_int * b) -{ - mp_int x0, x1, t1, t2, x0x0, x1x1; - int B, err; - - err = MP_MEM; - - /* min # of digits */ - B = a->used; - - /* now divide in two */ - B = (unsigned)B >> 1; - - /* init copy all the temps */ - if (mp_init_size (&x0, B) != MP_OKAY) - goto ERR; - if (mp_init_size (&x1, a->used - B) != MP_OKAY) - goto X0; - - /* init temps */ - if (mp_init_size (&t1, a->used * 2) != MP_OKAY) - goto X1; - if (mp_init_size (&t2, a->used * 2) != MP_OKAY) - goto T1; - if (mp_init_size (&x0x0, B * 2) != MP_OKAY) - goto T2; - if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY) - goto X0X0; - - { - int x; - mp_digit *dst, *src; - - src = a->dp; - - /* now shift the digits */ - dst = x0.dp; - for (x = 0; x < B; x++) { - *dst++ = *src++; - } - - dst = x1.dp; - for (x = B; x < a->used; x++) { - *dst++ = *src++; - } - } - - x0.used = B; - x1.used = a->used - B; - - mp_clamp (&x0); - - /* now calc the products x0*x0 and x1*x1 */ - if (mp_sqr (&x0, &x0x0) != MP_OKAY) - goto X1X1; /* x0x0 = x0*x0 */ - if (mp_sqr (&x1, &x1x1) != MP_OKAY) - goto X1X1; /* x1x1 = x1*x1 */ - - /* now calc (x1+x0)**2 */ - if (s_mp_add (&x1, &x0, &t1) != MP_OKAY) - goto X1X1; /* t1 = x1 - x0 */ - if (mp_sqr (&t1, &t1) != MP_OKAY) - goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */ - - /* add x0y0 */ - if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY) - goto X1X1; /* t2 = x0x0 + x1x1 */ - if (s_mp_sub (&t1, &t2, &t1) != MP_OKAY) - goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */ - - /* shift by B */ - if (mp_lshd (&t1, B) != MP_OKAY) - goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<used; + + /* now divide in two */ + B = (unsigned)B >> 1; + + /* init copy all the temps */ + if (mp_init_size(&x0, B) != MP_OKAY) { + goto ERR; + } + if (mp_init_size(&x1, a->used - B) != MP_OKAY) { + goto X0; + } + /* init temps */ + if (mp_init_size(&t1, a->used * 2) != MP_OKAY) { + goto X1; + } + if (mp_init_size(&t2, a->used * 2) != MP_OKAY) { + goto T1; + } + if (mp_init_size(&x0x0, B * 2) != MP_OKAY) { + goto T2; + } + if (mp_init_size(&x1x1, (a->used - B) * 2) != MP_OKAY) { + goto X0X0; + } + + memcpy(x0.dp, a->dp, B * sizeof(*x0.dp)); + memcpy(x1.dp, &a->dp[B], (a->used - B) * sizeof(*x1.dp)); + + x0.used = B; + x1.used = a->used - B; + + trim_unused_digits(&x0); + + /* now calc the products x0*x0 and x1*x1 */ + if (square(&x0, &x0x0) != MP_OKAY) { + goto X1X1; /* x0x0 = x0*x0 */ + } + if (square(&x1, &x1x1) != MP_OKAY) { + goto X1X1; /* x1x1 = x1*x1 */ + } + /* now calc (x1+x0)**2 */ + if (basic_add(&x1, &x0, &t1) != MP_OKAY) { + goto X1X1; /* t1 = x1 - x0 */ + } + if (square(&t1, &t1) != MP_OKAY) { + goto X1X1; /* t1 = (x1 - x0) * (x1 - x0) */ + } + /* add x0y0 */ + if (basic_add(&x0x0, &x1x1, &t2) != MP_OKAY) { + goto X1X1; /* t2 = x0x0 + x1x1 */ + } + if (basic_subtract(&t1, &t2, &t1) != MP_OKAY) { + goto X1X1; /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */ + } + /* shift by B */ + if (lshift_digits(&t1, B) != MP_OKAY) { + goto X1X1; /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<used + a->used; - if (b->alloc < pa) { - if ((res = mp_grow (b, pa)) != MP_OKAY) { - return res; - } - } - - /* number of output digits to produce */ - W1 = 0; - for (ix = 0; ix < pa; ix++) { - int tx, ty, iy; - mp_word _W; - mp_digit *tmpy; - - /* clear counter */ - _W = 0; - - /* get offsets into the two bignums */ - ty = MIN(a->used-1, ix); - tx = ix - ty; - - /* setup temp aliases */ - tmpx = a->dp + tx; - tmpy = a->dp + ty; - - /* this is the number of times the loop will iterrate, essentially - while (tx++ < a->used && ty-- >= 0) { ... } - */ - iy = MIN(a->used-tx, ty+1); - - /* now for squaring tx can never equal ty - * we halve the distance since they approach at a rate of 2x - * and we have to round because odd cases need to be executed - */ - iy = MIN(iy, (int)((unsigned)(ty-tx+1)>>1)); - - /* execute loop */ - for (iz = 0; iz < iy; iz++) { - _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); - } - - /* double the inner product and add carry */ - _W = _W + _W + W1; - - /* even columns have the square term in them */ - if ((ix&1) == 0) { - _W += ((mp_word)a->dp[(unsigned)ix>>1])*((mp_word)a->dp[(unsigned)ix>>1]); - } - - /* store it */ - W[ix] = (mp_digit)(_W & MP_MASK); - - /* make next carry */ - W1 = _W >> ((mp_word)DIGIT_BIT); - } - - /* setup dest */ - olduse = b->used; - b->used = a->used+a->used; - - { - mp_digit *tmpb; - tmpb = b->dp; - for (ix = 0; ix < pa; ix++) { - *tmpb++ = W[ix] & MP_MASK; - } - - /* clear unused digits [that existed in the old copy of c] */ - for (; ix < olduse; ix++) { - *tmpb++ = 0; - } - } - mp_clamp (b); - return MP_OKAY; +static int +fast_basic_square(mp_int * a, mp_int * b) +{ + int olduse, res, pa, ix, iz; + mp_digit W[MP_WARRAY], *tmpx; + mp_word W1; + + /* grow the destination as required */ + pa = a->used + a->used; + if (b->alloc < pa) { + if ((res = mp_grow(b, pa)) != MP_OKAY) { + return res; + } + } + + /* number of output digits to produce */ + W1 = 0; + for (ix = 0; ix < pa; ix++) { + int tx, ty, iy; + mp_word _W; + mp_digit *tmpy; + + /* clear counter */ + _W = 0; + + /* get offsets into the two bignums */ + ty = MIN(a->used-1, ix); + tx = ix - ty; + + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = a->dp + ty; + + /* this is the number of times the loop will iterrate, essentially + while (tx++ < a->used && ty-- >= 0) { ... } + */ + iy = MIN(a->used-tx, ty+1); + + /* now for squaring tx can never equal ty + * we halve the distance since they approach at a rate of 2x + * and we have to round because odd cases need to be executed + */ + iy = MIN(iy, (int)((unsigned)(ty-tx+1)>>1)); + + /* execute loop */ + for (iz = 0; iz < iy; iz++) { + _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); + } + + /* double the inner product and add carry */ + _W = _W + _W + W1; + + /* even columns have the square term in them */ + if ((ix&1) == 0) { + _W += ((mp_word)a->dp[(unsigned)ix>>1])*((mp_word)a->dp[(unsigned)ix>>1]); + } + + /* store it */ + W[ix] = (mp_digit)(_W & MP_MASK); + + /* make next carry */ + W1 = _W >> ((mp_word)DIGIT_BIT); + } + + /* setup dest */ + olduse = b->used; + b->used = a->used+a->used; + + { + mp_digit *tmpb; + tmpb = b->dp; + for (ix = 0; ix < pa; ix++) { + *tmpb++ = W[ix] & MP_MASK; + } + + /* clear unused digits [that existed in the old copy of c] */ + for (; ix < olduse; ix++) { + *tmpb++ = 0; + } + } + trim_unused_digits(b); + return MP_OKAY; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_s_mp_sqr.c,v $ */ @@ -3171,66 +3134,66 @@ static int fast_s_mp_sqr (mp_int * a, mp_int * b) /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */ static int -s_mp_sqr (mp_int * a, mp_int * b) -{ - mp_int t; - int res, ix, iy, pa; - mp_word r; - mp_digit u, tmpx, *tmpt; - - pa = a->used; - if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) { - return res; - } - - /* default used is maximum possible size */ - t.used = 2*pa + 1; - - for (ix = 0; ix < pa; ix++) { - /* first calculate the digit at 2*ix */ - /* calculate double precision result */ - r = ((mp_word) t.dp[2*ix]) + - ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]); - - /* store lower part in result */ - t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK)); - - /* get the carry */ - u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); - - /* left hand side of A[ix] * A[iy] */ - tmpx = a->dp[ix]; - - /* alias for where to store the results */ - tmpt = t.dp + (2*ix + 1); - - for (iy = ix + 1; iy < pa; iy++) { - /* first calculate the product */ - r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]); - - /* now calculate the double precision result, note we use - * addition instead of *2 since it's easier to optimize - */ - r = ((mp_word) *tmpt) + r + r + ((mp_word) u); - - /* store lower part */ - *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); - - /* get carry */ - u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); - } - /* propagate upwards */ - while (u != ((mp_digit) 0)) { - r = ((mp_word) *tmpt) + ((mp_word) u); - *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); - u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); - } - } - - mp_clamp (&t); - mp_exch (&t, b); - mp_clear (&t); - return MP_OKAY; +basic_square(mp_int * a, mp_int * b) +{ + mp_int t; + int res, ix, iy, pa; + mp_word r; + mp_digit carry, tmpx, *tmpt; + + pa = a->used; + if ((res = mp_init_size(&t, 2*pa + 1)) != MP_OKAY) { + return res; + } + + /* default used is maximum possible size */ + t.used = 2*pa + 1; + + for (ix = 0; ix < pa; ix++) { + /* first calculate the digit at 2*ix */ + /* calculate double precision result */ + r = ((mp_word) t.dp[2*ix]) + + ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]); + + /* store lower part in result */ + t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK)); + + /* get the carry */ + carry = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); + + /* left hand side of A[ix] * A[iy] */ + tmpx = a->dp[ix]; + + /* alias for where to store the results */ + tmpt = t.dp + (2*ix + 1); + + for (iy = ix + 1; iy < pa; iy++) { + /* first calculate the product */ + r = ((mp_word)tmpx) * ((mp_word)a->dp[iy]); + + /* now calculate the double precision result, note we use + * addition instead of *2 since it's easier to optimize + */ + r = ((mp_word) *tmpt) + r + r + ((mp_word) carry); + + /* store lower part */ + *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); + + /* get carry */ + carry = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); + } + /* propagate upwards */ + while (carry != ((mp_digit) 0)) { + r = ((mp_word) *tmpt) + ((mp_word) carry); + *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK)); + carry = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); + } + } + + trim_unused_digits(&t); + mp_exch(&t, b); + mp_clear(&t); + return MP_OKAY; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_s_mp_sqr.c,v $ */ @@ -3242,29 +3205,36 @@ s_mp_sqr (mp_int * a, mp_int * b) /* computes b = a*a */ static int -mp_sqr (mp_int * a, mp_int * b) -{ - int res; - - /* use Toom-Cook? */ - if (a->used >= TOOM_SQR_CUTOFF) { - res = mp_toom_sqr(a, b); - /* Karatsuba? */ - } else -if (a->used >= KARATSUBA_SQR_CUTOFF) { - res = mp_karatsuba_sqr (a, b); - } else - { - /* can we use the fast comba multiplier? */ - if (((unsigned)a->used * 2 + 1) < MP_WARRAY && - a->used < - (1 << (unsigned)(sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) { - res = fast_s_mp_sqr (a, b); - } else - res = s_mp_sqr (a, b); - } - b->sign = MP_ZPOS; - return res; +square(mp_int * a, mp_int * b) +{ + int res; + + /* use Toom-Cook? */ + if (a->used >= TOOM_SQR_CUTOFF) { + res = toom_cook_square(a, b); + /* Karatsuba? */ + } else if (a->used >= KARATSUBA_SQR_CUTOFF) { + res = karatsuba_square(a, b); + } else { + /* can we use the fast comba multiplier? */ + if (can_use_fast_column_array(a->used + a->used + 1, a->used)) { + res = fast_basic_square(a, b); + } else { + res = basic_square(a, b); + } + } + b->sign = MP_ZPOS; + return res; +} + +/* find window size */ +static inline int +find_window_size(mp_int *X) +{ + int x; + + x = mp_count_bits(X); + return (x <= 7) ? 2 : (x <= 36) ? 3 : (x <= 140) ? 4 : (x <= 450) ? 5 : (x <= 1303) ? 6 : (x <= 3529) ? 7 : 8; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_sqr.c,v $ */ @@ -3273,246 +3243,233 @@ if (a->used >= KARATSUBA_SQR_CUTOFF) { #define TAB_SIZE 256 -static int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) -{ - mp_int M[TAB_SIZE], res, mu; - mp_digit buf; - int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; - int (*redux)(mp_int*,mp_int*,mp_int*); - - /* find window size */ - x = mp_count_bits (X); - if (x <= 7) { - winsize = 2; - } else if (x <= 36) { - winsize = 3; - } else if (x <= 140) { - winsize = 4; - } else if (x <= 450) { - winsize = 5; - } else if (x <= 1303) { - winsize = 6; - } else if (x <= 3529) { - winsize = 7; - } else { - winsize = 8; - } - - /* init M array */ - /* init first cell */ - if ((err = mp_init(&M[1])) != MP_OKAY) { - return err; - } - - /* now init the second half of the array */ - for (x = 1<<(winsize-1); x < (1 << winsize); x++) { - if ((err = mp_init(&M[x])) != MP_OKAY) { - for (y = 1<<(winsize-1); y < x; y++) { - mp_clear (&M[y]); - } - mp_clear(&M[1]); - return err; - } - } - - /* create mu, used for Barrett reduction */ - if ((err = mp_init (&mu)) != MP_OKAY) { - goto LBL_M; - } - - if (redmode == 0) { - if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) { - goto LBL_MU; - } - redux = mp_reduce; - } else { - if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) { - goto LBL_MU; - } - redux = mp_reduce_2k_l; - } - - /* create M table - * - * The M table contains powers of the base, - * e.g. M[x] = G**x mod P - * - * The first half of the table is not - * computed though accept for M[0] and M[1] - */ - if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) { - goto LBL_MU; - } - - /* compute the value at M[1<<(winsize-1)] by squaring - * M[1] (winsize-1) times - */ - if ((err = mp_copy ( &M[1], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto LBL_MU; - } - - for (x = 0; x < (winsize - 1); x++) { - /* square it */ - if ((err = mp_sqr (&M[1 << (winsize - 1)], - &M[1 << (winsize - 1)])) != MP_OKAY) { - goto LBL_MU; - } - - /* reduce modulo P */ - if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) { - goto LBL_MU; - } - } - - /* create upper table, that is M[x] = M[x-1] * M[1] (mod P) - * for x = (2**(winsize - 1) + 1) to (2**winsize - 1) - */ - for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { - if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) { - goto LBL_MU; - } - if ((err = redux (&M[x], P, &mu)) != MP_OKAY) { - goto LBL_MU; - } - } - - /* setup result */ - if ((err = mp_init (&res)) != MP_OKAY) { - goto LBL_MU; - } - mp_set (&res, 1); - - /* set initial mode and bit cnt */ - mode = 0; - bitcnt = 1; - buf = 0; - digidx = X->used - 1; - bitcpy = 0; - bitbuf = 0; - - for (;;) { - /* grab next digit as required */ - if (--bitcnt == 0) { - /* if digidx == -1 we are out of digits */ - if (digidx == -1) { - break; - } - /* read next digit and reset the bitcnt */ - buf = X->dp[digidx--]; - bitcnt = (int) DIGIT_BIT; - } - - /* grab the next msb from the exponent */ - y = (unsigned)(buf >> (mp_digit)(DIGIT_BIT - 1)) & 1; - buf <<= (mp_digit)1; - - /* if the bit is zero and mode == 0 then we ignore it - * These represent the leading zero bits before the first 1 bit - * in the exponent. Technically this opt is not required but it - * does lower the # of trivial squaring/reductions used - */ - if (mode == 0 && y == 0) { - continue; - } - - /* if the bit is zero and mode == 1 then we square */ - if (mode == 1 && y == 0) { - if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, &mu)) != MP_OKAY) { - goto LBL_RES; - } - continue; - } - - /* else we add it to the window */ - bitbuf |= (y << (winsize - ++bitcpy)); - mode = 2; - - if (bitcpy == winsize) { - /* ok window is filled so square as required and multiply */ - /* square first */ - for (x = 0; x < winsize; x++) { - if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, &mu)) != MP_OKAY) { - goto LBL_RES; - } - } - - /* then multiply */ - if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, &mu)) != MP_OKAY) { - goto LBL_RES; - } - - /* empty window and reset */ - bitcpy = 0; - bitbuf = 0; - mode = 1; - } - } - - /* if bits remain then square/multiply */ - if (mode == 2 && bitcpy > 0) { - /* square then multiply if the bit is set */ - for (x = 0; x < bitcpy; x++) { - if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, &mu)) != MP_OKAY) { - goto LBL_RES; - } - - bitbuf <<= 1; - if ((bitbuf & (1 << winsize)) != 0) { - /* then multiply */ - if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, &mu)) != MP_OKAY) { - goto LBL_RES; - } - } - } - } - - mp_exch (&res, Y); - err = MP_OKAY; -LBL_RES:mp_clear (&res); -LBL_MU:mp_clear (&mu); +static int +basic_exponent_mod(mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) +{ + mp_digit buf; + mp_int M[TAB_SIZE], res, mu; + int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; + int (*redux)(mp_int*,mp_int*,mp_int*); + + winsize = find_window_size(X); + + /* init M array */ + /* init first cell */ + if ((err = mp_init(&M[1])) != MP_OKAY) { + return err; + } + + /* now init the second half of the array */ + for (x = 1<<(winsize-1); x < (1 << winsize); x++) { + if ((err = mp_init(&M[x])) != MP_OKAY) { + for (y = 1<<(winsize-1); y < x; y++) { + mp_clear(&M[y]); + } + mp_clear(&M[1]); + return err; + } + } + + /* create mu, used for Barrett reduction */ + if ((err = mp_init(&mu)) != MP_OKAY) { + goto LBL_M; + } + + if (redmode == 0) { + if ((err = mp_reduce_setup(&mu, P)) != MP_OKAY) { + goto LBL_MU; + } + redux = mp_reduce; + } else { + if ((err = mp_reduce_2k_setup_l(P, &mu)) != MP_OKAY) { + goto LBL_MU; + } + redux = mp_reduce_2k_l; + } + + /* create M table + * + * The M table contains powers of the base, + * e.g. M[x] = G**x mod P + * + * The first half of the table is not + * computed though accept for M[0] and M[1] + */ + if ((err = modulo(G, P, &M[1])) != MP_OKAY) { + goto LBL_MU; + } + + /* compute the value at M[1<<(winsize-1)] by squaring + * M[1] (winsize-1) times + */ + if ((err = mp_copy( &M[1], &M[1 << (winsize - 1)])) != MP_OKAY) { + goto LBL_MU; + } + + for (x = 0; x < (winsize - 1); x++) { + /* square it */ + if ((err = square(&M[1 << (winsize - 1)], + &M[1 << (winsize - 1)])) != MP_OKAY) { + goto LBL_MU; + } + + /* reduce modulo P */ + if ((err = redux(&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) { + goto LBL_MU; + } + } + + /* create upper table, that is M[x] = M[x-1] * M[1] (mod P) + * for x = (2**(winsize - 1) + 1) to (2**winsize - 1) + */ + for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { + if ((err = signed_multiply(&M[x - 1], &M[1], &M[x])) != MP_OKAY) { + goto LBL_MU; + } + if ((err = redux(&M[x], P, &mu)) != MP_OKAY) { + goto LBL_MU; + } + } + + /* setup result */ + if ((err = mp_init(&res)) != MP_OKAY) { + goto LBL_MU; + } + set_word(&res, 1); + + /* set initial mode and bit cnt */ + mode = 0; + bitcnt = 1; + buf = 0; + digidx = X->used - 1; + bitcpy = 0; + bitbuf = 0; + + for (;;) { + /* grab next digit as required */ + if (--bitcnt == 0) { + /* if digidx == -1 we are out of digits */ + if (digidx == -1) { + break; + } + /* read next digit and reset the bitcnt */ + buf = X->dp[digidx--]; + bitcnt = (int) DIGIT_BIT; + } + + /* grab the next msb from the exponent */ + y = (unsigned)(buf >> (mp_digit)(DIGIT_BIT - 1)) & 1; + buf <<= (mp_digit)1; + + /* if the bit is zero and mode == 0 then we ignore it + * These represent the leading zero bits before the first 1 bit + * in the exponent. Technically this opt is not required but it + * does lower the # of trivial squaring/reductions used + */ + if (mode == 0 && y == 0) { + continue; + } + + /* if the bit is zero and mode == 1 then we square */ + if (mode == 1 && y == 0) { + if ((err = square(&res, &res)) != MP_OKAY) { + goto LBL_RES; + } + if ((err = redux(&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; + } + continue; + } + + /* else we add it to the window */ + bitbuf |= (y << (winsize - ++bitcpy)); + mode = 2; + + if (bitcpy == winsize) { + /* ok window is filled so square as required and multiply */ + /* square first */ + for (x = 0; x < winsize; x++) { + if ((err = square(&res, &res)) != MP_OKAY) { + goto LBL_RES; + } + if ((err = redux(&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; + } + } + + /* then multiply */ + if ((err = signed_multiply(&res, &M[bitbuf], &res)) != MP_OKAY) { + goto LBL_RES; + } + if ((err = redux(&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; + } + + /* empty window and reset */ + bitcpy = 0; + bitbuf = 0; + mode = 1; + } + } + + /* if bits remain then square/multiply */ + if (mode == 2 && bitcpy > 0) { + /* square then multiply if the bit is set */ + for (x = 0; x < bitcpy; x++) { + if ((err = square(&res, &res)) != MP_OKAY) { + goto LBL_RES; + } + if ((err = redux(&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; + } + + bitbuf <<= 1; + if ((bitbuf & (1 << winsize)) != 0) { + /* then multiply */ + if ((err = signed_multiply(&res, &M[1], &res)) != MP_OKAY) { + goto LBL_RES; + } + if ((err = redux(&res, P, &mu)) != MP_OKAY) { + goto LBL_RES; + } + } + } + } + + mp_exch(&res, Y); + err = MP_OKAY; +LBL_RES: + mp_clear(&res); +LBL_MU: + mp_clear(&mu); LBL_M: - mp_clear(&M[1]); - for (x = 1<<(winsize-1); x < (1 << winsize); x++) { - mp_clear (&M[x]); - } - return err; + mp_clear(&M[1]); + for (x = 1<<(winsize-1); x < (1 << winsize); x++) { + mp_clear(&M[x]); + } + return err; } /* determines if a number is a valid DR modulus */ static int -mp_dr_is_modulus(mp_int *a) +is_diminished_radix_modulus(mp_int *a) { - int ix; + int ix; - /* must be at least two digits */ - if (a->used < 2) { - return 0; - } + /* must be at least two digits */ + if (a->used < 2) { + return 0; + } - /* must be of the form b**k - a [a <= b] so all - * but the first digit must be equal to -1 (mod b). - */ - for (ix = 1; ix < a->used; ix++) { - if (a->dp[ix] != MP_MASK) { - return 0; - } - } - return 1; + /* must be of the form b**k - a [a <= b] so all + * but the first digit must be equal to -1 (mod b). + */ + for (ix = 1; ix < a->used; ix++) { + if (a->dp[ix] != MP_MASK) { + return 0; + } + } + return 1; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_dr_is_modulus.c,v $ */ @@ -3520,33 +3477,36 @@ mp_dr_is_modulus(mp_int *a) /* Date: 2011/03/12 22:58:18 $ */ /* determines if mp_reduce_2k can be used */ -static int mp_reduce_is_2k(mp_int *a) -{ - int ix, iy, iw; - mp_digit iz; - - if (a->used == 0) { - return MP_NO; - } else if (a->used == 1) { - return MP_YES; - } else if (a->used > 1) { - iy = mp_count_bits(a); - iz = 1; - iw = 1; - - /* Test every bit from the second digit up, must be 1 */ - for (ix = DIGIT_BIT; ix < iy; ix++) { - if ((a->dp[iw] & iz) == 0) { - return MP_NO; - } - iz <<= 1; - if (iz > (mp_digit)MP_MASK) { - ++iw; - iz = 1; - } - } - } - return MP_YES; +static int +mp_reduce_is_2k(mp_int *a) +{ + int ix, iy, iw; + mp_digit iz; + + if (a->used == 0) { + return MP_NO; + } + if (a->used == 1) { + return MP_YES; + } + if (a->used > 1) { + iy = mp_count_bits(a); + iz = 1; + iw = 1; + + /* Test every bit from the second digit up, must be 1 */ + for (ix = DIGIT_BIT; ix < iy; ix++) { + if ((a->dp[iw] & iz) == 0) { + return MP_NO; + } + iz <<= 1; + if (iz > (mp_digit)MP_MASK) { + ++iw; + iz = 1; + } + } + } + return MP_YES; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_is_2k.c,v $ */ @@ -3556,22 +3516,22 @@ static int mp_reduce_is_2k(mp_int *a) /* d = a * b (mod c) */ static int -mp_mulmod (mp_int *d, mp_int * a, mp_int * b, mp_int * c) +multiply_modulo(mp_int *d, mp_int * a, mp_int * b, mp_int * c) { - int res; - mp_int t; + mp_int t; + int res; - if ((res = mp_init (&t)) != MP_OKAY) { - return res; - } + if ((res = mp_init(&t)) != MP_OKAY) { + return res; + } - if ((res = mp_mul (a, b, &t)) != MP_OKAY) { - mp_clear (&t); - return res; - } - res = mp_mod (&t, c, d); - mp_clear (&t); - return res; + if ((res = signed_multiply(a, b, &t)) != MP_OKAY) { + mp_clear(&t); + return res; + } + res = modulo(&t, c, d); + mp_clear(&t); + return res; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_mulmod.c,v $ */ @@ -3580,36 +3540,36 @@ mp_mulmod (mp_int *d, mp_int * a, mp_int * b, mp_int * c) /* setups the montgomery reduction stuff */ static int -mp_montgomery_setup (mp_int * n, mp_digit * rho) +mp_montgomery_setup(mp_int * n, mp_digit * rho) { - mp_digit x, b; + mp_digit x, b; -/* fast inversion mod 2**k - * - * Based on the fact that - * - * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n) - * => 2*X*A - X*X*A*A = 1 - * => 2*(1) - (1) = 1 - */ - b = n->dp[0]; + /* fast inversion mod 2**k + * + * Based on the fact that + * + * XA = 1 (mod 2**n) => (X(2-XA)) A = 1 (mod 2**2n) + * => 2*X*A - X*X*A*A = 1 + * => 2*(1) - (1) = 1 + */ + b = n->dp[0]; - if ((b & 1) == 0) { - return MP_VAL; - } + if ((b & 1) == 0) { + return MP_VAL; + } - x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */ - x *= 2 - b * x; /* here x*a==1 mod 2**8 */ - x *= 2 - b * x; /* here x*a==1 mod 2**16 */ - x *= 2 - b * x; /* here x*a==1 mod 2**32 */ - if (/*CONSTCOND*/sizeof(mp_digit) == 8) { - x *= 2 - b * x; /* here x*a==1 mod 2**64 */ - } + x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */ + x *= 2 - b * x; /* here x*a==1 mod 2**8 */ + x *= 2 - b * x; /* here x*a==1 mod 2**16 */ + x *= 2 - b * x; /* here x*a==1 mod 2**32 */ + if (/*CONSTCOND*/sizeof(mp_digit) == 8) { + x *= 2 - b * x; /* here x*a==1 mod 2**64 */ + } - /* rho = -1/m mod b */ - *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; + /* rho = -1/m mod b */ + *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; - return MP_OKAY; + return MP_OKAY; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_montgomery_setup.c,v $ */ @@ -3625,148 +3585,148 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho) * Based on Algorithm 14.32 on pp.601 of HAC. */ static int -fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) -{ - int ix, res, olduse; - /*LINTED*/ - mp_word W[MP_WARRAY]; - - /* get old used count */ - olduse = x->used; - - /* grow a as required */ - if (x->alloc < n->used + 1) { - if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) { - return res; - } - } - - /* first we have to get the digits of the input into - * an array of double precision words W[...] - */ - { - mp_word *_W; - mp_digit *tmpx; - - /* alias for the W[] array */ - _W = W; - - /* alias for the digits of x*/ - tmpx = x->dp; - - /* copy the digits of a into W[0..a->used-1] */ - for (ix = 0; ix < x->used; ix++) { - *_W++ = *tmpx++; - } - - /* zero the high words of W[a->used..m->used*2] */ - for (; ix < n->used * 2 + 1; ix++) { - *_W++ = 0; - } - } - - /* now we proceed to zero successive digits - * from the least significant upwards - */ - for (ix = 0; ix < n->used; ix++) { - /* mu = ai * m' mod b - * - * We avoid a double precision multiplication (which isn't required) - * by casting the value down to a mp_digit. Note this requires - * that W[ix-1] have the carry cleared (see after the inner loop) - */ - mp_digit mu; - mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK); - - /* a = a + mu * m * b**i - * - * This is computed in place and on the fly. The multiplication - * by b**i is handled by offseting which columns the results - * are added to. - * - * Note the comba method normally doesn't handle carries in the - * inner loop In this case we fix the carry from the previous - * column since the Montgomery reduction requires digits of the - * result (so far) [see above] to work. This is - * handled by fixing up one carry after the inner loop. The - * carry fixups are done in order so after these loops the - * first m->used words of W[] have the carries fixed - */ - { - int iy; - mp_digit *tmpn; - mp_word *_W; - - /* alias for the digits of the modulus */ - tmpn = n->dp; - - /* Alias for the columns set by an offset of ix */ - _W = W + ix; - - /* inner loop */ - for (iy = 0; iy < n->used; iy++) { - *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++); - } - } - - /* now fix carry for next digit, W[ix+1] */ - W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT); - } - - /* now we have to propagate the carries and - * shift the words downward [all those least - * significant digits we zeroed]. - */ - { - mp_digit *tmpx; - mp_word *_W, *_W1; - - /* nox fix rest of carries */ - - /* alias for current word */ - _W1 = W + ix; - - /* alias for next word, where the carry goes */ - _W = W + ++ix; - - for (; ix <= n->used * 2 + 1; ix++) { - *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT); - } - - /* copy out, A = A/b**n - * - * The result is A/b**n but instead of converting from an - * array of mp_word to mp_digit than calling mp_rshd - * we just copy them in the right order - */ - - /* alias for destination word */ - tmpx = x->dp; - - /* alias for shifted double precision result */ - _W = W + n->used; - - for (ix = 0; ix < n->used + 1; ix++) { - *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK)); - } - - /* zero oldused digits, if the input a was larger than - * m->used+1 we'll have to clear the digits - */ - for (; ix < olduse; ix++) { - *tmpx++ = 0; - } - } - - /* set the max used and clamp */ - x->used = n->used + 1; - mp_clamp (x); - - /* if A >= m then A = A - m */ - if (mp_cmp_mag (x, n) != MP_LT) { - return s_mp_sub (x, n, x); - } - return MP_OKAY; +fast_mp_montgomery_reduce(mp_int * x, mp_int * n, mp_digit rho) +{ + int ix, res, olduse; + /*LINTED*/ + mp_word W[MP_WARRAY]; + + /* get old used count */ + olduse = x->used; + + /* grow a as required */ + if (x->alloc < n->used + 1) { + if ((res = mp_grow(x, n->used + 1)) != MP_OKAY) { + return res; + } + } + + /* first we have to get the digits of the input into + * an array of double precision words W[...] + */ + { + mp_word *_W; + mp_digit *tmpx; + + /* alias for the W[] array */ + _W = W; + + /* alias for the digits of x*/ + tmpx = x->dp; + + /* copy the digits of a into W[0..a->used-1] */ + for (ix = 0; ix < x->used; ix++) { + *_W++ = *tmpx++; + } + + /* zero the high words of W[a->used..m->used*2] */ + for (; ix < n->used * 2 + 1; ix++) { + *_W++ = 0; + } + } + + /* now we proceed to zero successive digits + * from the least significant upwards + */ + for (ix = 0; ix < n->used; ix++) { + /* mu = ai * m' mod b + * + * We avoid a double precision multiplication (which isn't required) + * by casting the value down to a mp_digit. Note this requires + * that W[ix-1] have the carry cleared (see after the inner loop) + */ + mp_digit mu; + mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK); + + /* a = a + mu * m * b**i + * + * This is computed in place and on the fly. The multiplication + * by b**i is handled by offseting which columns the results + * are added to. + * + * Note the comba method normally doesn't handle carries in the + * inner loop In this case we fix the carry from the previous + * column since the Montgomery reduction requires digits of the + * result (so far) [see above] to work. This is + * handled by fixing up one carry after the inner loop. The + * carry fixups are done in order so after these loops the + * first m->used words of W[] have the carries fixed + */ + { + int iy; + mp_digit *tmpn; + mp_word *_W; + + /* alias for the digits of the modulus */ + tmpn = n->dp; + + /* Alias for the columns set by an offset of ix */ + _W = W + ix; + + /* inner loop */ + for (iy = 0; iy < n->used; iy++) { + *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++); + } + } + + /* now fix carry for next digit, W[ix+1] */ + W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT); + } + + /* now we have to propagate the carries and + * shift the words downward [all those least + * significant digits we zeroed]. + */ + { + mp_digit *tmpx; + mp_word *_W, *_W1; + + /* nox fix rest of carries */ + + /* alias for current word */ + _W1 = W + ix; + + /* alias for next word, where the carry goes */ + _W = W + ++ix; + + for (; ix <= n->used * 2 + 1; ix++) { + *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT); + } + + /* copy out, A = A/b**n + * + * The result is A/b**n but instead of converting from an + * array of mp_word to mp_digit than calling rshift_digits + * we just copy them in the right order + */ + + /* alias for destination word */ + tmpx = x->dp; + + /* alias for shifted double precision result */ + _W = W + n->used; + + for (ix = 0; ix < n->used + 1; ix++) { + *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK)); + } + + /* zero oldused digits, if the input a was larger than + * m->used+1 we'll have to clear the digits + */ + for (; ix < olduse; ix++) { + *tmpx++ = 0; + } + } + + /* set the max used and clamp */ + x->used = n->used + 1; + trim_unused_digits(x); + + /* if A >= m then A = A - m */ + if (compare_magnitude(x, n) != MP_LT) { + return basic_subtract(x, n, x); + } + return MP_OKAY; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_mp_montgomery_reduce.c,v $ */ @@ -3775,99 +3735,97 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) /* computes xR**-1 == x (mod N) via Montgomery Reduction */ static int -mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) -{ - int ix, res, digs; - mp_digit mu; - - /* can the fast reduction [comba] method be used? - * - * Note that unlike in mul you're safely allowed *less* - * than the available columns [255 per default] since carries - * are fixed up in the inner loop. - */ - digs = n->used * 2 + 1; - if (((unsigned)digs < MP_WARRAY) && - n->used < - (1 << (unsigned)((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { - return fast_mp_montgomery_reduce (x, n, rho); - } - - /* grow the input as required */ - if (x->alloc < digs) { - if ((res = mp_grow (x, digs)) != MP_OKAY) { - return res; - } - } - x->used = digs; - - for (ix = 0; ix < n->used; ix++) { - /* mu = ai * rho mod b - * - * The value of rho must be precalculated via - * montgomery_setup() such that - * it equals -1/n0 mod b this allows the - * following inner loop to reduce the - * input one digit at a time - */ - mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK); - - /* a = a + mu * m * b**i */ - { - int iy; - mp_digit *tmpn, *tmpx, u; - mp_word r; - - /* alias for digits of the modulus */ - tmpn = n->dp; - - /* alias for the digits of x [the input] */ - tmpx = x->dp + ix; - - /* set the carry to zero */ - u = 0; - - /* Multiply and add in place */ - for (iy = 0; iy < n->used; iy++) { - /* compute product and sum */ - r = ((mp_word)mu) * ((mp_word)*tmpn++) + - ((mp_word) u) + ((mp_word) * tmpx); - - /* get carry */ - u = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); - - /* fix digit */ - *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK)); - } - /* At this point the ix'th digit of x should be zero */ - - - /* propagate carries upwards as required*/ - while (u) { - *tmpx += u; - u = *tmpx >> DIGIT_BIT; - *tmpx++ &= MP_MASK; - } - } - } - - /* at this point the n.used'th least - * significant digits of x are all zero - * which means we can shift x to the - * right by n.used digits and the - * residue is unchanged. - */ - - /* x = x/b**n.used */ - mp_clamp(x); - mp_rshd (x, n->used); - - /* if x >= n then x = x - n */ - if (mp_cmp_mag (x, n) != MP_LT) { - return s_mp_sub (x, n, x); - } - - return MP_OKAY; +mp_montgomery_reduce(mp_int * x, mp_int * n, mp_digit rho) +{ + int ix, res, digs; + mp_digit mu; + + /* can the fast reduction [comba] method be used? + * + * Note that unlike in mul you're safely allowed *less* + * than the available columns [255 per default] since carries + * are fixed up in the inner loop. + */ + digs = n->used * 2 + 1; + if (can_use_fast_column_array(digs, n->used)) { + return fast_mp_montgomery_reduce(x, n, rho); + } + + /* grow the input as required */ + if (x->alloc < digs) { + if ((res = mp_grow(x, digs)) != MP_OKAY) { + return res; + } + } + x->used = digs; + + for (ix = 0; ix < n->used; ix++) { + /* mu = ai * rho mod b + * + * The value of rho must be precalculated via + * montgomery_setup() such that + * it equals -1/n0 mod b this allows the + * following inner loop to reduce the + * input one digit at a time + */ + mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK); + + /* a = a + mu * m * b**i */ + { + int iy; + mp_digit *tmpn, *tmpx, carry; + mp_word r; + + /* alias for digits of the modulus */ + tmpn = n->dp; + + /* alias for the digits of x [the input] */ + tmpx = x->dp + ix; + + /* set the carry to zero */ + carry = 0; + + /* Multiply and add in place */ + for (iy = 0; iy < n->used; iy++) { + /* compute product and sum */ + r = ((mp_word)mu) * ((mp_word)*tmpn++) + + ((mp_word) carry) + ((mp_word) * tmpx); + + /* get carry */ + carry = (mp_digit)(r >> ((mp_word) DIGIT_BIT)); + + /* fix digit */ + *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK)); + } + /* At this point the ix'th digit of x should be zero */ + + + /* propagate carries upwards as required*/ + while (carry) { + *tmpx += carry; + carry = *tmpx >> DIGIT_BIT; + *tmpx++ &= MP_MASK; + } + } + } + + /* at this point the n.used'th least + * significant digits of x are all zero + * which means we can shift x to the + * right by n.used digits and the + * residue is unchanged. + */ + + /* x = x/b**n.used */ + trim_unused_digits(x); + rshift_digits(x, n->used); + + /* if x >= n then x = x - n */ + if (compare_magnitude(x, n) != MP_LT) { + return basic_subtract(x, n, x); + } + + return MP_OKAY; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_montgomery_reduce.c,v $ */ @@ -3876,13 +3834,13 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho) /* determines the setup value */ static void -mp_dr_setup(mp_int *a, mp_digit *d) +diminished_radix_setup(mp_int *a, mp_digit *d) { - /* the casts are required if DIGIT_BIT is one less than - * the number of bits in a mp_digit [e.g. DIGIT_BIT==31] - */ - *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - - ((mp_word)a->dp[0])); + /* the casts are required if DIGIT_BIT is one less than + * the number of bits in a mp_digit [e.g. DIGIT_BIT==31] + */ + *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - + ((mp_word)a->dp[0])); } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_dr_setup.c,v $ */ @@ -3904,62 +3862,62 @@ mp_dr_setup(mp_int *a, mp_digit *d) * Input x must be in the range 0 <= x <= (n-1)**2 */ static int -mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k) +diminished_radix_reduce(mp_int * x, mp_int * n, mp_digit k) { - int err, i, m; - mp_word r; - mp_digit mu, *tmpx1, *tmpx2; + int err, i, m; + mp_word r; + mp_digit mu, *tmpx1, *tmpx2; - /* m = digits in modulus */ - m = n->used; + /* m = digits in modulus */ + m = n->used; - /* ensure that "x" has at least 2m digits */ - if (x->alloc < m + m) { - if ((err = mp_grow (x, m + m)) != MP_OKAY) { - return err; - } - } + /* ensure that "x" has at least 2m digits */ + if (x->alloc < m + m) { + if ((err = mp_grow(x, m + m)) != MP_OKAY) { + return err; + } + } -/* top of loop, this is where the code resumes if - * another reduction pass is required. - */ + /* top of loop, this is where the code resumes if + * another reduction pass is required. + */ top: - /* aliases for digits */ - /* alias for lower half of x */ - tmpx1 = x->dp; + /* aliases for digits */ + /* alias for lower half of x */ + tmpx1 = x->dp; - /* alias for upper half of x, or x/B**m */ - tmpx2 = x->dp + m; + /* alias for upper half of x, or x/B**m */ + tmpx2 = x->dp + m; - /* set carry to zero */ - mu = 0; + /* set carry to zero */ + mu = 0; - /* compute (x mod B**m) + k * [x/B**m] inline and inplace */ - for (i = 0; i < m; i++) { - r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu; - *tmpx1++ = (mp_digit)(r & MP_MASK); - mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT)); - } + /* compute (x mod B**m) + k * [x/B**m] inline and inplace */ + for (i = 0; i < m; i++) { + r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu; + *tmpx1++ = (mp_digit)(r & MP_MASK); + mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT)); + } - /* set final carry */ - *tmpx1++ = mu; + /* set final carry */ + *tmpx1++ = mu; - /* zero words above m */ - for (i = m + 1; i < x->used; i++) { - *tmpx1++ = 0; - } + /* zero words above m */ + for (i = m + 1; i < x->used; i++) { + *tmpx1++ = 0; + } - /* clamp, sub and return */ - mp_clamp (x); + /* clamp, sub and return */ + trim_unused_digits(x); - /* if x >= n then subtract and reduce again - * Each successive "recursion" makes the input smaller and smaller. - */ - if (mp_cmp_mag (x, n) != MP_LT) { - s_mp_sub(x, n, x); - goto top; - } - return MP_OKAY; + /* if x >= n then subtract and reduce again + * Each successive "recursion" makes the input smaller and smaller. + */ + if (compare_magnitude(x, n) != MP_LT) { + basic_subtract(x, n, x); + goto top; + } + return MP_OKAY; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_dr_reduce.c,v $ */ @@ -3970,27 +3928,27 @@ top: static int mp_reduce_2k_setup(mp_int *a, mp_digit *d) { - int res, p; - mp_int tmp; - - if ((res = mp_init(&tmp)) != MP_OKAY) { - return res; - } - - p = mp_count_bits(a); - if ((res = mp_2expt(&tmp, p)) != MP_OKAY) { - mp_clear(&tmp); - return res; - } - - if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) { - mp_clear(&tmp); - return res; - } - - *d = tmp.dp[0]; - mp_clear(&tmp); - return MP_OKAY; + int res, p; + mp_int tmp; + + if ((res = mp_init(&tmp)) != MP_OKAY) { + return res; + } + + p = mp_count_bits(a); + if ((res = mp_2expt(&tmp, p)) != MP_OKAY) { + mp_clear(&tmp); + return res; + } + + if ((res = basic_subtract(&tmp, a, &tmp)) != MP_OKAY) { + mp_clear(&tmp); + return res; + } + + *d = tmp.dp[0]; + mp_clear(&tmp); + return MP_OKAY; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_2k_setup.c,v $ */ @@ -4001,353 +3959,336 @@ mp_reduce_2k_setup(mp_int *a, mp_digit *d) static int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d) { - mp_int q; - int p, res; - - if ((res = mp_init(&q)) != MP_OKAY) { - return res; - } - - p = mp_count_bits(n); + mp_int q; + int p, res; + + if ((res = mp_init(&q)) != MP_OKAY) { + return res; + } + + p = mp_count_bits(n); top: - /* q = a/2**p, a = a mod 2**p */ - if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) { - goto ERR; - } - - if (d != 1) { - /* q = q * d */ - if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) { - goto ERR; - } - } - - /* a = a + q */ - if ((res = s_mp_add(a, &q, a)) != MP_OKAY) { - goto ERR; - } - - if (mp_cmp_mag(a, n) != MP_LT) { - s_mp_sub(a, n, a); - goto top; - } - + /* q = a/2**p, a = a mod 2**p */ + if ((res = rshift_bits(a, p, &q, a)) != MP_OKAY) { + goto ERR; + } + + if (d != 1) { + /* q = q * d */ + if ((res = multiply_digit(&q, d, &q)) != MP_OKAY) { + goto ERR; + } + } + + /* a = a + q */ + if ((res = basic_add(a, &q, a)) != MP_OKAY) { + goto ERR; + } + + if (compare_magnitude(a, n) != MP_LT) { + basic_subtract(a, n, a); + goto top; + } + ERR: - mp_clear(&q); - return res; + mp_clear(&q); + return res; } /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_2k.c,v $ */ /* Revision: 1.1.1.1 $ */ /* Date: 2011/03/12 22:58:18 $ */ -/* - * shifts with subtractions when the result is greater than b. - * - * The method is slightly modified to shift B unconditionally upto just under - * the leading bit of b. This saves alot of multiple precision shifting. - */ -static int -mp_montgomery_calc_normalization (mp_int * a, mp_int * b) -{ - int x, bits, res; +/* + * shifts with subtractions when the result is greater than b. + * + * The method is slightly modified to shift B unconditionally upto just under + * the leading bit of b. This saves alot of multiple precision shifting. + */ +static int +mp_montgomery_calc_normalization(mp_int * a, mp_int * b) +{ + int x, bits, res; + + /* how many bits of last digit does b use */ + bits = mp_count_bits(b) % DIGIT_BIT; + + if (b->used > 1) { + if ((res = mp_2expt(a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { + return res; + } + } else { + set_word(a, 1); + bits = 1; + } + + + /* now compute C = A * B mod b */ + for (x = bits - 1; x < (int)DIGIT_BIT; x++) { + if ((res = doubled(a, a)) != MP_OKAY) { + return res; + } + if (compare_magnitude(a, b) != MP_LT) { + if ((res = basic_subtract(a, b, a)) != MP_OKAY) { + return res; + } + } + } + + return MP_OKAY; +} + +/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_montgomery_calc_normalization.c,v $ */ +/* Revision: 1.1.1.1 $ */ +/* Date: 2011/03/12 22:58:18 $ */ + +/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85 + * + * Uses a left-to-right k-ary sliding window to compute the modular exponentiation. + * The value of k changes based on the size of the exponent. + * + * Uses Montgomery or Diminished Radix reduction [whichever appropriate] + */ + +#define TAB_SIZE 256 + +static int +fast_exponent_modulo(mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) +{ + mp_int M[TAB_SIZE], res; + mp_digit buf, mp; + int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; + + /* use a pointer to the reduction algorithm. This allows us to use + * one of many reduction algorithms without modding the guts of + * the code with if statements everywhere. + */ + int (*redux)(mp_int*,mp_int*,mp_digit); + + winsize = find_window_size(X); + + /* init M array */ + /* init first cell */ + if ((err = mp_init(&M[1])) != MP_OKAY) { + return err; + } + + /* now init the second half of the array */ + for (x = 1<<(winsize-1); x < (1 << winsize); x++) { + if ((err = mp_init(&M[x])) != MP_OKAY) { + for (y = 1<<(winsize-1); y < x; y++) { + mp_clear(&M[y]); + } + mp_clear(&M[1]); + return err; + } + } + + /* determine and setup reduction code */ + if (redmode == 0) { + /* now setup montgomery */ + if ((err = mp_montgomery_setup(P, &mp)) != MP_OKAY) { + goto LBL_M; + } + + /* automatically pick the comba one if available (saves quite a few calls/ifs) */ + if (can_use_fast_column_array(P->used + P->used + 1, P->used)) { + redux = fast_mp_montgomery_reduce; + } else { + /* use slower baseline Montgomery method */ + redux = mp_montgomery_reduce; + } + } else if (redmode == 1) { + /* setup DR reduction for moduli of the form B**k - b */ + diminished_radix_setup(P, &mp); + redux = diminished_radix_reduce; + } else { + /* setup DR reduction for moduli of the form 2**k - b */ + if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) { + goto LBL_M; + } + redux = mp_reduce_2k; + } + + /* setup result */ + if ((err = mp_init(&res)) != MP_OKAY) { + goto LBL_M; + } + + /* create M table + * + + * + * The first half of the table is not computed though accept for M[0] and M[1] + */ + + if (redmode == 0) { + /* now we need R mod m */ + if ((err = mp_montgomery_calc_normalization(&res, P)) != MP_OKAY) { + goto LBL_RES; + } + + /* now set M[1] to G * R mod m */ + if ((err = multiply_modulo(&M[1], G, &res, P)) != MP_OKAY) { + goto LBL_RES; + } + } else { + set_word(&res, 1); + if ((err = modulo(G, P, &M[1])) != MP_OKAY) { + goto LBL_RES; + } + } - /* how many bits of last digit does b use */ - bits = mp_count_bits (b) % DIGIT_BIT; + /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */ + if ((err = mp_copy( &M[1], &M[1 << (winsize - 1)])) != MP_OKAY) { + goto LBL_RES; + } - if (b->used > 1) { - if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { - return res; - } - } else { - mp_set(a, 1); - bits = 1; - } + for (x = 0; x < (winsize - 1); x++) { + if ((err = square(&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) { + goto LBL_RES; + } + if ((err = (*redux)(&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) { + goto LBL_RES; + } + } + /* create upper table */ + for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { + if ((err = signed_multiply(&M[x - 1], &M[1], &M[x])) != MP_OKAY) { + goto LBL_RES; + } + if ((err = (*redux)(&M[x], P, mp)) != MP_OKAY) { + goto LBL_RES; + } + } - /* now compute C = A * B mod b */ - for (x = bits - 1; x < (int)DIGIT_BIT; x++) { - if ((res = mp_mul_2 (a, a)) != MP_OKAY) { - return res; - } - if (mp_cmp_mag (a, b) != MP_LT) { - if ((res = s_mp_sub (a, b, a)) != MP_OKAY) { - return res; - } - } - } + /* set initial mode and bit cnt */ + mode = 0; + bitcnt = 1; + buf = 0; + digidx = X->used - 1; + bitcpy = 0; + bitbuf = 0; + + for (;;) { + /* grab next digit as required */ + if (--bitcnt == 0) { + /* if digidx == -1 we are out of digits so break */ + if (digidx == -1) { + break; + } + /* read next digit and reset bitcnt */ + buf = X->dp[digidx--]; + bitcnt = (int)DIGIT_BIT; + } - return MP_OKAY; -} + /* grab the next msb from the exponent */ + y = (int)(mp_digit)((mp_digit)buf >> (unsigned)(DIGIT_BIT - 1)) & 1; + buf <<= (mp_digit)1; + + /* if the bit is zero and mode == 0 then we ignore it + * These represent the leading zero bits before the first 1 bit + * in the exponent. Technically this opt is not required but it + * does lower the # of trivial squaring/reductions used + */ + if (mode == 0 && y == 0) { + continue; + } -/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_montgomery_calc_normalization.c,v $ */ -/* Revision: 1.1.1.1 $ */ -/* Date: 2011/03/12 22:58:18 $ */ + /* if the bit is zero and mode == 1 then we square */ + if (mode == 1 && y == 0) { + if ((err = square(&res, &res)) != MP_OKAY) { + goto LBL_RES; + } + if ((err = (*redux)(&res, P, mp)) != MP_OKAY) { + goto LBL_RES; + } + continue; + } -/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85 - * - * Uses a left-to-right k-ary sliding window to compute the modular exponentiation. - * The value of k changes based on the size of the exponent. - * - * Uses Montgomery or Diminished Radix reduction [whichever appropriate] - */ + /* else we add it to the window */ + bitbuf |= (y << (winsize - ++bitcpy)); + mode = 2; + + if (bitcpy == winsize) { + /* ok window is filled so square as required and multiply */ + /* square first */ + for (x = 0; x < winsize; x++) { + if ((err = square(&res, &res)) != MP_OKAY) { + goto LBL_RES; + } + if ((err = (*redux)(&res, P, mp)) != MP_OKAY) { + goto LBL_RES; + } + } + + /* then multiply */ + if ((err = signed_multiply(&res, &M[bitbuf], &res)) != MP_OKAY) { + goto LBL_RES; + } + if ((err = (*redux)(&res, P, mp)) != MP_OKAY) { + goto LBL_RES; + } + + /* empty window and reset */ + bitcpy = 0; + bitbuf = 0; + mode = 1; + } + } -#define TAB_SIZE 256 + /* if bits remain then square/multiply */ + if (mode == 2 && bitcpy > 0) { + /* square then multiply if the bit is set */ + for (x = 0; x < bitcpy; x++) { + if ((err = square(&res, &res)) != MP_OKAY) { + goto LBL_RES; + } + if ((err = (*redux)(&res, P, mp)) != MP_OKAY) { + goto LBL_RES; + } + + /* get next bit of the window */ + bitbuf <<= 1; + if ((bitbuf & (1 << winsize)) != 0) { + /* then multiply */ + if ((err = signed_multiply(&res, &M[1], &res)) != MP_OKAY) { + goto LBL_RES; + } + if ((err = (*redux)(&res, P, mp)) != MP_OKAY) { + goto LBL_RES; + } + } + } + } -static int -mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode) -{ - mp_int M[TAB_SIZE], res; - mp_digit buf, mp; - int err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize; - - /* use a pointer to the reduction algorithm. This allows us to use - * one of many reduction algorithms without modding the guts of - * the code with if statements everywhere. - */ - int (*redux)(mp_int*,mp_int*,mp_digit); - - /* find window size */ - x = mp_count_bits (X); - if (x <= 7) { - winsize = 2; - } else if (x <= 36) { - winsize = 3; - } else if (x <= 140) { - winsize = 4; - } else if (x <= 450) { - winsize = 5; - } else if (x <= 1303) { - winsize = 6; - } else if (x <= 3529) { - winsize = 7; - } else { - winsize = 8; - } - - /* init M array */ - /* init first cell */ - if ((err = mp_init(&M[1])) != MP_OKAY) { - return err; - } - - /* now init the second half of the array */ - for (x = 1<<(winsize-1); x < (1 << winsize); x++) { - if ((err = mp_init(&M[x])) != MP_OKAY) { - for (y = 1<<(winsize-1); y < x; y++) { - mp_clear (&M[y]); - } - mp_clear(&M[1]); - return err; - } - } - - /* determine and setup reduction code */ - if (redmode == 0) { - /* now setup montgomery */ - if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) { - goto LBL_M; - } - - /* automatically pick the comba one if available (saves quite a few calls/ifs) */ - if (((unsigned)(P->used * 2 + 1) < MP_WARRAY) && - P->used < (1 << (unsigned)((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { - redux = fast_mp_montgomery_reduce; - } else - { - /* use slower baseline Montgomery method */ - redux = mp_montgomery_reduce; - } - } else if (redmode == 1) { - /* setup DR reduction for moduli of the form B**k - b */ - mp_dr_setup(P, &mp); - redux = mp_dr_reduce; - } else { - /* setup DR reduction for moduli of the form 2**k - b */ - if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) { - goto LBL_M; - } - redux = mp_reduce_2k; - } - - /* setup result */ - if ((err = mp_init (&res)) != MP_OKAY) { - goto LBL_M; - } - - /* create M table - * - - * - * The first half of the table is not computed though accept for M[0] and M[1] - */ - - if (redmode == 0) { - /* now we need R mod m */ - if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) { - goto LBL_RES; - } - - /* now set M[1] to G * R mod m */ - if ((err = mp_mulmod (&M[1], G, &res, P)) != MP_OKAY) { - goto LBL_RES; - } - } else { - mp_set(&res, 1); - if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) { - goto LBL_RES; - } - } - - /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */ - if ((err = mp_copy ( &M[1], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto LBL_RES; - } - - for (x = 0; x < (winsize - 1); x++) { - if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) { - goto LBL_RES; - } - } - - /* create upper table */ - for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) { - if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&M[x], P, mp)) != MP_OKAY) { - goto LBL_RES; - } - } - - /* set initial mode and bit cnt */ - mode = 0; - bitcnt = 1; - buf = 0; - digidx = X->used - 1; - bitcpy = 0; - bitbuf = 0; - - for (;;) { - /* grab next digit as required */ - if (--bitcnt == 0) { - /* if digidx == -1 we are out of digits so break */ - if (digidx == -1) { - break; - } - /* read next digit and reset bitcnt */ - buf = X->dp[digidx--]; - bitcnt = (int)DIGIT_BIT; - } - - /* grab the next msb from the exponent */ - y = (int)(mp_digit)((mp_digit)buf >> (unsigned)(DIGIT_BIT - 1)) & 1; - buf <<= (mp_digit)1; - - /* if the bit is zero and mode == 0 then we ignore it - * These represent the leading zero bits before the first 1 bit - * in the exponent. Technically this opt is not required but it - * does lower the # of trivial squaring/reductions used - */ - if (mode == 0 && y == 0) { - continue; - } - - /* if the bit is zero and mode == 1 then we square */ - if (mode == 1 && y == 0) { - if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - continue; - } - - /* else we add it to the window */ - bitbuf |= (y << (winsize - ++bitcpy)); - mode = 2; - - if (bitcpy == winsize) { - /* ok window is filled so square as required and multiply */ - /* square first */ - for (x = 0; x < winsize; x++) { - if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - } - - /* then multiply */ - if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - - /* empty window and reset */ - bitcpy = 0; - bitbuf = 0; - mode = 1; - } - } - - /* if bits remain then square/multiply */ - if (mode == 2 && bitcpy > 0) { - /* square then multiply if the bit is set */ - for (x = 0; x < bitcpy; x++) { - if ((err = mp_sqr (&res, &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - - /* get next bit of the window */ - bitbuf <<= 1; - if ((bitbuf & (1 << winsize)) != 0) { - /* then multiply */ - if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) { - goto LBL_RES; - } - if ((err = redux (&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - } - } - } - - if (redmode == 0) { - /* fixup result if Montgomery reduction is used - * recall that any value in a Montgomery system is - * actually multiplied by R mod n. So we have - * to reduce one more time to cancel out the factor - * of R. - */ - if ((err = redux(&res, P, mp)) != MP_OKAY) { - goto LBL_RES; - } - } - - /* swap res with Y */ - mp_exch (&res, Y); - err = MP_OKAY; -LBL_RES:mp_clear (&res); + if (redmode == 0) { + /* fixup result if Montgomery reduction is used + * recall that any value in a Montgomery system is + * actually multiplied by R mod n. So we have + * to reduce one more time to cancel out the factor + * of R. + */ + if ((err = (*redux)(&res, P, mp)) != MP_OKAY) { + goto LBL_RES; + } + } + + /* swap res with Y */ + mp_exch(&res, Y); + err = MP_OKAY; +LBL_RES: + mp_clear(&res); LBL_M: - mp_clear(&M[1]); - for (x = 1<<(winsize-1); x < (1 << winsize); x++) { - mp_clear (&M[x]); - } - return err; + mp_clear(&M[1]); + for (x = 1<<(winsize-1); x < (1 << winsize); x++) { + mp_clear(&M[x]); + } + return err; } -/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_exptmod_fast.c,v $ */ +/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_exponent_modulo.c,v $ */ /* Revision: 1.4 $ */ /* Date: 2011/03/18 16:43:04 $ */ @@ -4357,541 +4298,533 @@ LBL_M: * for nothing (since 99% of the time the Montgomery code would be called) */ static int -mp_exptmod(mp_int * G, mp_int * X, mp_int * P, mp_int *Y) -{ - int dr; - - /* modulus P must be positive */ - if (P->sign == MP_NEG) { - return MP_VAL; - } - - /* if exponent X is negative we have to recurse */ - if (X->sign == MP_NEG) { - mp_int tmpG, tmpX; - int err; - - /* first compute 1/G mod P */ - if ((err = mp_init(&tmpG)) != MP_OKAY) { - return err; - } - if ((err = mp_invmod(&tmpG, G, P)) != MP_OKAY) { - mp_clear(&tmpG); - return err; - } - - /* now get |X| */ - if ((err = mp_init(&tmpX)) != MP_OKAY) { - mp_clear(&tmpG); - return err; - } - if ((err = mp_abs(X, &tmpX)) != MP_OKAY) { - mp_clear_multi(&tmpG, &tmpX, NULL); - return err; - } - - /* and now compute (1/G)**|X| instead of G**X [X < 0] */ - err = mp_exptmod(&tmpG, &tmpX, P, Y); - mp_clear_multi(&tmpG, &tmpX, NULL); - return err; - } - -/* modified diminished radix reduction */ - if (mp_reduce_is_2k_l(P) == MP_YES) { - return s_mp_exptmod(G, X, P, Y, 1); - } - - /* is it a DR modulus? */ - dr = mp_dr_is_modulus(P); - - /* if not, is it a unrestricted DR modulus? */ - if (dr == 0) { - dr = mp_reduce_is_2k(P) << 1; - } - - /* if the modulus is odd or dr != 0 use the montgomery method */ - if (BN_is_odd (P) == 1 || dr != 0) { - return mp_exptmod_fast (G, X, P, Y, dr); - } else { - /* otherwise use the generic Barrett reduction technique */ - return s_mp_exptmod (G, X, P, Y, 0); - } +exponent_modulo(mp_int * G, mp_int * X, mp_int * P, mp_int *Y) +{ + int diminished_radix; + + /* modulus P must be positive */ + if (P->sign == MP_NEG) { + return MP_VAL; + } + + /* if exponent X is negative we have to recurse */ + if (X->sign == MP_NEG) { + mp_int tmpG, tmpX; + int err; + + /* first compute 1/G mod P */ + if ((err = mp_init(&tmpG)) != MP_OKAY) { + return err; + } + if ((err = modular_inverse(&tmpG, G, P)) != MP_OKAY) { + mp_clear(&tmpG); + return err; + } + + /* now get |X| */ + if ((err = mp_init(&tmpX)) != MP_OKAY) { + mp_clear(&tmpG); + return err; + } + if ((err = absolute(X, &tmpX)) != MP_OKAY) { + mp_clear_multi(&tmpG, &tmpX, NULL); + return err; + } + + /* and now compute (1/G)**|X| instead of G**X [X < 0] */ + err = exponent_modulo(&tmpG, &tmpX, P, Y); + mp_clear_multi(&tmpG, &tmpX, NULL); + return err; + } + + /* modified diminished radix reduction */ + if (mp_reduce_is_2k_l(P) == MP_YES) { + return basic_exponent_mod(G, X, P, Y, 1); + } + + /* is it a DR modulus? */ + diminished_radix = is_diminished_radix_modulus(P); + + /* if not, is it a unrestricted DR modulus? */ + if (!diminished_radix) { + diminished_radix = mp_reduce_is_2k(P) << 1; + } + + /* if the modulus is odd or diminished_radix, use the montgomery method */ + if (BN_is_odd(P) == 1 || diminished_radix) { + return fast_exponent_modulo(G, X, P, Y, diminished_radix); + } + /* otherwise use the generic Barrett reduction technique */ + return basic_exponent_mod(G, X, P, Y, 0); } /* reverse an array, used for radix code */ static void bn_reverse(unsigned char *s, int len) { - int ix, iy; - unsigned char t; + int ix, iy; + uint8_t t; - ix = 0; - iy = len - 1; - while (ix < iy) { - t = s[ix]; - s[ix] = s[iy]; - s[iy] = t; - ++ix; - --iy; - } + for (ix = 0, iy = len - 1; ix < iy ; ix++, --iy) { + t = s[ix]; + s[ix] = s[iy]; + s[iy] = t; + } } -static int -s_is_power_of_two(mp_digit b, int *p) +static inline int +is_power_of_two(mp_digit b, int *p) { - int x; + int x; - /* fast return if no power of two */ - if ((b==0) || (b & (b-1))) { - return 0; - } + /* fast return if no power of two */ + if ((b==0) || (b & (b-1))) { + return 0; + } - for (x = 0; x < DIGIT_BIT; x++) { - if (b == (((mp_digit)1)<dp[0] & ((((mp_digit)1)<used)) != MP_OKAY) { - return res; - } - - q.used = a->used; - q.sign = a->sign; - w = 0; - for (ix = a->used - 1; ix >= 0; ix--) { - w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]); - - if (w >= b) { - t = (mp_digit)(w / b); - w -= ((mp_word)t) * ((mp_word)b); - } else { - t = 0; - } - q.dp[ix] = (mp_digit)t; - } - - if (d != NULL) { - *d = (mp_digit)w; - } - - if (c != NULL) { - mp_clamp(&q); - mp_exch(&q, c); - } - mp_clear(&q); - - return res; -} + /* cannot divide by zero */ + if (b == 0) { + return MP_VAL; + } -static int -mp_mod_d(mp_int *a, mp_digit b, mp_digit *c) -{ - return mp_div_d(a, b, NULL, c); + /* quick outs */ + if (b == 1 || MP_ISZERO(a) == 1) { + if (d != NULL) { + *d = 0; + } + if (c != NULL) { + return mp_copy(a, c); + } + return MP_OKAY; + } + + /* power of two ? */ + if (is_power_of_two(b, &ix) == 1) { + if (d != NULL) { + *d = a->dp[0] & ((((mp_digit)1)<used)) != MP_OKAY) { + return res; + } + + q.used = a->used; + q.sign = a->sign; + w = 0; + for (ix = a->used - 1; ix >= 0; ix--) { + w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]); + + if (w >= b) { + t = (mp_digit)(w / b); + w -= ((mp_word)t) * ((mp_word)b); + } else { + t = 0; + } + q.dp[ix] = (mp_digit)t; + } + + if (d != NULL) { + *d = (mp_digit)w; + } + + if (c != NULL) { + trim_unused_digits(&q); + mp_exch(&q, c); + } + mp_clear(&q); + + return res; } static const mp_digit ltm_prime_tab[] = { - 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, - 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, - 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059, - 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, + 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, + 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, + 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059, + 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, #ifndef MP_8BIT - 0x0083, - 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD, - 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF, - 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107, - 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137, - - 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167, - 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199, - 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9, - 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7, - 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239, - 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265, - 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293, - 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF, - - 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301, - 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B, - 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371, - 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD, - 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5, - 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419, - 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449, - 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B, - - 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7, - 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503, - 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529, - 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F, - 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3, - 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7, - 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623, - 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 + 0x0083, + 0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD, + 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF, + 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107, + 0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137, + + 0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167, + 0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199, + 0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9, + 0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7, + 0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239, + 0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265, + 0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293, + 0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF, + + 0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301, + 0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B, + 0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371, + 0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD, + 0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5, + 0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419, + 0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449, + 0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B, + + 0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7, + 0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503, + 0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529, + 0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F, + 0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3, + 0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7, + 0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623, + 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 #endif }; #define PRIME_SIZE __arraycount(ltm_prime_tab) -static int +static inline int mp_prime_is_divisible(mp_int *a, int *result) { - int err, ix; - mp_digit res; + int err, ix; + mp_digit res; - /* default to not */ - *result = MP_NO; + /* default to not */ + *result = MP_NO; - for (ix = 0; ix < (int)PRIME_SIZE; ix++) { - /* what is a mod LBL_prime_tab[ix] */ - if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) { - return err; - } + for (ix = 0; ix < (int)PRIME_SIZE; ix++) { + /* what is a mod LBL_prime_tab[ix] */ + if ((err = signed_divide_word(a, ltm_prime_tab[ix], NULL, &res)) != MP_OKAY) { + return err; + } - /* is the residue zero? */ - if (res == 0) { - *result = MP_YES; - return MP_OKAY; - } - } + /* is the residue zero? */ + if (res == 0) { + *result = MP_YES; + return MP_OKAY; + } + } - return MP_OKAY; + return MP_OKAY; } /* single digit addition */ static int -mp_add_d(mp_int *a, mp_digit b, mp_int *c) -{ - int res, ix, oldused; - mp_digit *tmpa, *tmpc, mu; - - /* grow c as required */ - if (c->alloc < a->used + 1) { - if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) { - return res; - } - } - - /* if a is negative and |a| >= b, call c = |a| - b */ - if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) { - /* temporarily fix sign of a */ - a->sign = MP_ZPOS; - - /* c = |a| - b */ - res = mp_sub_d(a, b, c); - - /* fix sign */ - a->sign = c->sign = MP_NEG; - - /* clamp */ - mp_clamp(c); - - return res; - } - - /* old number of used digits in c */ - oldused = c->used; - - /* sign always positive */ - c->sign = MP_ZPOS; - - /* source alias */ - tmpa = a->dp; - - /* destination alias */ - tmpc = c->dp; - - /* if a is positive */ - if (a->sign == MP_ZPOS) { - /* add digit, after this we're propagating - * the carry. - */ - *tmpc = *tmpa++ + b; - mu = *tmpc >> DIGIT_BIT; - *tmpc++ &= MP_MASK; - - /* now handle rest of the digits */ - for (ix = 1; ix < a->used; ix++) { - *tmpc = *tmpa++ + mu; - mu = *tmpc >> DIGIT_BIT; - *tmpc++ &= MP_MASK; - } - /* set final carry */ - ix++; - *tmpc++ = mu; - - /* setup size */ - c->used = a->used + 1; - } else { - /* a was negative and |a| < b */ - c->used = 1; - - /* the result is a single digit */ - if (a->used == 1) { - *tmpc++ = b - a->dp[0]; - } else { - *tmpc++ = b; - } - - /* setup count so the clearing of oldused - * can fall through correctly - */ - ix = 1; - } - - /* now zero to oldused */ - while (ix++ < oldused) { - *tmpc++ = 0; - } - mp_clamp(c); - - return MP_OKAY; +add_single_digit(mp_int *a, mp_digit b, mp_int *c) +{ + int res, ix, oldused; + mp_digit *tmpa, *tmpc, mu; + + /* grow c as required */ + if (c->alloc < a->used + 1) { + if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) { + return res; + } + } + + /* if a is negative and |a| >= b, call c = |a| - b */ + if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) { + /* temporarily fix sign of a */ + a->sign = MP_ZPOS; + + /* c = |a| - b */ + res = signed_subtract_word(a, b, c); + + /* fix sign */ + a->sign = c->sign = MP_NEG; + + /* clamp */ + trim_unused_digits(c); + + return res; + } + + /* old number of used digits in c */ + oldused = c->used; + + /* sign always positive */ + c->sign = MP_ZPOS; + + /* source alias */ + tmpa = a->dp; + + /* destination alias */ + tmpc = c->dp; + + /* if a is positive */ + if (a->sign == MP_ZPOS) { + /* add digit, after this we're propagating + * the carry. + */ + *tmpc = *tmpa++ + b; + mu = *tmpc >> DIGIT_BIT; + *tmpc++ &= MP_MASK; + + /* now handle rest of the digits */ + for (ix = 1; ix < a->used; ix++) { + *tmpc = *tmpa++ + mu; + mu = *tmpc >> DIGIT_BIT; + *tmpc++ &= MP_MASK; + } + /* set final carry */ + ix++; + *tmpc++ = mu; + + /* setup size */ + c->used = a->used + 1; + } else { + /* a was negative and |a| < b */ + c->used = 1; + + /* the result is a single digit */ + if (a->used == 1) { + *tmpc++ = b - a->dp[0]; + } else { + *tmpc++ = b; + } + + /* setup count so the clearing of oldused + * can fall through correctly + */ + ix = 1; + } + + /* now zero to oldused */ + while (ix++ < oldused) { + *tmpc++ = 0; + } + trim_unused_digits(c); + + return MP_OKAY; } /* single digit subtraction */ static int -mp_sub_d(mp_int *a, mp_digit b, mp_int *c) -{ - mp_digit *tmpa, *tmpc, mu; - int res, ix, oldused; - - /* grow c as required */ - if (c->alloc < a->used + 1) { - if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) { - return res; - } - } - - /* if a is negative just do an unsigned - * addition [with fudged signs] - */ - if (a->sign == MP_NEG) { - a->sign = MP_ZPOS; - res = mp_add_d(a, b, c); - a->sign = c->sign = MP_NEG; - - /* clamp */ - mp_clamp(c); - - return res; - } - - /* setup regs */ - oldused = c->used; - tmpa = a->dp; - tmpc = c->dp; - - /* if a <= b simply fix the single digit */ - if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) { - if (a->used == 1) { - *tmpc++ = b - *tmpa; - } else { - *tmpc++ = b; - } - ix = 1; - - /* negative/1digit */ - c->sign = MP_NEG; - c->used = 1; - } else { - /* positive/size */ - c->sign = MP_ZPOS; - c->used = a->used; - - /* subtract first digit */ - *tmpc = *tmpa++ - b; - mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1); - *tmpc++ &= MP_MASK; - - /* handle rest of the digits */ - for (ix = 1; ix < a->used; ix++) { - *tmpc = *tmpa++ - mu; - mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1); - *tmpc++ &= MP_MASK; - } - } - - /* zero excess digits */ - while (ix++ < oldused) { - *tmpc++ = 0; - } - mp_clamp(c); - return MP_OKAY; +signed_subtract_word(mp_int *a, mp_digit b, mp_int *c) +{ + mp_digit *tmpa, *tmpc, mu; + int res, ix, oldused; + + /* grow c as required */ + if (c->alloc < a->used + 1) { + if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) { + return res; + } + } + + /* if a is negative just do an unsigned + * addition [with fudged signs] + */ + if (a->sign == MP_NEG) { + a->sign = MP_ZPOS; + res = add_single_digit(a, b, c); + a->sign = c->sign = MP_NEG; + + /* clamp */ + trim_unused_digits(c); + + return res; + } + + /* setup regs */ + oldused = c->used; + tmpa = a->dp; + tmpc = c->dp; + + /* if a <= b simply fix the single digit */ + if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) { + if (a->used == 1) { + *tmpc++ = b - *tmpa; + } else { + *tmpc++ = b; + } + ix = 1; + + /* negative/1digit */ + c->sign = MP_NEG; + c->used = 1; + } else { + /* positive/size */ + c->sign = MP_ZPOS; + c->used = a->used; + + /* subtract first digit */ + *tmpc = *tmpa++ - b; + mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1); + *tmpc++ &= MP_MASK; + + /* handle rest of the digits */ + for (ix = 1; ix < a->used; ix++) { + *tmpc = *tmpa++ - mu; + mu = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1); + *tmpc++ &= MP_MASK; + } + } + + /* zero excess digits */ + while (ix++ < oldused) { + *tmpc++ = 0; + } + trim_unused_digits(c); + return MP_OKAY; } static const int lnz[16] = { - 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0 + 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0 }; /* Counts the number of lsbs which are zero before the first zero bit */ static int mp_cnt_lsb(mp_int *a) { - int x; - mp_digit q, qq; - - /* easy out */ - if (mp_iszero(a) == 1) { - return 0; - } + int x; + mp_digit q, qq; - /* scan lower digits until non-zero */ - for (x = 0; x < a->used && a->dp[x] == 0; x++); - q = a->dp[x]; - x *= DIGIT_BIT; + /* easy out */ + if (MP_ISZERO(a) == 1) { + return 0; + } - /* now scan this digit until a 1 is found */ - if ((q & 1) == 0) { - do { - qq = q & 15; - /* LINTED previous op ensures range of qq */ - x += lnz[qq]; - q >>= 4; - } while (qq == 0); - } - return x; + /* scan lower digits until non-zero */ + for (x = 0; x < a->used && a->dp[x] == 0; x++) { + } + q = a->dp[x]; + x *= DIGIT_BIT; + + /* now scan this digit until a 1 is found */ + if ((q & 1) == 0) { + do { + qq = q & 15; + /* LINTED previous op ensures range of qq */ + x += lnz[qq]; + q >>= 4; + } while (qq == 0); + } + return x; } /* c = a * a (mod b) */ static int -mp_sqrmod(mp_int *a, mp_int *b, mp_int *c) +square_modulo(mp_int *a, mp_int *b, mp_int *c) { - int res; - mp_int t; + int res; + mp_int t; - if ((res = mp_init (&t)) != MP_OKAY) { - return res; - } + if ((res = mp_init(&t)) != MP_OKAY) { + return res; + } - if ((res = mp_sqr (a, &t)) != MP_OKAY) { - mp_clear (&t); - return res; - } - res = mp_mod (&t, b, c); - mp_clear (&t); - return res; + if ((res = square(a, &t)) != MP_OKAY) { + mp_clear(&t); + return res; + } + res = modulo(&t, b, c); + mp_clear(&t); + return res; } + static int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result) { - mp_int n1, y, r; - int s, j, err; - - /* default */ - *result = MP_NO; - - /* ensure b > 1 */ - if (mp_cmp_d(b, 1) != MP_GT) { - return MP_VAL; - } - - /* get n1 = a - 1 */ - if ((err = mp_init_copy (&n1, a)) != MP_OKAY) { - return err; - } - if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) { - goto LBL_N1; - } - - /* set 2**s * r = n1 */ - if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) { - goto LBL_N1; - } - - /* count the number of least significant bits - * which are zero - */ - s = mp_cnt_lsb(&r); - - /* now divide n - 1 by 2**s */ - if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) { - goto LBL_R; - } - - /* compute y = b**r mod a */ - if ((err = mp_init (&y)) != MP_OKAY) { - goto LBL_R; - } - if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) { - goto LBL_Y; - } - - /* if y != 1 and y != n1 do */ - if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) { - j = 1; - /* while j <= s-1 and y != n1 */ - while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) { - if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) { - goto LBL_Y; - } - - /* if y == 1 then composite */ - if (mp_cmp_d (&y, 1) == MP_EQ) { - goto LBL_Y; - } - - ++j; - } - - /* if y != n1 then composite */ - if (mp_cmp (&y, &n1) != MP_EQ) { - goto LBL_Y; - } - } - - /* probably prime now */ - *result = MP_YES; -LBL_Y:mp_clear (&y); -LBL_R:mp_clear (&r); -LBL_N1:mp_clear (&n1); - return err; + mp_int n1, y, r; + int s, j, err; + + /* default */ + *result = MP_NO; + + /* ensure b > 1 */ + if (compare_digit(b, 1) != MP_GT) { + return MP_VAL; + } + + /* get n1 = a - 1 */ + if ((err = mp_init_copy(&n1, a)) != MP_OKAY) { + return err; + } + if ((err = signed_subtract_word(&n1, 1, &n1)) != MP_OKAY) { + goto LBL_N1; + } + + /* set 2**s * r = n1 */ + if ((err = mp_init_copy(&r, &n1)) != MP_OKAY) { + goto LBL_N1; + } + + /* count the number of least significant bits + * which are zero + */ + s = mp_cnt_lsb(&r); + + /* now divide n - 1 by 2**s */ + if ((err = rshift_bits(&r, s, &r, NULL)) != MP_OKAY) { + goto LBL_R; + } + + /* compute y = b**r mod a */ + if ((err = mp_init(&y)) != MP_OKAY) { + goto LBL_R; + } + if ((err = exponent_modulo(b, &r, a, &y)) != MP_OKAY) { + goto LBL_Y; + } + + /* if y != 1 and y != n1 do */ + if (compare_digit(&y, 1) != MP_EQ && signed_compare(&y, &n1) != MP_EQ) { + j = 1; + /* while j <= s-1 and y != n1 */ + while ((j <= (s - 1)) && signed_compare(&y, &n1) != MP_EQ) { + if ((err = square_modulo(&y, a, &y)) != MP_OKAY) { + goto LBL_Y; + } + + /* if y == 1 then composite */ + if (compare_digit(&y, 1) == MP_EQ) { + goto LBL_Y; + } + + ++j; + } + + /* if y != n1 then composite */ + if (signed_compare(&y, &n1) != MP_EQ) { + goto LBL_Y; + } + } + + /* probably prime now */ + *result = MP_YES; +LBL_Y: + mp_clear(&y); +LBL_R: + mp_clear(&r); +LBL_N1: + mp_clear(&n1); + return err; } /* performs a variable number of rounds of Miller-Rabin @@ -4904,114 +4837,115 @@ LBL_N1:mp_clear (&n1); static int mp_prime_is_prime(mp_int *a, int t, int *result) { - mp_int b; - int ix, err, res; + mp_int b; + int ix, err, res; - /* default to no */ - *result = MP_NO; + /* default to no */ + *result = MP_NO; - /* valid value of t? */ - if (t <= 0 || t > (int)PRIME_SIZE) { - return MP_VAL; - } + /* valid value of t? */ + if (t <= 0 || t > (int)PRIME_SIZE) { + return MP_VAL; + } - /* is the input equal to one of the primes in the table? */ - for (ix = 0; ix < (int)PRIME_SIZE; ix++) { - if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) { - *result = 1; - return MP_OKAY; - } - } + /* is the input equal to one of the primes in the table? */ + for (ix = 0; ix < (int)PRIME_SIZE; ix++) { + if (compare_digit(a, ltm_prime_tab[ix]) == MP_EQ) { + *result = 1; + return MP_OKAY; + } + } - /* first perform trial division */ - if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) { - return err; - } + /* first perform trial division */ + if ((err = mp_prime_is_divisible(a, &res)) != MP_OKAY) { + return err; + } - /* return if it was trivially divisible */ - if (res == MP_YES) { - return MP_OKAY; - } + /* return if it was trivially divisible */ + if (res == MP_YES) { + return MP_OKAY; + } - /* now perform the miller-rabin rounds */ - if ((err = mp_init (&b)) != MP_OKAY) { - return err; - } + /* now perform the miller-rabin rounds */ + if ((err = mp_init(&b)) != MP_OKAY) { + return err; + } - for (ix = 0; ix < t; ix++) { - /* set the prime */ - mp_set (&b, ltm_prime_tab[ix]); + for (ix = 0; ix < t; ix++) { + /* set the prime */ + set_word(&b, ltm_prime_tab[ix]); - if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) { - goto LBL_B; - } + if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) { + goto LBL_B; + } - if (res == MP_NO) { - goto LBL_B; - } - } + if (res == MP_NO) { + goto LBL_B; + } + } - /* passed the test */ - *result = MP_YES; -LBL_B:mp_clear (&b); - return err; + /* passed the test */ + *result = MP_YES; +LBL_B: + mp_clear(&b); + return err; } /* returns size of ASCII reprensentation */ static int -mp_radix_size (mp_int *a, int radix, int *size) +mp_radix_size(mp_int *a, int radix, int *size) { - int res, digs; - mp_int t; - mp_digit d; + int res, digs; + mp_int t; + mp_digit d; - *size = 0; + *size = 0; - /* special case for binary */ - if (radix == 2) { - *size = mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1; - return MP_OKAY; - } + /* special case for binary */ + if (radix == 2) { + *size = mp_count_bits(a) + (a->sign == MP_NEG ? 1 : 0) + 1; + return MP_OKAY; + } - /* make sure the radix is in range */ - if (radix < 2 || radix > 64) { - return MP_VAL; - } + /* make sure the radix is in range */ + if (radix < 2 || radix > 64) { + return MP_VAL; + } - if (mp_iszero(a) == MP_YES) { - *size = 2; - return MP_OKAY; - } + if (MP_ISZERO(a) == MP_YES) { + *size = 2; + return MP_OKAY; + } - /* digs is the digit count */ - digs = 0; + /* digs is the digit count */ + digs = 0; - /* if it's negative add one for the sign */ - if (a->sign == MP_NEG) { - ++digs; - } + /* if it's negative add one for the sign */ + if (a->sign == MP_NEG) { + ++digs; + } - /* init a copy of the input */ - if ((res = mp_init_copy (&t, a)) != MP_OKAY) { - return res; - } + /* init a copy of the input */ + if ((res = mp_init_copy(&t, a)) != MP_OKAY) { + return res; + } - /* force temp to positive */ - t.sign = MP_ZPOS; + /* force temp to positive */ + t.sign = MP_ZPOS; - /* fetch out all of the digits */ - while (mp_iszero (&t) == MP_NO) { - if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { - mp_clear (&t); - return res; - } - ++digs; - } - mp_clear (&t); + /* fetch out all of the digits */ + while (MP_ISZERO(&t) == MP_NO) { + if ((res = signed_divide_word(&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { + mp_clear(&t); + return res; + } + ++digs; + } + mp_clear(&t); - /* return digs + 1, the 1 is for the NULL byte that would be required. */ - *size = digs + 1; - return MP_OKAY; + /* return digs + 1, the 1 is for the NULL byte that would be required. */ + *size = digs + 1; + return MP_OKAY; } static const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; @@ -5023,65 +4957,65 @@ static const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijkl static int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen) { - int res, digs; - mp_int t; - mp_digit d; - char *_s = str; - - /* check range of the maxlen, radix */ - if (maxlen < 2 || radix < 2 || radix > 64) { - return MP_VAL; - } - - /* quick out if its zero */ - if (mp_iszero(a) == MP_YES) { - *str++ = '0'; - *str = '\0'; - return MP_OKAY; - } - - if ((res = mp_init_copy (&t, a)) != MP_OKAY) { - return res; - } - - /* if it is negative output a - */ - if (t.sign == MP_NEG) { - /* we have to reverse our digits later... but not the - sign!! */ - ++_s; - - /* store the flag and mark the number as positive */ - *str++ = '-'; - t.sign = MP_ZPOS; - - /* subtract a char */ - --maxlen; - } - - digs = 0; - while (mp_iszero (&t) == 0) { - if (--maxlen < 1) { - /* no more room */ - break; - } - if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { - mp_clear (&t); - return res; - } - /* LINTED -- radix' range is checked above, limits d's range */ - *str++ = mp_s_rmap[d]; - ++digs; - } - - /* reverse the digits of the string. In this case _s points - * to the first digit [exluding the sign] of the number - */ - bn_reverse ((unsigned char *)_s, digs); - - /* append a NULL so the string is properly terminated */ - *str = '\0'; - - mp_clear (&t); - return MP_OKAY; + int res, digs; + mp_int t; + mp_digit d; + char *_s = str; + + /* check range of the maxlen, radix */ + if (maxlen < 2 || radix < 2 || radix > 64) { + return MP_VAL; + } + + /* quick out if its zero */ + if (MP_ISZERO(a) == MP_YES) { + *str++ = '0'; + *str = '\0'; + return MP_OKAY; + } + + if ((res = mp_init_copy(&t, a)) != MP_OKAY) { + return res; + } + + /* if it is negative output a - */ + if (t.sign == MP_NEG) { + /* we have to reverse our digits later... but not the - sign!! */ + ++_s; + + /* store the flag and mark the number as positive */ + *str++ = '-'; + t.sign = MP_ZPOS; + + /* subtract a char */ + --maxlen; + } + + digs = 0; + while (MP_ISZERO(&t) == 0) { + if (--maxlen < 1) { + /* no more room */ + break; + } + if ((res = signed_divide_word(&t, (mp_digit) radix, &t, &d)) != MP_OKAY) { + mp_clear(&t); + return res; + } + /* LINTED -- radix' range is checked above, limits d's range */ + *str++ = mp_s_rmap[d]; + ++digs; + } + + /* reverse the digits of the string. In this case _s points + * to the first digit [exluding the sign] of the number + */ + bn_reverse((unsigned char *)_s, digs); + + /* append a NULL so the string is properly terminated */ + *str = '\0'; + + mp_clear(&t); + return MP_OKAY; } static char * @@ -5093,9 +5027,9 @@ formatbn(const BIGNUM *a, const int radix) if (mp_radix_size(__UNCONST(a), radix, &len) != MP_OKAY) { return NULL; } - if ((s = netpgp_allocate(1, (size_t)len)) != NULL) { + if ((s = allocate(1, (size_t)len)) != NULL) { if (mp_toradix_n(__UNCONST(a), s, radix, len) != MP_OKAY) { - netpgp_deallocate(s, (size_t)len); + deallocate(s, (size_t)len); return NULL; } } @@ -5105,45 +5039,45 @@ formatbn(const BIGNUM *a, const int radix) static int mp_getradix_num(mp_int *a, int radix, char *s) { - int err, ch, neg, y; - - /* clear a */ - mp_zero(a); - - /* if first digit is - then set negative */ - if ((ch = *s++) == '-') { - neg = MP_NEG; - ch = *s++; - } else { - neg = MP_ZPOS; - } - - for (;;) { - /* find y in the radix map */ - for (y = 0; y < radix; y++) { - if (mp_s_rmap[y] == ch) { - break; - } - } - if (y == radix) { - break; - } - - /* shift up and add */ - if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) { - return err; - } - if ((err = mp_add_d(a, y, a)) != MP_OKAY) { - return err; - } - - ch = *s++; - } - if (mp_cmp_d(a, 0) != MP_EQ) { - a->sign = neg; - } - - return MP_OKAY; + int err, ch, neg, y; + + /* clear a */ + mp_zero(a); + + /* if first digit is - then set negative */ + if ((ch = *s++) == '-') { + neg = MP_NEG; + ch = *s++; + } else { + neg = MP_ZPOS; + } + + for (;;) { + /* find y in the radix map */ + for (y = 0; y < radix; y++) { + if (mp_s_rmap[y] == ch) { + break; + } + } + if (y == radix) { + break; + } + + /* shift up and add */ + if ((err = multiply_digit(a, radix, a)) != MP_OKAY) { + return err; + } + if ((err = add_single_digit(a, y, a)) != MP_OKAY) { + return err; + } + + ch = *s++; + } + if (compare_digit(a, 0) != MP_EQ) { + a->sign = neg; + } + + return MP_OKAY; } static int @@ -5157,29 +5091,29 @@ getbn(BIGNUM **a, const char *str, int radix) if (mp_getradix_num(*a, radix, __UNCONST(str)) != MP_OKAY) { return 0; } - mp_radix_size(__UNCONST(a), radix, &len); + mp_radix_size(__UNCONST(*a), radix, &len); return len - 1; } /* d = a - b (mod c) */ static int -mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d) +subtract_modulo(mp_int *a, mp_int *b, mp_int *c, mp_int *d) { - int res; - mp_int t; + int res; + mp_int t; - if ((res = mp_init (&t)) != MP_OKAY) { - return res; - } + if ((res = mp_init(&t)) != MP_OKAY) { + return res; + } - if ((res = mp_sub (a, b, &t)) != MP_OKAY) { - mp_clear (&t); - return res; - } - res = mp_mod (&t, c, d); - mp_clear (&t); - return res; + if ((res = signed_subtract(a, b, &t)) != MP_OKAY) { + mp_clear(&t); + return res; + } + res = modulo(&t, c, d); + mp_clear(&t); + return res; } /**************************************************************************/ @@ -5218,7 +5152,7 @@ BN_bn2bin(const BIGNUM *a, unsigned char *b) } for (x = 0; !BN_is_zero(&t) ; ) { b[x++] = (unsigned char) (t.dp[0] & 0xff); - if (mp_div_2d (&t, 8, &t, NULL) != MP_OKAY) { + if (rshift_bits(&t, 8, &t, NULL) != MP_OKAY) { mp_clear(&t); return -1; } @@ -5241,7 +5175,7 @@ BN_new(void) { BIGNUM *a; - if ((a = netpgp_allocate(1, sizeof(*a))) != NULL) { + if ((a = allocate(1, sizeof(*a))) != NULL) { mp_init(a); } return a; @@ -5286,7 +5220,7 @@ BN_lshift(BIGNUM *r, const BIGNUM *a, int n) return 0; } BN_copy(r, a); - return mp_lshd(r, n) == MP_OKAY; + return lshift_digits(r, n) == MP_OKAY; } int @@ -5296,7 +5230,7 @@ BN_lshift1(BIGNUM *r, BIGNUM *a) return 0; } BN_copy(r, a); - return mp_lshd(r, 1) == MP_OKAY; + return lshift_digits(r, 1) == MP_OKAY; } int @@ -5306,7 +5240,7 @@ BN_rshift(BIGNUM *r, const BIGNUM *a, int n) return MP_VAL; } BN_copy(r, a); - return mp_rshd(r, n) == MP_OKAY; + return rshift_digits(r, n) == MP_OKAY; } int @@ -5316,7 +5250,7 @@ BN_rshift1(BIGNUM *r, BIGNUM *a) return 0; } BN_copy(r, a); - return mp_rshd(r, 1) == MP_OKAY; + return rshift_digits(r, 1) == MP_OKAY; } int @@ -5325,7 +5259,7 @@ BN_set_word(BIGNUM *a, BN_ULONG w) if (a == NULL) { return 0; } - mp_set(a, w); + set_word(a, w); return 1; } @@ -5335,7 +5269,7 @@ BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) if (a == NULL || b == NULL || r == NULL) { return 0; } - return mp_add(__UNCONST(a), __UNCONST(b), r) == MP_OKAY; + return signed_add(__UNCONST(a), __UNCONST(b), r) == MP_OKAY; } int @@ -5344,7 +5278,7 @@ BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b) if (a == NULL || b == NULL || r == NULL) { return 0; } - return mp_sub(__UNCONST(a), __UNCONST(b), r) == MP_OKAY; + return signed_subtract(__UNCONST(a), __UNCONST(b), r) == MP_OKAY; } int @@ -5354,7 +5288,7 @@ BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) return 0; } USE_ARG(ctx); - return mp_mul(__UNCONST(a), __UNCONST(b), r) == MP_OKAY; + return signed_multiply(__UNCONST(a), __UNCONST(b), r) == MP_OKAY; } int @@ -5364,7 +5298,46 @@ BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d, BN_CTX *ctx) return 0; } USE_ARG(ctx); - return mp_div(dv, rem, __UNCONST(a), __UNCONST(d)) == MP_OKAY; + return signed_divide(dv, rem, __UNCONST(a), __UNCONST(d)) == MP_OKAY; +} + +/* perform a bit operation on the 2 bignums */ +int +BN_bitop(BIGNUM *r, const BIGNUM *a, char op, const BIGNUM *b) +{ + unsigned ndigits; + mp_digit ad; + mp_digit bd; + int i; + + if (a == NULL || b == NULL || r == NULL) { + return 0; + } + if (BN_cmp(__UNCONST(a), __UNCONST(b)) >= 0) { + BN_copy(r, a); + ndigits = a->used; + } else { + BN_copy(r, b); + ndigits = b->used; + } + for (i = 0 ; i < (int)ndigits ; i++) { + ad = (i > a->used) ? 0 : a->dp[i]; + bd = (i > b->used) ? 0 : b->dp[i]; + switch(op) { + case '&': + r->dp[i] = (ad & bd); + break; + case '|': + r->dp[i] = (ad | bd); + break; + case '^': + r->dp[i] = (ad ^ bd); + break; + default: + break; + } + } + return 1; } void @@ -5423,7 +5396,7 @@ BN_cmp(BIGNUM *a, BIGNUM *b) if (a == NULL || b == NULL) { return MP_VAL; } - switch(mp_cmp(a, b)) { + switch(signed_compare(a, b)) { case MP_LT: return -1; case MP_GT: @@ -5441,7 +5414,7 @@ BN_mod_exp(BIGNUM *Y, BIGNUM *G, BIGNUM *X, BIGNUM *P, BN_CTX *ctx) return MP_VAL; } USE_ARG(ctx); - return mp_exptmod(G, X, P, Y) == MP_OKAY; + return exponent_modulo(G, X, P, Y) == MP_OKAY; } BIGNUM * @@ -5451,7 +5424,7 @@ BN_mod_inverse(BIGNUM *r, BIGNUM *a, const BIGNUM *n, BN_CTX *ctx) if (r == NULL || a == NULL || n == NULL) { return NULL; } - return (mp_invmod(r, a, __UNCONST(n)) == MP_OKAY) ? r : NULL; + return (modular_inverse(r, a, __UNCONST(n)) == MP_OKAY) ? r : NULL; } int @@ -5461,13 +5434,13 @@ BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx) if (ret == NULL || a == NULL || b == NULL || m == NULL) { return 0; } - return mp_mulmod(ret, a, b, __UNCONST(m)) == MP_OKAY; + return multiply_modulo(ret, a, b, __UNCONST(m)) == MP_OKAY; } BN_CTX * BN_CTX_new(void) { - return netpgp_allocate(1, sizeof(BN_CTX)); + return allocate(1, sizeof(BN_CTX)); } void @@ -5475,7 +5448,7 @@ BN_CTX_init(BN_CTX *c) { if (c != NULL) { c->arraysize = 15; - if ((c->v = netpgp_allocate(sizeof(*c->v), c->arraysize)) == NULL) { + if ((c->v = allocate(sizeof(*c->v), c->arraysize)) == NULL) { c->arraysize = 0; } } @@ -5505,7 +5478,7 @@ BN_CTX_free(BN_CTX *c) for (i = 0 ; i < c->count ; i++) { BN_clear_free(c->v[i]); } - netpgp_deallocate(c->v, sizeof(*c->v) * c->arraysize); + deallocate(c->v, sizeof(*c->v) * c->arraysize); } } @@ -5527,6 +5500,12 @@ BN_bn2dec(const BIGNUM *a) return (a == NULL) ? NULL : formatbn(a, 10); } +char * +BN_bn2radix(const BIGNUM *a, unsigned radix) +{ + return (a == NULL) ? NULL : formatbn(a, (int)radix); +} + #ifndef _KERNEL int BN_print_fp(FILE *fp, const BIGNUM *a) @@ -5539,7 +5518,7 @@ BN_print_fp(FILE *fp, const BIGNUM *a) } s = BN_bn2hex(a); ret = fprintf(fp, "%s", s); - netpgp_deallocate(s, strlen(s) + 1); + deallocate(s, strlen(s) + 1); return ret; } #endif @@ -5582,7 +5561,7 @@ BN_rand_range(BIGNUM *rnd, BIGNUM *range) return 0; } BN_rand(rnd, BN_num_bits(range), 1, 0); - return mp_mod(rnd, range, rnd) == MP_OKAY; + return modulo(rnd, range, rnd) == MP_OKAY; } #endif @@ -5621,6 +5600,12 @@ BN_dec2bn(BIGNUM **a, const char *str) return getbn(a, str, 10); } +int +BN_radix2bn(BIGNUM **a, const char *str, unsigned radix) +{ + return getbn(a, str, (int)radix); +} + int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx) { @@ -5628,7 +5613,7 @@ BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx) if (r == NULL || a == NULL || b == NULL || m == NULL) { return 0; } - return mp_submod(a, b, __UNCONST(m), r) == MP_OKAY; + return subtract_modulo(a, b, __UNCONST(m), r) == MP_OKAY; } int @@ -5639,3 +5624,55 @@ BN_is_bit_set(const BIGNUM *a, int n) } return (a->dp[n / DIGIT_BIT] & (1 << (n % DIGIT_BIT))) ? 1 : 0; } + +/* raise 'a' to power of 'b' */ +int +BN_raise(BIGNUM *res, BIGNUM *a, BIGNUM *b) +{ + uint64_t exponent; + BIGNUM *power; + BIGNUM *temp; + char *t; + + t = BN_bn2dec(b); + exponent = (uint64_t)strtoull(t, NULL, 10); + free(t); + if (exponent == 0) { + BN_copy(res, BN_value_one()); + } else { + power = BN_dup(a); + for ( ; (exponent & 1) == 0 ; exponent >>= 1) { + BN_mul(power, power, power, NULL); + } + temp = BN_dup(power); + for (exponent >>= 1 ; exponent > 0 ; exponent >>= 1) { + BN_mul(power, power, power, NULL); + if (exponent & 1) { + BN_mul(temp, power, temp, NULL); + } + } + BN_copy(res, temp); + BN_free(power); + BN_free(temp); + } + return 1; +} + +/* compute the factorial */ +int +BN_factorial(BIGNUM *res, BIGNUM *f) +{ + BIGNUM *one; + BIGNUM *i; + + i = BN_dup(f); + one = __UNCONST(BN_value_one()); + BN_sub(i, i, one); + BN_copy(res, f); + while (BN_cmp(i, one) > 0) { + BN_mul(res, res, i, NULL); + BN_sub(i, i, one); + } + BN_free(i); + return 1; +} diff --git a/security/netpgpverify/files/bn.h b/security/netpgpverify/files/bn.h index fdc49d8760a..c4e772f583c 100644 --- a/security/netpgpverify/files/bn.h +++ b/security/netpgpverify/files/bn.h @@ -100,8 +100,10 @@ BIGNUM *BN_bin2bn(const uint8_t */*buf*/, int /*size*/, BIGNUM */*bn*/); int BN_bn2bin(const BIGNUM */*a*/, unsigned char */*b*/); char *BN_bn2hex(const BIGNUM */*a*/); char *BN_bn2dec(const BIGNUM */*a*/); +char *BN_bn2radix(const BIGNUM */*a*/, unsigned /*radix*/); int BN_hex2bn(BIGNUM **/*a*/, const char */*str*/); int BN_dec2bn(BIGNUM **/*a*/, const char */*str*/); +int BN_radix2bn(BIGNUM **/*a*/, const char */*str*/, unsigned /*radix*/); #ifndef _KERNEL int BN_print_fp(FILE */*fp*/, const BIGNUM */*a*/); #endif @@ -111,6 +113,7 @@ int BN_sub(BIGNUM */*r*/, const BIGNUM */*a*/, const BIGNUM */*b*/); int BN_mul(BIGNUM */*r*/, const BIGNUM */*a*/, const BIGNUM */*b*/, BN_CTX */*ctx*/); int BN_div(BIGNUM */*q*/, BIGNUM */*r*/, const BIGNUM */*a*/, const BIGNUM */*b*/, BN_CTX */*ctx*/); void BN_swap(BIGNUM */*a*/, BIGNUM */*b*/); +int BN_bitop(BIGNUM */*r*/, const BIGNUM */*a*/, char /*op*/, const BIGNUM */*b*/); int BN_lshift(BIGNUM */*r*/, const BIGNUM */*a*/, int /*n*/); int BN_lshift1(BIGNUM */*r*/, BIGNUM */*a*/); int BN_rshift(BIGNUM */*r*/, const BIGNUM */*a*/, int /*n*/); @@ -126,6 +129,9 @@ BIGNUM *BN_mod_inverse(BIGNUM */*ret*/, BIGNUM */*a*/, const BIGNUM */*n*/, BN_C int BN_mod_mul(BIGNUM */*ret*/, BIGNUM */*a*/, BIGNUM */*b*/, const BIGNUM */*m*/, BN_CTX */*ctx*/); int BN_mod_sub(BIGNUM */*r*/, BIGNUM */*a*/, BIGNUM */*b*/, const BIGNUM */*m*/, BN_CTX */*ctx*/); +int BN_raise(BIGNUM */*res*/, BIGNUM */*a*/, BIGNUM */*b*/); +int BN_factorial(BIGNUM */*fact*/, BIGNUM */*f*/); + BN_CTX *BN_CTX_new(void); BIGNUM *BN_CTX_get(BN_CTX */*ctx*/); void BN_CTX_start(BN_CTX */*ctx*/); -- cgit v1.2.3