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+/*
+ * ***** BEGIN LICENSE BLOCK *****
+ * Version: MPL 1.1/GPL 2.0/LGPL 2.1
+ *
+ * The contents of this file are subject to the Mozilla Public License Version
+ * 1.1 (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ * http://www.mozilla.org/MPL/
+ *
+ * Software distributed under the License is distributed on an "AS IS" basis,
+ * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
+ * for the specific language governing rights and limitations under the
+ * License.
+ *
+ * The Original Code is the Multi-precision Binary Polynomial Arithmetic Library.
+ *
+ * The Initial Developer of the Original Code is
+ * Sun Microsystems, Inc.
+ * Portions created by the Initial Developer are Copyright (C) 2003
+ * the Initial Developer. All Rights Reserved.
+ *
+ * Contributor(s):
+ * Sheueling Chang Shantz <sheueling.chang@sun.com> and
+ * Douglas Stebila <douglas@stebila.ca> of Sun Laboratories.
+ *
+ * Alternatively, the contents of this file may be used under the terms of
+ * either the GNU General Public License Version 2 or later (the "GPL"), or
+ * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
+ * in which case the provisions of the GPL or the LGPL are applicable instead
+ * of those above. If you wish to allow use of your version of this file only
+ * under the terms of either the GPL or the LGPL, and not to allow others to
+ * use your version of this file under the terms of the MPL, indicate your
+ * decision by deleting the provisions above and replace them with the notice
+ * and other provisions required by the GPL or the LGPL. If you do not delete
+ * the provisions above, a recipient may use your version of this file under
+ * the terms of any one of the MPL, the GPL or the LGPL.
+ *
+ * ***** END LICENSE BLOCK ***** */
+/*
+ * Copyright 2007 Sun Microsystems, Inc. All rights reserved.
+ * Use is subject to license terms.
+ *
+ * Sun elects to use this software under the MPL license.
+ */
+
+#pragma ident "%Z%%M% %I% %E% SMI"
+
+#include "mp_gf2m.h"
+#include "mp_gf2m-priv.h"
+#include "mplogic.h"
+#include "mpi-priv.h"
+
+const mp_digit mp_gf2m_sqr_tb[16] =
+{
+ 0, 1, 4, 5, 16, 17, 20, 21,
+ 64, 65, 68, 69, 80, 81, 84, 85
+};
+
+/* Multiply two binary polynomials mp_digits a, b.
+ * Result is a polynomial with degree < 2 * MP_DIGIT_BITS - 1.
+ * Output in two mp_digits rh, rl.
+ */
+#if MP_DIGIT_BITS == 32
+void
+s_bmul_1x1(mp_digit *rh, mp_digit *rl, const mp_digit a, const mp_digit b)
+{
+ register mp_digit h, l, s;
+ mp_digit tab[8], top2b = a >> 30;
+ register mp_digit a1, a2, a4;
+
+ a1 = a & (0x3FFFFFFF); a2 = a1 << 1; a4 = a2 << 1;
+
+ tab[0] = 0; tab[1] = a1; tab[2] = a2; tab[3] = a1^a2;
+ tab[4] = a4; tab[5] = a1^a4; tab[6] = a2^a4; tab[7] = a1^a2^a4;
+
+ s = tab[b & 0x7]; l = s;
+ s = tab[b >> 3 & 0x7]; l ^= s << 3; h = s >> 29;
+ s = tab[b >> 6 & 0x7]; l ^= s << 6; h ^= s >> 26;
+ s = tab[b >> 9 & 0x7]; l ^= s << 9; h ^= s >> 23;
+ s = tab[b >> 12 & 0x7]; l ^= s << 12; h ^= s >> 20;
+ s = tab[b >> 15 & 0x7]; l ^= s << 15; h ^= s >> 17;
+ s = tab[b >> 18 & 0x7]; l ^= s << 18; h ^= s >> 14;
+ s = tab[b >> 21 & 0x7]; l ^= s << 21; h ^= s >> 11;
+ s = tab[b >> 24 & 0x7]; l ^= s << 24; h ^= s >> 8;
+ s = tab[b >> 27 & 0x7]; l ^= s << 27; h ^= s >> 5;
+ s = tab[b >> 30 ]; l ^= s << 30; h ^= s >> 2;
+
+ /* compensate for the top two bits of a */
+
+ if (top2b & 01) { l ^= b << 30; h ^= b >> 2; }
+ if (top2b & 02) { l ^= b << 31; h ^= b >> 1; }
+
+ *rh = h; *rl = l;
+}
+#else
+void
+s_bmul_1x1(mp_digit *rh, mp_digit *rl, const mp_digit a, const mp_digit b)
+{
+ register mp_digit h, l, s;
+ mp_digit tab[16], top3b = a >> 61;
+ register mp_digit a1, a2, a4, a8;
+
+ a1 = a & (0x1FFFFFFFFFFFFFFFULL); a2 = a1 << 1;
+ a4 = a2 << 1; a8 = a4 << 1;
+ tab[ 0] = 0; tab[ 1] = a1; tab[ 2] = a2; tab[ 3] = a1^a2;
+ tab[ 4] = a4; tab[ 5] = a1^a4; tab[ 6] = a2^a4; tab[ 7] = a1^a2^a4;
+ tab[ 8] = a8; tab[ 9] = a1^a8; tab[10] = a2^a8; tab[11] = a1^a2^a8;
+ tab[12] = a4^a8; tab[13] = a1^a4^a8; tab[14] = a2^a4^a8; tab[15] = a1^a2^a4^a8;
+
+ s = tab[b & 0xF]; l = s;
+ s = tab[b >> 4 & 0xF]; l ^= s << 4; h = s >> 60;
+ s = tab[b >> 8 & 0xF]; l ^= s << 8; h ^= s >> 56;
+ s = tab[b >> 12 & 0xF]; l ^= s << 12; h ^= s >> 52;
+ s = tab[b >> 16 & 0xF]; l ^= s << 16; h ^= s >> 48;
+ s = tab[b >> 20 & 0xF]; l ^= s << 20; h ^= s >> 44;
+ s = tab[b >> 24 & 0xF]; l ^= s << 24; h ^= s >> 40;
+ s = tab[b >> 28 & 0xF]; l ^= s << 28; h ^= s >> 36;
+ s = tab[b >> 32 & 0xF]; l ^= s << 32; h ^= s >> 32;
+ s = tab[b >> 36 & 0xF]; l ^= s << 36; h ^= s >> 28;
+ s = tab[b >> 40 & 0xF]; l ^= s << 40; h ^= s >> 24;
+ s = tab[b >> 44 & 0xF]; l ^= s << 44; h ^= s >> 20;
+ s = tab[b >> 48 & 0xF]; l ^= s << 48; h ^= s >> 16;
+ s = tab[b >> 52 & 0xF]; l ^= s << 52; h ^= s >> 12;
+ s = tab[b >> 56 & 0xF]; l ^= s << 56; h ^= s >> 8;
+ s = tab[b >> 60 ]; l ^= s << 60; h ^= s >> 4;
+
+ /* compensate for the top three bits of a */
+
+ if (top3b & 01) { l ^= b << 61; h ^= b >> 3; }
+ if (top3b & 02) { l ^= b << 62; h ^= b >> 2; }
+ if (top3b & 04) { l ^= b << 63; h ^= b >> 1; }
+
+ *rh = h; *rl = l;
+}
+#endif
+
+/* Compute xor-multiply of two binary polynomials (a1, a0) x (b1, b0)
+ * result is a binary polynomial in 4 mp_digits r[4].
+ * The caller MUST ensure that r has the right amount of space allocated.
+ */
+void
+s_bmul_2x2(mp_digit *r, const mp_digit a1, const mp_digit a0, const mp_digit b1,
+ const mp_digit b0)
+{
+ mp_digit m1, m0;
+ /* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */
+ s_bmul_1x1(r+3, r+2, a1, b1);
+ s_bmul_1x1(r+1, r, a0, b0);
+ s_bmul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1);
+ /* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */
+ r[2] ^= m1 ^ r[1] ^ r[3]; /* h0 ^= m1 ^ l1 ^ h1; */
+ r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0; /* l1 ^= l0 ^ h0 ^ m0; */
+}
+
+/* Compute xor-multiply of two binary polynomials (a2, a1, a0) x (b2, b1, b0)
+ * result is a binary polynomial in 6 mp_digits r[6].
+ * The caller MUST ensure that r has the right amount of space allocated.
+ */
+void
+s_bmul_3x3(mp_digit *r, const mp_digit a2, const mp_digit a1, const mp_digit a0,
+ const mp_digit b2, const mp_digit b1, const mp_digit b0)
+{
+ mp_digit zm[4];
+
+ s_bmul_1x1(r+5, r+4, a2, b2); /* fill top 2 words */
+ s_bmul_2x2(zm, a1, a2^a0, b1, b2^b0); /* fill middle 4 words */
+ s_bmul_2x2(r, a1, a0, b1, b0); /* fill bottom 4 words */
+
+ zm[3] ^= r[3];
+ zm[2] ^= r[2];
+ zm[1] ^= r[1] ^ r[5];
+ zm[0] ^= r[0] ^ r[4];
+
+ r[5] ^= zm[3];
+ r[4] ^= zm[2];
+ r[3] ^= zm[1];
+ r[2] ^= zm[0];
+}
+
+/* Compute xor-multiply of two binary polynomials (a3, a2, a1, a0) x (b3, b2, b1, b0)
+ * result is a binary polynomial in 8 mp_digits r[8].
+ * The caller MUST ensure that r has the right amount of space allocated.
+ */
+void s_bmul_4x4(mp_digit *r, const mp_digit a3, const mp_digit a2, const mp_digit a1,
+ const mp_digit a0, const mp_digit b3, const mp_digit b2, const mp_digit b1,
+ const mp_digit b0)
+{
+ mp_digit zm[4];
+
+ s_bmul_2x2(r+4, a3, a2, b3, b2); /* fill top 4 words */
+ s_bmul_2x2(zm, a3^a1, a2^a0, b3^b1, b2^b0); /* fill middle 4 words */
+ s_bmul_2x2(r, a1, a0, b1, b0); /* fill bottom 4 words */
+
+ zm[3] ^= r[3] ^ r[7];
+ zm[2] ^= r[2] ^ r[6];
+ zm[1] ^= r[1] ^ r[5];
+ zm[0] ^= r[0] ^ r[4];
+
+ r[5] ^= zm[3];
+ r[4] ^= zm[2];
+ r[3] ^= zm[1];
+ r[2] ^= zm[0];
+}
+
+/* Compute addition of two binary polynomials a and b,
+ * store result in c; c could be a or b, a and b could be equal;
+ * c is the bitwise XOR of a and b.
+ */
+mp_err
+mp_badd(const mp_int *a, const mp_int *b, mp_int *c)
+{
+ mp_digit *pa, *pb, *pc;
+ mp_size ix;
+ mp_size used_pa, used_pb;
+ mp_err res = MP_OKAY;
+
+ /* Add all digits up to the precision of b. If b had more
+ * precision than a initially, swap a, b first
+ */
+ if (MP_USED(a) >= MP_USED(b)) {
+ pa = MP_DIGITS(a);
+ pb = MP_DIGITS(b);
+ used_pa = MP_USED(a);
+ used_pb = MP_USED(b);
+ } else {
+ pa = MP_DIGITS(b);
+ pb = MP_DIGITS(a);
+ used_pa = MP_USED(b);
+ used_pb = MP_USED(a);
+ }
+
+ /* Make sure c has enough precision for the output value */
+ MP_CHECKOK( s_mp_pad(c, used_pa) );
+
+ /* Do word-by-word xor */
+ pc = MP_DIGITS(c);
+ for (ix = 0; ix < used_pb; ix++) {
+ (*pc++) = (*pa++) ^ (*pb++);
+ }
+
+ /* Finish the rest of digits until we're actually done */
+ for (; ix < used_pa; ++ix) {
+ *pc++ = *pa++;
+ }
+
+ MP_USED(c) = used_pa;
+ MP_SIGN(c) = ZPOS;
+ s_mp_clamp(c);
+
+CLEANUP:
+ return res;
+}
+
+#define s_mp_div2(a) MP_CHECKOK( mpl_rsh((a), (a), 1) );
+
+/* Compute binary polynomial multiply d = a * b */
+static void
+s_bmul_d(const mp_digit *a, mp_size a_len, mp_digit b, mp_digit *d)
+{
+ mp_digit a_i, a0b0, a1b1, carry = 0;
+ while (a_len--) {
+ a_i = *a++;
+ s_bmul_1x1(&a1b1, &a0b0, a_i, b);
+ *d++ = a0b0 ^ carry;
+ carry = a1b1;
+ }
+ *d = carry;
+}
+
+/* Compute binary polynomial xor multiply accumulate d ^= a * b */
+static void
+s_bmul_d_add(const mp_digit *a, mp_size a_len, mp_digit b, mp_digit *d)
+{
+ mp_digit a_i, a0b0, a1b1, carry = 0;
+ while (a_len--) {
+ a_i = *a++;
+ s_bmul_1x1(&a1b1, &a0b0, a_i, b);
+ *d++ ^= a0b0 ^ carry;
+ carry = a1b1;
+ }
+ *d ^= carry;
+}
+
+/* Compute binary polynomial xor multiply c = a * b.
+ * All parameters may be identical.
+ */
+mp_err
+mp_bmul(const mp_int *a, const mp_int *b, mp_int *c)
+{
+ mp_digit *pb, b_i;
+ mp_int tmp;
+ mp_size ib, a_used, b_used;
+ mp_err res = MP_OKAY;
+
+ MP_DIGITS(&tmp) = 0;
+
+ ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
+
+ if (a == c) {
+ MP_CHECKOK( mp_init_copy(&tmp, a) );
+ if (a == b)
+ b = &tmp;
+ a = &tmp;
+ } else if (b == c) {
+ MP_CHECKOK( mp_init_copy(&tmp, b) );
+ b = &tmp;
+ }
+
+ if (MP_USED(a) < MP_USED(b)) {
+ const mp_int *xch = b; /* switch a and b if b longer */
+ b = a;
+ a = xch;
+ }
+
+ MP_USED(c) = 1; MP_DIGIT(c, 0) = 0;
+ MP_CHECKOK( s_mp_pad(c, USED(a) + USED(b)) );
+
+ pb = MP_DIGITS(b);
+ s_bmul_d(MP_DIGITS(a), MP_USED(a), *pb++, MP_DIGITS(c));
+
+ /* Outer loop: Digits of b */
+ a_used = MP_USED(a);
+ b_used = MP_USED(b);
+ MP_USED(c) = a_used + b_used;
+ for (ib = 1; ib < b_used; ib++) {
+ b_i = *pb++;
+
+ /* Inner product: Digits of a */
+ if (b_i)
+ s_bmul_d_add(MP_DIGITS(a), a_used, b_i, MP_DIGITS(c) + ib);
+ else
+ MP_DIGIT(c, ib + a_used) = b_i;
+ }
+
+ s_mp_clamp(c);
+
+ SIGN(c) = ZPOS;
+
+CLEANUP:
+ mp_clear(&tmp);
+ return res;
+}
+
+
+/* Compute modular reduction of a and store result in r.
+ * r could be a.
+ * For modular arithmetic, the irreducible polynomial f(t) is represented
+ * as an array of int[], where f(t) is of the form:
+ * f(t) = t^p[0] + t^p[1] + ... + t^p[k]
+ * where m = p[0] > p[1] > ... > p[k] = 0.
+ */
+mp_err
+mp_bmod(const mp_int *a, const unsigned int p[], mp_int *r)
+{
+ int j, k;
+ int n, dN, d0, d1;
+ mp_digit zz, *z, tmp;
+ mp_size used;
+ mp_err res = MP_OKAY;
+
+ /* The algorithm does the reduction in place in r,
+ * if a != r, copy a into r first so reduction can be done in r
+ */
+ if (a != r) {
+ MP_CHECKOK( mp_copy(a, r) );
+ }
+ z = MP_DIGITS(r);
+
+ /* start reduction */
+ dN = p[0] / MP_DIGIT_BITS;
+ used = MP_USED(r);
+
+ for (j = used - 1; j > dN;) {
+
+ zz = z[j];
+ if (zz == 0) {
+ j--; continue;
+ }
+ z[j] = 0;
+
+ for (k = 1; p[k] > 0; k++) {
+ /* reducing component t^p[k] */
+ n = p[0] - p[k];
+ d0 = n % MP_DIGIT_BITS;
+ d1 = MP_DIGIT_BITS - d0;
+ n /= MP_DIGIT_BITS;
+ z[j-n] ^= (zz>>d0);
+ if (d0)
+ z[j-n-1] ^= (zz<<d1);
+ }
+
+ /* reducing component t^0 */
+ n = dN;
+ d0 = p[0] % MP_DIGIT_BITS;
+ d1 = MP_DIGIT_BITS - d0;
+ z[j-n] ^= (zz >> d0);
+ if (d0)
+ z[j-n-1] ^= (zz << d1);
+
+ }
+
+ /* final round of reduction */
+ while (j == dN) {
+
+ d0 = p[0] % MP_DIGIT_BITS;
+ zz = z[dN] >> d0;
+ if (zz == 0) break;
+ d1 = MP_DIGIT_BITS - d0;
+
+ /* clear up the top d1 bits */
+ if (d0) z[dN] = (z[dN] << d1) >> d1;
+ *z ^= zz; /* reduction t^0 component */
+
+ for (k = 1; p[k] > 0; k++) {
+ /* reducing component t^p[k]*/
+ n = p[k] / MP_DIGIT_BITS;
+ d0 = p[k] % MP_DIGIT_BITS;
+ d1 = MP_DIGIT_BITS - d0;
+ z[n] ^= (zz << d0);
+ tmp = zz >> d1;
+ if (d0 && tmp)
+ z[n+1] ^= tmp;
+ }
+ }
+
+ s_mp_clamp(r);
+CLEANUP:
+ return res;
+}
+
+/* Compute the product of two polynomials a and b, reduce modulo p,
+ * Store the result in r. r could be a or b; a could be b.
+ */
+mp_err
+mp_bmulmod(const mp_int *a, const mp_int *b, const unsigned int p[], mp_int *r)
+{
+ mp_err res;
+
+ if (a == b) return mp_bsqrmod(a, p, r);
+ if ((res = mp_bmul(a, b, r) ) != MP_OKAY)
+ return res;
+ return mp_bmod(r, p, r);
+}
+
+/* Compute binary polynomial squaring c = a*a mod p .
+ * Parameter r and a can be identical.
+ */
+
+mp_err
+mp_bsqrmod(const mp_int *a, const unsigned int p[], mp_int *r)
+{
+ mp_digit *pa, *pr, a_i;
+ mp_int tmp;
+ mp_size ia, a_used;
+ mp_err res;
+
+ ARGCHK(a != NULL && r != NULL, MP_BADARG);
+ MP_DIGITS(&tmp) = 0;
+
+ if (a == r) {
+ MP_CHECKOK( mp_init_copy(&tmp, a) );
+ a = &tmp;
+ }
+
+ MP_USED(r) = 1; MP_DIGIT(r, 0) = 0;
+ MP_CHECKOK( s_mp_pad(r, 2*USED(a)) );
+
+ pa = MP_DIGITS(a);
+ pr = MP_DIGITS(r);
+ a_used = MP_USED(a);
+ MP_USED(r) = 2 * a_used;
+
+ for (ia = 0; ia < a_used; ia++) {
+ a_i = *pa++;
+ *pr++ = gf2m_SQR0(a_i);
+ *pr++ = gf2m_SQR1(a_i);
+ }
+
+ MP_CHECKOK( mp_bmod(r, p, r) );
+ s_mp_clamp(r);
+ SIGN(r) = ZPOS;
+
+CLEANUP:
+ mp_clear(&tmp);
+ return res;
+}
+
+/* Compute binary polynomial y/x mod p, y divided by x, reduce modulo p.
+ * Store the result in r. r could be x or y, and x could equal y.
+ * Uses algorithm Modular_Division_GF(2^m) from
+ * Chang-Shantz, S. "From Euclid's GCD to Montgomery Multiplication to
+ * the Great Divide".
+ */
+int
+mp_bdivmod(const mp_int *y, const mp_int *x, const mp_int *pp,
+ const unsigned int p[], mp_int *r)
+{
+ mp_int aa, bb, uu;
+ mp_int *a, *b, *u, *v;
+ mp_err res = MP_OKAY;
+
+ MP_DIGITS(&aa) = 0;
+ MP_DIGITS(&bb) = 0;
+ MP_DIGITS(&uu) = 0;
+
+ MP_CHECKOK( mp_init_copy(&aa, x) );
+ MP_CHECKOK( mp_init_copy(&uu, y) );
+ MP_CHECKOK( mp_init_copy(&bb, pp) );
+ MP_CHECKOK( s_mp_pad(r, USED(pp)) );
+ MP_USED(r) = 1; MP_DIGIT(r, 0) = 0;
+
+ a = &aa; b= &bb; u=&uu; v=r;
+ /* reduce x and y mod p */
+ MP_CHECKOK( mp_bmod(a, p, a) );
+ MP_CHECKOK( mp_bmod(u, p, u) );
+
+ while (!mp_isodd(a)) {
+ s_mp_div2(a);
+ if (mp_isodd(u)) {
+ MP_CHECKOK( mp_badd(u, pp, u) );
+ }
+ s_mp_div2(u);
+ }
+
+ do {
+ if (mp_cmp_mag(b, a) > 0) {
+ MP_CHECKOK( mp_badd(b, a, b) );
+ MP_CHECKOK( mp_badd(v, u, v) );
+ do {
+ s_mp_div2(b);
+ if (mp_isodd(v)) {
+ MP_CHECKOK( mp_badd(v, pp, v) );
+ }
+ s_mp_div2(v);
+ } while (!mp_isodd(b));
+ }
+ else if ((MP_DIGIT(a,0) == 1) && (MP_USED(a) == 1))
+ break;
+ else {
+ MP_CHECKOK( mp_badd(a, b, a) );
+ MP_CHECKOK( mp_badd(u, v, u) );
+ do {
+ s_mp_div2(a);
+ if (mp_isodd(u)) {
+ MP_CHECKOK( mp_badd(u, pp, u) );
+ }
+ s_mp_div2(u);
+ } while (!mp_isodd(a));
+ }
+ } while (1);
+
+ MP_CHECKOK( mp_copy(u, r) );
+
+CLEANUP:
+ /* XXX this appears to be a memory leak in the NSS code */
+ mp_clear(&aa);
+ mp_clear(&bb);
+ mp_clear(&uu);
+ return res;
+
+}
+
+/* Convert the bit-string representation of a polynomial a into an array
+ * of integers corresponding to the bits with non-zero coefficient.
+ * Up to max elements of the array will be filled. Return value is total
+ * number of coefficients that would be extracted if array was large enough.
+ */
+int
+mp_bpoly2arr(const mp_int *a, unsigned int p[], int max)
+{
+ int i, j, k;
+ mp_digit top_bit, mask;
+
+ top_bit = 1;
+ top_bit <<= MP_DIGIT_BIT - 1;
+
+ for (k = 0; k < max; k++) p[k] = 0;
+ k = 0;
+
+ for (i = MP_USED(a) - 1; i >= 0; i--) {
+ mask = top_bit;
+ for (j = MP_DIGIT_BIT - 1; j >= 0; j--) {
+ if (MP_DIGITS(a)[i] & mask) {
+ if (k < max) p[k] = MP_DIGIT_BIT * i + j;
+ k++;
+ }
+ mask >>= 1;
+ }
+ }
+
+ return k;
+}
+
+/* Convert the coefficient array representation of a polynomial to a
+ * bit-string. The array must be terminated by 0.
+ */
+mp_err
+mp_barr2poly(const unsigned int p[], mp_int *a)
+{
+
+ mp_err res = MP_OKAY;
+ int i;
+
+ mp_zero(a);
+ for (i = 0; p[i] > 0; i++) {
+ MP_CHECKOK( mpl_set_bit(a, p[i], 1) );
+ }
+ MP_CHECKOK( mpl_set_bit(a, 0, 1) );
+
+CLEANUP:
+ return res;
+}
generated by cgit v1.2.3 (git 2.39.1) at 2025-05-08 19:55:35 +0000