Add an RSA-OAEP implementation.

R=rsc
APPROVED=rsc
DELTA=734  (734 added, 0 deleted, 0 changed)
OCL=35738
CL=35879

1 files changed, 413 insertions, 0 deletions

diff --git a/src/pkg/crypto/rsa/rsa.go b/src/pkg/crypto/rsa/rsa.go
new file mode 100644
index 000000000..de98d3074
--- /dev/null
+++ b/src/pkg/crypto/rsa/rsa.go
@@ -0,0 +1,413 @@
+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// This package implements RSA encryption as specified in PKCS#1.
+package rsa
+
+// TODO(agl): Add support for PSS padding.
+
+import (
+		"bytes";
+	big	"gmp";
+		"hash";
+		"io";
+		"os";
+)
+
+var bigOne = big.NewInt(1)
+
+// randomSafePrime returns a number, p, of the given size, such that p and
+// (p-1)/2 are both prime with high probability.
+func randomSafePrime(rand io.Reader, bits int) (p *big.Int, err os.Error) {
+	if bits < 1 {
+		err = os.EINVAL;
+	}
+
+	bytes := make([]byte, (bits+7)/8);
+	p = new(big.Int);
+	p2 := new(big.Int);
+
+	for {
+		_, err = io.ReadFull(rand, bytes);
+		if err != nil {
+			return;
+		}
+
+		// Don't let the value be too small.
+		bytes[0] |= 0x80;
+		// Make the value odd since an even number this large certainly isn't prime.
+		bytes[len(bytes)-1] |= 1;
+
+		p.SetBytes(bytes);
+		if p.ProbablyPrime(20) {
+			p2.Rsh(p, 1);	// p2 = (p - 1)/2
+			if p2.ProbablyPrime(20) {
+				return;
+			}
+		}
+	}
+
+	return;
+}
+
+// randomNumber returns a uniform random value in [0, max).
+func randomNumber(rand io.Reader, max *big.Int) (n *big.Int, err os.Error) {
+	k := (max.Len() + 7)/8;
+
+	// r is the number of bits in the used in the most significant byte of
+	// max.
+	r := uint(max.Len() % 8);
+	if r == 0 {
+		r = 8;
+	}
+
+	bytes := make([]byte, k);
+	n = new(big.Int);
+
+	for {
+		_, err = io.ReadFull(rand, bytes);
+		if err != nil {
+			return;
+		}
+
+		// Clear bits in the first byte to increase the probability
+		// that the candidate is < max.
+		bytes[0] &= uint8(int(1<<r)-1);
+
+		n.SetBytes(bytes);
+		if big.CmpInt(n, max) < 0 {
+			return;
+		}
+	}
+
+	return;
+}
+
+// A PublicKey represents the public part of an RSA key.
+type PublicKey struct {
+	N	*big.Int;	// modulus
+	E	int;		// public exponent
+}
+
+// A PrivateKey represents an RSA key
+type PrivateKey struct {
+	PublicKey;	// public part.
+	D		*big.Int;	// private exponent
+	P, Q		*big.Int;	// prime factors of N
+}
+
+// GenerateKeyPair generates an RSA keypair of the given bit size.
+func GenerateKey(rand io.Reader, bits int) (priv *PrivateKey, err os.Error) {
+	priv = new(PrivateKey);
+	// Smaller public exponents lead to faster public key
+	// operations. Since the exponent must be coprime to
+	// (p-1)(q-1), the smallest possible value is 3. Some have
+	// suggested that a larger exponent (often 2**16+1) be used
+	// since previous implementation bugs[1] were avoided when this
+	// was the case. However, there are no current reasons not to use
+	// small exponents.
+	// [1] http://marc.info/?l=cryptography&m=115694833312008&w=2
+	priv.E = 3;
+
+	pminus1 := new(big.Int);
+	qminus1 := new(big.Int);
+	totient := new(big.Int);
+
+	for {
+		p, err := randomSafePrime(rand, bits/2);
+		if err != nil {
+			return;
+		}
+
+		q, err := randomSafePrime(rand, bits/2);
+		if err != nil {
+			return;
+		}
+
+		if big.CmpInt(p, q) == 0 {
+			continue;
+		}
+
+		n := new(big.Int).Mul(p, q);
+		pminus1.Sub(p, bigOne);
+		qminus1.Sub(q, bigOne);
+		totient.Mul(pminus1, qminus1);
+
+		g := new(big.Int);
+		priv.D = new(big.Int);
+		y := new(big.Int);
+		e := big.NewInt(int64(priv.E));
+		big.GcdInt(g, priv.D, y, e, totient);
+
+		if big.CmpInt(g, bigOne) == 0 {
+			priv.D.Add(priv.D, totient);
+			priv.P = p;
+			priv.Q = q;
+			priv.N = n;
+
+			break;
+		}
+	}
+
+	return;
+}
+
+// incCounter increments a four byte, big-endian counter.
+func incCounter(c *[4]byte) {
+	if c[3]++; c[3] != 0 {
+		return;
+	}
+	if c[2]++; c[2] != 0 {
+		return;
+	}
+	if c[1]++; c[1] != 0 {
+		return;
+	}
+	c[0]++;
+}
+
+// mgf1XOR XORs the bytes in out with a mask generated using the MGF1 function
+// specified in PKCS#1 v2.1.
+func mgf1XOR(out []byte, hash hash.Hash, seed []byte) {
+	var counter [4]byte;
+
+	done := 0;
+	for done < len(out) {
+		hash.Write(seed);
+		hash.Write(counter[0:4]);
+		digest := hash.Sum();
+		hash.Reset();
+
+		for i := 0; i < len(digest) && done < len(out); i++ {
+			out[done] ^= digest[i];
+			done++;
+		}
+		incCounter(&counter);
+	}
+}
+
+// MessageTooLongError is returned when attempting to encrypt a message which
+// is too large for the size of the public key.
+type MessageTooLongError struct{}
+
+func (MessageTooLongError) String() string {
+	return "message too long for RSA public key size";
+}
+
+func encrypt(c *big.Int, pub *PublicKey, m *big.Int) *big.Int {
+	e := big.NewInt(int64(pub.E));
+	c.Exp(m, e, pub.N);
+	return c;
+}
+
+// EncryptOAEP encrypts the given message with RSA-OAEP.
+// The message must be no longer than the length of the public modulus less
+// twice the hash length plus 2.
+func EncryptOAEP(hash hash.Hash, rand io.Reader, pub *PublicKey, msg []byte, label []byte) (out []byte, err os.Error) {
+	hash.Reset();
+	k := (pub.N.Len() + 7)/8;
+	if len(msg) > k - 2 * hash.Size() - 2 {
+		err = MessageTooLongError{};
+		return;
+	}
+
+	hash.Write(label);
+	lHash := hash.Sum();
+	hash.Reset();
+
+	em := make([]byte, k);
+	seed := em[1 : 1 + hash.Size()];
+	db := em[1 + hash.Size() : len(em)];
+
+	bytes.Copy(db[0 : hash.Size()], lHash);
+	db[len(db)-len(msg)-1] = 1;
+	bytes.Copy(db[len(db)-len(msg) : len(db)], msg);
+
+	_, err = io.ReadFull(rand, seed);
+	if err != nil {
+		return;
+	}
+
+	mgf1XOR(db, hash, seed);
+	mgf1XOR(seed, hash, db);
+
+	m := new(big.Int);
+	m.SetBytes(em);
+	c := encrypt(new(big.Int), pub, m);
+	out = c.Bytes();
+	return;
+}
+
+// A DecryptionError represents a failure to decrypt a message.
+// It is deliberately vague to avoid adaptive attacks.
+type DecryptionError struct{}
+
+func (DecryptionError) String() string {
+	return "RSA decryption error";
+}
+
+// modInverse returns ia, the inverse of a in the multiplicative group of prime
+// order n. It requires that a be a member of the group (i.e. less than n).
+func modInverse(a, n *big.Int) (ia *big.Int) {
+	g := new(big.Int);
+	x := new(big.Int);
+	y := new(big.Int);
+	big.GcdInt(g, x, y, a, n);
+	if big.CmpInt(x, bigOne) < 0 {
+		// 0 is not the multiplicative inverse of any element so, if x
+		// < 1, then x is negative.
+		x.Add(x, n);
+	}
+
+	return x;
+}
+
+// constantTimeCompare returns 1 iff the two equal length slices, x
+// and y, have equal contents. The time taken is a function of the length of
+// the slices and is independent of the contents.
+func constantTimeCompare(x, y []byte) int {
+	var v byte;
+
+	for i := 0; i < len(x); i++ {
+		v |= x[i]^y[i];
+	}
+
+	return constantTimeByteEq(v, 0);
+}
+
+// constantTimeSelect returns a if mask is 1 and b if mask is 0.
+// Its behaviour is undefined if mask takes any other value.
+func constantTimeSelect(mask, a, b int) int {
+	return ^(mask-1)&a | (mask-1)&b;
+}
+
+// constantTimeByteEq returns 1 if a == b and 0 otherwise.
+func constantTimeByteEq(a, b uint8) (mask int) {
+	x := ^(a^b);
+	x &= x>>4;
+	x &= x>>2;
+	x &= x>>1;
+
+	return int(x);
+}
+
+// decrypt performs an RSA decryption, resulting in a plaintext integer. If a
+// random source is given, RSA blinding is used.
+func decrypt(rand io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err os.Error) {
+	// TODO(agl): can we get away with reusing blinds?
+	if big.CmpInt(c, priv.N) > 0 {
+		err = DecryptionError{};
+		return;
+	}
+
+	var ir *big.Int;
+	if rand != nil {
+		// Blinding enabled. Blinding involves multiplying c by r^e.
+		// Then the decryption operation performs (m^e * r^e)^d mod n
+		// which equals mr mod n. The factor of r can then be removed
+		// by multipling by the multiplicative inverse of r.
+
+		r, err := randomNumber(rand, priv.N);
+		if err != nil {
+			return;
+		}
+		ir = modInverse(r, priv.N);
+		bigE := big.NewInt(int64(priv.E));
+		rpowe := new(big.Int).Exp(r, bigE, priv.N);
+		c.Mul(c, rpowe);
+		c.Mod(c, priv.N);
+	}
+
+	m = new(big.Int).Exp(c, priv.D, priv.N);
+
+	if ir != nil {
+		// Unblind.
+		m.Mul(m, ir);
+		m.Mod(m, priv.N);
+	}
+
+	return;
+}
+
+// DecryptOAEP decrypts ciphertext using RSA-OAEP.
+// If rand != nil, DecryptOAEP uses RSA blinding to avoid timing side-channel attacks.
+func DecryptOAEP(hash hash.Hash, rand io.Reader, priv *PrivateKey, ciphertext []byte, label []byte) (msg []byte, err os.Error) {
+	k := (priv.N.Len() + 7)/8;
+	if len(ciphertext) > k ||
+		k < hash.Size() * 2 + 2 {
+		err = DecryptionError{};
+		return;
+	}
+
+	c := new(big.Int).SetBytes(ciphertext);
+
+	m, err := decrypt(rand, priv, c);
+	if err != nil {
+		return;
+	}
+
+	hash.Write(label);
+	lHash := hash.Sum();
+	hash.Reset();
+
+	// Converting the plaintext number to bytes will strip any
+	// leading zeros so we may have to left pad. We do this unconditionally
+	// to avoid leaking timing information. (Although we still probably
+	// leak the number of leading zeros. It's not clear that we can do
+	// anything about this.)
+	em := leftPad(m.Bytes(), k);
+
+	firstByteIsZero := constantTimeByteEq(em[0], 0);
+
+	seed := em[1 : hash.Size() + 1];
+	db := em[hash.Size() + 1 : len(em)];
+
+	mgf1XOR(seed, hash, db);
+	mgf1XOR(db, hash, seed);
+
+	lHash2 := db[0 : hash.Size()];
+
+	// We have to validate the plaintext in contanst time in order to avoid
+	// attacks like: J. Manger. A Chosen Ciphertext Attack on RSA Optimal
+	// Asymmetric Encryption Padding (OAEP) as Standardized in PKCS #1
+	// v2.0. In J. Kilian, editor, Advances in Cryptology.
+	lHash2Good := constantTimeCompare(lHash, lHash2);
+
+	// The remainder of the plaintext must be zero or more 0x00, followed
+	// by 0x01, followed by the message.
+	//   lookingForIndex: 1 iff we are still looking for the 0x01
+	//   index: the offset of the first 0x01 byte
+	//   invalid: 1 iff we saw a non-zero byte before the 0x01.
+	var lookingForIndex, index, invalid int;
+	lookingForIndex = 1;
+	rest := db[hash.Size() : len(db)];
+
+	for i := 0; i < len(rest); i++ {
+		equals0 := constantTimeByteEq(rest[i], 0);
+		equals1 := constantTimeByteEq(rest[i], 1);
+		index = constantTimeSelect(lookingForIndex & equals1, i, index);
+		lookingForIndex = constantTimeSelect(equals1, 0, lookingForIndex);
+		invalid = constantTimeSelect(lookingForIndex & ^equals0, 1, invalid);
+	}
+
+	if firstByteIsZero & lHash2Good & ^invalid & ^lookingForIndex != 1 {
+		err = DecryptionError{};
+		return;
+	}
+
+	msg = rest[index+1 : len(rest)];
+	return;
+}
+
+// leftPad returns a new slice of length size. The contents of input are right
+// aligned in the new slice.
+func leftPad(input []byte, size int) (out []byte) {
+	n := len(input);
+	if n > size {
+		n = size;
+	}
+	out = make([]byte, size);
+	bytes.Copy(out[len(out)-n : len(out)], input);
+	return;
+}