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scalar multiplication for x25519

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orignal 2018-06-12 12:42:20 -04:00
parent a8278fc78b
commit 046a80cfe4
3 changed files with 103 additions and 9 deletions
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101
libi2pd/Ed25519.cpp
View File

@ -411,12 +411,103 @@ namespace crypto
}
}
void Ed25519::Mul (const uint8_t * p, const uint8_t * e, uint8_t * buf, BN_CTX * ctx) const
BIGNUM * Ed25519::ScalarMul (const BIGNUM * p, const BIGNUM * n, BN_CTX * ctx) const
{
auto P = DecodePublicKey (p, ctx);
BIGNUM * e1 = DecodeBN<32> (e);
EncodePublicKey (Mul (P, e1, ctx), buf, ctx);
BN_free (e1);
BN_CTX_start (ctx);
auto x1 = BN_CTX_get (ctx); BN_copy (x1, p);
auto x2 = BN_CTX_get (ctx); BN_one (x2);
auto z2 = BN_CTX_get (ctx); BN_zero (z2);
auto x3 = BN_CTX_get (ctx); BN_copy (x1, p);
auto z3 = BN_CTX_get (ctx); BN_one (z3);
auto a24 = BN_CTX_get (ctx); BN_set_word (a24, 121665);
auto a = BN_CTX_get (ctx); auto aa = BN_CTX_get (ctx);
auto b = BN_CTX_get (ctx); auto bb = BN_CTX_get (ctx);
auto e = BN_CTX_get (ctx); auto c = BN_CTX_get (ctx);
auto d = BN_CTX_get (ctx);
auto da = BN_CTX_get (ctx); auto cb = BN_CTX_get (ctx);
auto tmp1 = BN_CTX_get (ctx); auto tmp2 = BN_CTX_get (ctx);
unsigned int swap = 0;
auto bits = BN_num_bits (n);
while(bits)
{
--bits;
auto k_t = BN_is_bit_set(n, bits) ? 1 : 0;
swap ^= k_t;
if (swap)
{
std::swap (x2, x3);
std::swap (z2, z3);
}
swap = k_t;
// a = x2 + z2
BN_mod_add(a, x2, z2, q, ctx);
// aa = a^2
BN_mod_sqr(aa, a, q, ctx);
// b = x2 - z2
BN_mod_sub(b, x2, z2, q, ctx);
// bb = b^2
BN_mod_sqr(bb, b, q, ctx);
// e = aa - bb
BN_mod_sub(e, aa, bb, q, ctx);
// c = x3 + z3
BN_mod_add(c, x3, z3, q, ctx);
// d = x3 - z3
BN_mod_sub(d, x3, z3, q, ctx);
// da = d * a
BN_mod_mul(da, d, a, q, ctx);
// cb = c * b
BN_mod_mul(cb, c, b, q, ctx);
// x3 = ( da + cb )^2
BN_mod_add(tmp1, da, cb, q, ctx);
BN_mod_sqr(x3, tmp1, q, ctx);
// z3 == x1 * (da - cb)^2
BN_mod_sub(tmp1, da, cb, q, ctx);
BN_mod_sqr(tmp2, tmp1, q, ctx);
BN_mod_mul(z3, x1, tmp2, q, ctx);
// x2 = aa * bb
BN_mod_mul(x2, aa, bb, q, ctx);
// z2 = e * (aa + a24 * e)
BN_mod_mul(tmp1, a24, e, q, ctx);
BN_mod_add(tmp2, aa, tmp1, q, ctx);
BN_mod_mul(z2, e, tmp2, q, ctx);
}
if (swap)
{
std::swap (x2, x3);
std::swap (z2, z3);
}
// x2 * (z2 ^ (q - 2))
BN_set_word(tmp1, 2);
BN_sub(tmp2, q, tmp1);
BN_mod_exp(tmp1, z2, tmp2, q, ctx);
BIGNUM * res = BN_new (); // not from ctx
BN_mod_mul(res, x2, tmp1, q, ctx);
BN_CTX_end (ctx);
return res;
}
void Ed25519::ScalarMul (const uint8_t * p, const uint8_t * e, uint8_t * buf, BN_CTX * ctx) const
{
BIGNUM * p1 = DecodeBN<32> (p);
uint8_t k[32];
memcpy (k, e, 32);
k[0] &= 248; k[31] &= 127; k[31] |= 64;
BIGNUM * n = DecodeBN<32> (k);
BIGNUM * q1 = ScalarMul (p1, n, ctx);
EncodeBN (q1, buf, 32);
BN_free (p1); BN_free (n); BN_free (q1);
}
void Ed25519::ScalarMulB (const uint8_t * e, uint8_t * buf, BN_CTX * ctx) const
{
BIGNUM *p1 = BN_new (); BN_set_word (p1, 9);
uint8_t k[32];
memcpy (k, e, 32);
k[0] &= 248; k[31] &= 127; k[31] |= 64;
BIGNUM * n = DecodeBN<32> (k);
BIGNUM * q1 = ScalarMul (p1, n, ctx);
EncodeBN (q1, buf, 32);
BN_free (p1); BN_free (n); BN_free (q1);
}
void Ed25519::ExpandPrivateKey (const uint8_t * key, uint8_t * expandedKey)

6
libi2pd/Ed25519.h
View File

@ -75,7 +75,8 @@ namespace crypto
EDDSAPoint GeneratePublicKey (const uint8_t * expandedPrivateKey, BN_CTX * ctx) const;
EDDSAPoint DecodePublicKey (const uint8_t * buf, BN_CTX * ctx) const;
void EncodePublicKey (const EDDSAPoint& publicKey, uint8_t * buf, BN_CTX * ctx) const;
void Mul (const uint8_t * p, const uint8_t * e, uint8_t * buf, BN_CTX * ctx) const; // p is point, e is number
void ScalarMul (const uint8_t * p, const uint8_t * e, uint8_t * buf, BN_CTX * ctx) const; // p is point, e is number for x25519
void ScalarMulB (const uint8_t * e, uint8_t * buf, BN_CTX * ctx) const;
bool Verify (const EDDSAPoint& publicKey, const uint8_t * digest, const uint8_t * signature) const;
void Sign (const uint8_t * expandedPrivateKey, const uint8_t * publicKeyEncoded, const uint8_t * buf, size_t len, uint8_t * signature) const;
@ -99,6 +100,9 @@ namespace crypto
BIGNUM * DecodeBN (const uint8_t * buf) const;
void EncodeBN (const BIGNUM * bn, uint8_t * buf, size_t len) const;
// for x25519
BIGNUM * ScalarMul (const BIGNUM * p, const BIGNUM * e, BN_CTX * ctx) const;
private:
BIGNUM * q, * l, * d, * I;

5
libi2pd/NTCP2.cpp
View File

@ -67,7 +67,7 @@ namespace transport
// x25519 between rs and priv
uint8_t inputKeyMaterial[32];
BN_CTX * ctx = BN_CTX_new ();
i2p::crypto::GetEd25519 ()->Mul (rs, m_ExpandedPrivateKey, inputKeyMaterial, ctx); // rs*priv
i2p::crypto::GetEd25519 ()->ScalarMul (rs, m_ExpandedPrivateKey, inputKeyMaterial, ctx); // rs*priv
BN_CTX_free (ctx);
// temp_key = HMAC-SHA256(ck, input_key_material)
uint8_t tempKey[32]; unsigned int len;
@ -87,8 +87,7 @@ namespace transport
RAND_bytes (key, 32);
i2p::crypto::Ed25519::ExpandPrivateKey (key, m_ExpandedPrivateKey);
BN_CTX * ctx = BN_CTX_new ();
auto publicKey = i2p::crypto::GetEd25519 ()->GeneratePublicKey (m_ExpandedPrivateKey, ctx);
i2p::crypto::GetEd25519 ()->EncodePublicKey (publicKey, pub, ctx);
i2p::crypto::GetEd25519 ()->ScalarMulB (m_ExpandedPrivateKey, pub, ctx);
BN_CTX_free (ctx);
}