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implemented Legendre

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orignal 2019-12-10 10:45:08 -05:00
parent 8d74905257
commit 7417867d0f
2 changed files with 75 additions and 44 deletions
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114
libi2pd/Elligator.cpp
View file

@ -40,8 +40,9 @@ namespace crypto
BN_free (u); BN_free (iu); BN_free (u); BN_free (iu);
} }
void Elligator2::Encode (const uint8_t * key, uint8_t * encoded) const bool Elligator2::Encode (const uint8_t * key, uint8_t * encoded) const
{ {
bool ret = true;
BN_CTX * ctx = BN_CTX_new (); BN_CTX * ctx = BN_CTX_new ();
BN_CTX_start (ctx); BN_CTX_start (ctx);
@ -56,27 +57,38 @@ namespace crypto
BIGNUM * xA = BN_CTX_get (ctx); BN_add (xA, x, A); // x + A BIGNUM * xA = BN_CTX_get (ctx); BN_add (xA, x, A); // x + A
BN_sub (xA, p, xA); // p - (x + A) BN_sub (xA, p, xA); // p - (x + A)
BIGNUM * r = BN_CTX_get (ctx); BIGNUM * uxxA = BN_CTX_get (ctx); // u*x*xA
BN_mod_inverse (r, xA, p, ctx); BN_mod_mul (uxxA, u, x, p, ctx);
BN_mod_mul (r, r, x, p, ctx); BN_mod_mul (uxxA, uxxA, xA, p, ctx);
BN_mod_mul (r, r, iu, p, ctx);
SquareRoot (r, r, ctx); if (Legendre (uxxA, ctx) != -1)
bn2buf (r, encoded, 32);
for (size_t i = 0; i < 16; i++) // To Little Endian
{ {
uint8_t tmp = encoded[i]; BIGNUM * r = BN_CTX_get (ctx);
encoded[i] = encoded[15 - i]; BN_mod_inverse (r, xA, p, ctx);
encoded[15 - i] = tmp; BN_mod_mul (r, r, x, p, ctx);
BN_mod_mul (r, r, iu, p, ctx);
SquareRoot (r, r, ctx);
bn2buf (r, encoded, 32);
for (size_t i = 0; i < 16; i++) // To Little Endian
{
uint8_t tmp = encoded[i];
encoded[i] = encoded[15 - i];
encoded[15 - i] = tmp;
}
} }
else
ret = false;
BN_CTX_end (ctx); BN_CTX_end (ctx);
BN_CTX_free (ctx); BN_CTX_free (ctx);
return ret;
} }
void Elligator2::Decode (const uint8_t * encoded, uint8_t * key) const bool Elligator2::Decode (const uint8_t * encoded, uint8_t * key) const
{ {
bool ret = true;
BN_CTX * ctx = BN_CTX_new (); BN_CTX * ctx = BN_CTX_new ();
BN_CTX_start (ctx); BN_CTX_start (ctx);
@ -89,41 +101,47 @@ namespace crypto
BIGNUM * r = BN_CTX_get (ctx); BN_bin2bn (encoded1, 32, r); BIGNUM * r = BN_CTX_get (ctx); BN_bin2bn (encoded1, 32, r);
// v=-A/(1+u*r^2) if (BN_cmp (r, p12) < 0) // r < (p-1)/2
BIGNUM * v = BN_CTX_get (ctx); BN_mod_sqr (v, r, p, ctx);
BN_mod_mul (v, v, u, p, ctx);
BN_add_word (v, 1);
BN_mod_inverse (v, v, p, ctx);
BN_mod_mul (v, v, nA, p, ctx);
BIGNUM * vpA = BN_CTX_get (ctx);
BN_add (vpA, v, A); // v + A
// t = v^3+A*v^2+v = v^2*(v+A)+v
BIGNUM * t = BN_CTX_get (ctx); BN_mod_sqr (t, v, p, ctx);
BN_mod_mul (t, t, vpA, p, ctx);
BN_mod_add (t, t, v, p, ctx);
int legendre = 0; // TODO:
BIGNUM * x = BN_CTX_get (ctx);
if (legendre == 1)
BN_copy (x, v);
else
{ {
BN_sub (x, p, v); // v = -A/(1+u*r^2)
BN_mod_sub (x, x, A, p, ctx); BIGNUM * v = BN_CTX_get (ctx); BN_mod_sqr (v, r, p, ctx);
} BN_mod_mul (v, v, u, p, ctx);
BN_add_word (v, 1);
BN_mod_inverse (v, v, p, ctx);
BN_mod_mul (v, v, nA, p, ctx);
BIGNUM * vpA = BN_CTX_get (ctx);
BN_add (vpA, v, A); // v + A
// t = v^3+A*v^2+v = v^2*(v+A)+v
BIGNUM * t = BN_CTX_get (ctx); BN_mod_sqr (t, v, p, ctx);
BN_mod_mul (t, t, vpA, p, ctx);
BN_mod_add (t, t, v, p, ctx);
int legendre = Legendre (t, ctx);
BIGNUM * x = BN_CTX_get (ctx);
if (legendre == 1)
BN_copy (x, v);
else
{
BN_sub (x, p, v);
BN_mod_sub (x, x, A, p, ctx);
}
bn2buf (x, key, 32); bn2buf (x, key, 32);
for (size_t i = 0; i < 16; i++) // To Little Endian for (size_t i = 0; i < 16; i++) // To Little Endian
{ {
uint8_t tmp = key[i]; uint8_t tmp = key[i];
key[i] = key[15 - i]; key[i] = key[15 - i];
key[15 - i] = tmp; key[15 - i] = tmp;
}
} }
else
ret = false;
BN_CTX_end (ctx); BN_CTX_end (ctx);
BN_CTX_free (ctx); BN_CTX_free (ctx);
return ret;
} }
void Elligator2::SquareRoot (const BIGNUM * x, BIGNUM * r, BN_CTX * ctx) const void Elligator2::SquareRoot (const BIGNUM * x, BIGNUM * r, BN_CTX * ctx) const
@ -140,6 +158,18 @@ namespace crypto
BN_sub (r, p, r); BN_sub (r, p, r);
} }
int Elligator2::Legendre (const BIGNUM * a, BN_CTX * ctx) const
{
// assume a < p, so don't check for a % p = 0
BIGNUM * r = BN_CTX_get (ctx);
BN_mod_exp (r, a, p12, p, ctx); // r = a^((p-1)/2) mod p
if (BN_is_word(r, 1))
return 1;
else if (BN_is_zero(r))
return 0;
return -1;
}
static std::unique_ptr<Elligator2> g_Elligator; static std::unique_ptr<Elligator2> g_Elligator;
std::unique_ptr<Elligator2>& GetElligator () std::unique_ptr<Elligator2>& GetElligator ()
{ {

5
libi2pd/Elligator.h
View file

@ -17,12 +17,13 @@ namespace crypto
Elligator2 (); Elligator2 ();
~Elligator2 (); ~Elligator2 ();
void Encode (const uint8_t * key, uint8_t * encoded) const; bool Encode (const uint8_t * key, uint8_t * encoded) const;
void Decode (const uint8_t * encoded, uint8_t * key) const; bool Decode (const uint8_t * encoded, uint8_t * key) const;
private: private:
void SquareRoot (const BIGNUM * x, BIGNUM * r, BN_CTX * ctx) const; void SquareRoot (const BIGNUM * x, BIGNUM * r, BN_CTX * ctx) const;
int Legendre (const BIGNUM * a, BN_CTX * ctx) const; // a/p
private: private: