From 7417867d0f974594ebbd56071a914ec46cfb1bbf Mon Sep 17 00:00:00 2001 From: orignal Date: Tue, 10 Dec 2019 10:45:08 -0500 Subject: [PATCH] implemented Legendre --- libi2pd/Elligator.cpp | 114 ++++++++++++++++++++++++++---------------- libi2pd/Elligator.h | 5 +- 2 files changed, 75 insertions(+), 44 deletions(-) diff --git a/libi2pd/Elligator.cpp b/libi2pd/Elligator.cpp index 1f67d641..07711ae0 100644 --- a/libi2pd/Elligator.cpp +++ b/libi2pd/Elligator.cpp @@ -40,8 +40,9 @@ namespace crypto 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_start (ctx); @@ -56,27 +57,38 @@ namespace crypto BIGNUM * xA = BN_CTX_get (ctx); BN_add (xA, x, A); // x + A BN_sub (xA, p, xA); // p - (x + A) - BIGNUM * r = BN_CTX_get (ctx); - BN_mod_inverse (r, xA, p, ctx); - BN_mod_mul (r, r, x, p, ctx); - BN_mod_mul (r, r, iu, p, ctx); + BIGNUM * uxxA = BN_CTX_get (ctx); // u*x*xA + BN_mod_mul (uxxA, u, x, p, ctx); + BN_mod_mul (uxxA, uxxA, xA, p, ctx); - SquareRoot (r, r, ctx); - bn2buf (r, encoded, 32); - - for (size_t i = 0; i < 16; i++) // To Little Endian + if (Legendre (uxxA, ctx) != -1) { - uint8_t tmp = encoded[i]; - encoded[i] = encoded[15 - i]; - encoded[15 - i] = tmp; + BIGNUM * r = BN_CTX_get (ctx); + BN_mod_inverse (r, xA, p, ctx); + 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_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_start (ctx); @@ -89,41 +101,47 @@ namespace crypto BIGNUM * r = BN_CTX_get (ctx); BN_bin2bn (encoded1, 32, r); - // v=-A/(1+u*r^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 + if (BN_cmp (r, p12) < 0) // r < (p-1)/2 { - BN_sub (x, p, v); - BN_mod_sub (x, x, A, p, ctx); - } + // v = -A/(1+u*r^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 = 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); - for (size_t i = 0; i < 16; i++) // To Little Endian - { - uint8_t tmp = key[i]; - key[i] = key[15 - i]; - key[15 - i] = tmp; + bn2buf (x, key, 32); + for (size_t i = 0; i < 16; i++) // To Little Endian + { + uint8_t tmp = key[i]; + key[i] = key[15 - i]; + key[15 - i] = tmp; + } } - + else + ret = false; BN_CTX_end (ctx); BN_CTX_free (ctx); + + return ret; } void Elligator2::SquareRoot (const BIGNUM * x, BIGNUM * r, BN_CTX * ctx) const @@ -140,6 +158,18 @@ namespace crypto 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 g_Elligator; std::unique_ptr& GetElligator () { diff --git a/libi2pd/Elligator.h b/libi2pd/Elligator.h index f2a1c805..6f9eaf2a 100644 --- a/libi2pd/Elligator.h +++ b/libi2pd/Elligator.h @@ -17,12 +17,13 @@ namespace crypto Elligator2 (); ~Elligator2 (); - void Encode (const uint8_t * key, uint8_t * encoded) const; - void Decode (const uint8_t * encoded, uint8_t * key) const; + bool Encode (const uint8_t * key, uint8_t * encoded) const; + bool Decode (const uint8_t * encoded, uint8_t * key) const; private: void SquareRoot (const BIGNUM * x, BIGNUM * r, BN_CTX * ctx) const; + int Legendre (const BIGNUM * a, BN_CTX * ctx) const; // a/p private: