mirror of
https://github.com/PurpleI2P/i2pd
synced 2024-11-05 15:11:13 +00:00
486 lines
14 KiB
C++
486 lines
14 KiB
C++
#include <memory>
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#include "Log.h"
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#include "Signature.h"
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namespace i2p
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{
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namespace crypto
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{
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class Ed25519
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{
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public:
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Ed25519 ()
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{
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BN_CTX * ctx = BN_CTX_new ();
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BIGNUM * tmp = BN_new ();
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q = BN_new ();
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// 2^255-19
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BN_set_bit (q, 255); // 2^255
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BN_sub_word (q, 19);
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l = BN_new ();
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// 2^252 + 27742317777372353535851937790883648493
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BN_set_bit (l, 252);
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two_252_2 = BN_dup (l);
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BN_dec2bn (&tmp, "27742317777372353535851937790883648493");
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BN_add (l, l, tmp);
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BN_sub_word (two_252_2, 2); // 2^252 - 2
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// -121665*inv(121666)
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d = BN_new ();
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BN_set_word (tmp, 121666);
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BN_mod_inverse (tmp, tmp, q, ctx);
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BN_set_word (d, 121665);
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BN_set_negative (d, 1);
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BN_mul (d, d, tmp, ctx);
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// 2^((q-1)/4)
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I = BN_new ();
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BN_free (tmp);
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tmp = BN_dup (q);
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BN_sub_word (tmp, 1);
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BN_div_word (tmp, 4);
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BN_set_word (I, 2);
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BN_mod_exp (I, I, tmp, q, ctx);
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BN_free (tmp);
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// 4*inv(5)
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BIGNUM * By = BN_new ();
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BN_set_word (By, 5);
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BN_mod_inverse (By, By, q, ctx);
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BN_mul_word (By, 4);
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BIGNUM * Bx = RecoverX (By, ctx);
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BN_mod (Bx, Bx, q, ctx); // % q
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BN_mod (By, By, q, ctx); // % q
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// precalculate Bi256 table
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Bi256Carry = { Bx, By }; // B
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for (int i = 0; i < 32; i++)
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{
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Bi256[i][0] = Bi256Carry; // first point
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for (int j = 1; j < 128; j++)
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Bi256[i][j] = Sum (Bi256[i][j-1], Bi256[i][0], ctx); // (256+j+1)^i*B
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Bi256Carry = Bi256[i][127];
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for (int j = 0; j < 128; j++) // add first point 128 more times
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Bi256Carry = Sum (Bi256Carry, Bi256[i][0], ctx);
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}
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BN_CTX_free (ctx);
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}
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Ed25519 (const Ed25519& other): q (BN_dup (other.q)), l (BN_dup (other.l)),
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d (BN_dup (other.d)), I (BN_dup (other.I)), two_252_2 (BN_dup (other.two_252_2)),
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Bi256Carry (other.Bi256Carry)
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{
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for (int i = 0; i < 32; i++)
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for (int j = 0; j < 128; j++)
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Bi256[i][j] = other.Bi256[i][j];
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}
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~Ed25519 ()
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{
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BN_free (q);
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BN_free (l);
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BN_free (d);
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BN_free (I);
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BN_free (two_252_2);
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}
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EDDSAPoint GeneratePublicKey (const uint8_t * expandedPrivateKey, BN_CTX * ctx) const
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{
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return MulB (expandedPrivateKey, ctx); // left half of expanded key, considered as Little Endian
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}
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EDDSAPoint DecodePublicKey (const uint8_t * buf, BN_CTX * ctx) const
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{
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return DecodePoint (buf, ctx);
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}
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void EncodePublicKey (const EDDSAPoint& publicKey, uint8_t * buf, BN_CTX * ctx) const
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{
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EncodePoint (Normalize (publicKey, ctx), buf);
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}
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bool Verify (const EDDSAPoint& publicKey, const uint8_t * digest, const uint8_t * signature) const
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{
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BN_CTX * ctx = BN_CTX_new ();
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BIGNUM * h = DecodeBN<64> (digest);
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// signature 0..31 - R, 32..63 - S
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// B*S = R + PK*h => R = B*S - PK*h
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// we don't decode R, but encode (B*S - PK*h)
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auto Bs = MulB (signature + EDDSA25519_SIGNATURE_LENGTH/2, ctx); // B*S;
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BN_mod (h, h, l, ctx); // public key is multiple of B, but B%l = 0
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auto PKh = Mul (publicKey, h, ctx); // PK*h
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uint8_t diff[32];
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EncodePoint (Normalize (Sum (Bs, -PKh, ctx), ctx), diff); // Bs - PKh encoded
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bool passed = !memcmp (signature, diff, 32); // R
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BN_free (h);
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BN_CTX_free (ctx);
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if (!passed)
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LogPrint (eLogError, "25519 signature verification failed");
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return passed;
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}
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void Sign (const uint8_t * expandedPrivateKey, const uint8_t * publicKeyEncoded, const uint8_t * buf, size_t len,
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uint8_t * signature) const
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{
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BN_CTX * bnCtx = BN_CTX_new ();
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// calculate r
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SHA512_CTX ctx;
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SHA512_Init (&ctx);
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SHA512_Update (&ctx, expandedPrivateKey + EDDSA25519_PRIVATE_KEY_LENGTH, EDDSA25519_PRIVATE_KEY_LENGTH); // right half of expanded key
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SHA512_Update (&ctx, buf, len); // data
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uint8_t digest[64];
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SHA512_Final (digest, &ctx);
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BIGNUM * r = DecodeBN<32> (digest); // DecodeBN<64> (digest); // for test vectors
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// calculate R
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uint8_t R[EDDSA25519_SIGNATURE_LENGTH/2]; // we must use separate buffer because signature might be inside buf
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EncodePoint (Normalize (MulB (digest, bnCtx), bnCtx), R); // EncodePoint (Mul (B, r, bnCtx), R); // for test vectors
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// calculate S
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SHA512_Init (&ctx);
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SHA512_Update (&ctx, R, EDDSA25519_SIGNATURE_LENGTH/2); // R
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SHA512_Update (&ctx, publicKeyEncoded, EDDSA25519_PUBLIC_KEY_LENGTH); // public key
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SHA512_Update (&ctx, buf, len); // data
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SHA512_Final (digest, &ctx);
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BIGNUM * h = DecodeBN<64> (digest);
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// S = (r + h*a) % l
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BIGNUM * a = DecodeBN<EDDSA25519_PRIVATE_KEY_LENGTH> (expandedPrivateKey); // left half of expanded key
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BN_mod_mul (h, h, a, l, bnCtx); // %l
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BN_mod_add (h, h, r, l, bnCtx); // %l
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memcpy (signature, R, EDDSA25519_SIGNATURE_LENGTH/2);
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EncodeBN (h, signature + EDDSA25519_SIGNATURE_LENGTH/2, EDDSA25519_SIGNATURE_LENGTH/2); // S
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BN_free (r); BN_free (h); BN_free (a);
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BN_CTX_free (bnCtx);
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}
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private:
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EDDSAPoint Sum (const EDDSAPoint& p1, const EDDSAPoint& p2, BN_CTX * ctx) const
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{
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// x3 = (x1*y2+y1*x2)*(z1*z2-d*t1*t2)
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// y3 = (y1*y2+x1*x2)*(z1*z2+d*t1*t2)
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// z3 = (z1*z2-d*t1*t2)*(z1*z2+d*t1*t2)
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// t3 = (y1*y2+x1*x2)*(x1*y2+y1*x2)
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BIGNUM * x3 = BN_new (), * y3 = BN_new (), * z3 = BN_new (), * t3 = BN_new ();
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BN_mul (x3, p1.x, p2.x, ctx); // A = x1*x2
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BN_mul (y3, p1.y, p2.y, ctx); // B = y1*y2
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BIGNUM * t1 = p1.t, * t2 = p2.t;
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if (!t1) { t1 = BN_new (); BN_mul (t1, p1.x, p1.y, ctx); }
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if (!t2) { t2 = BN_new (); BN_mul (t2, p2.x, p2.y, ctx); }
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BN_mul (t3, t1, t2, ctx);
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BN_mul (t3, t3, d, ctx); // C = d*t1*t2
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if (!p1.t) BN_free (t1);
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if (!p2.t) BN_free (t2);
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if (p1.z)
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{
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if (p2.z)
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BN_mul (z3, p1.z, p2.z, ctx); // D = z1*z2
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else
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BN_copy (z3, p1.z); // D = z1
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}
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else
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{
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if (p2.z)
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BN_copy (z3, p2.z); // D = z2
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else
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BN_one (z3); // D = 1
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}
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BIGNUM * E = BN_new (), * F = BN_new (), * G = BN_new (), * H = BN_new ();
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BN_add (E, p1.x, p1.y);
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BN_add (F, p2.x, p2.y);
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BN_mul (E, E, F, ctx); // (x1 + y1)*(x2 + y2)
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BN_sub (E, E, x3);
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BN_sub (E, E, y3); // E = (x1 + y1)*(x2 + y2) - A - B
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BN_sub (F, z3, t3); // F = D - C
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BN_add (G, z3, t3); // G = D + C
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BN_add (H, y3, x3); // H = B + A
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BN_mod_mul (x3, E, F, q, ctx); // x3 = E*F
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BN_mod_mul (y3, G, H, q, ctx); // y3 = G*H
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BN_mod_mul (z3, F, G, q, ctx); // z3 = F*G
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BN_mod_mul (t3, E, H, q, ctx); // t3 = E*H
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BN_free (E); BN_free (F); BN_free (G); BN_free (H);
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return EDDSAPoint {x3, y3, z3, t3};
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}
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EDDSAPoint Double (const EDDSAPoint& p, BN_CTX * ctx) const
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{
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BIGNUM * x2 = BN_new (), * y2 = BN_new (), * z2 = BN_new (), * t2 = BN_new ();
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BN_sqr (x2, p.x, ctx); // x2 = A = x^2
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BN_sqr (y2, p.y, ctx); // y2 = B = y^2
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if (p.t)
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BN_sqr (t2, p.t, ctx); // t2 = t^2
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else
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{
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BN_mul (t2, p.x, p.y, ctx); // t = x*y
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BN_sqr (t2, t2, ctx); // t2 = t^2
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}
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BN_mul (t2, t2, d, ctx); // t2 = C = d*t^2
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if (p.z)
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BN_sqr (z2, p.z, ctx); // z2 = D = z^2
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else
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BN_one (z2); // z2 = 1
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BIGNUM * E = BN_new (), * F = BN_new (), * G = BN_new (), * H = BN_new ();
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// E = (x+y)*(x+y)-A-B = x^2+y^2+2xy-A-B = 2xy
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BN_mul (E, p.x, p.y, ctx);
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BN_lshift1 (E, E); // E =2*x*y
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BN_sub (F, z2, t2); // F = D - C
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BN_add (G, z2, t2); // G = D + C
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BN_add (H, y2, x2); // H = B + A
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BN_mod_mul (x2, E, F, q, ctx); // x2 = E*F
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BN_mod_mul (y2, G, H, q, ctx); // y2 = G*H
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BN_mod_mul (z2, F, G, q, ctx); // z2 = F*G
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BN_mod_mul (t2, E, H, q, ctx); // t2 = E*H
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BN_free (E); BN_free (F); BN_free (G); BN_free (H);
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return EDDSAPoint {x2, y2, z2, t2};
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}
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EDDSAPoint Mul (const EDDSAPoint& p, const BIGNUM * e, BN_CTX * ctx) const
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{
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BIGNUM * zero = BN_new (), * one = BN_new ();
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BN_zero (zero); BN_one (one);
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EDDSAPoint res {zero, one};
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if (!BN_is_zero (e))
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{
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int bitCount = BN_num_bits (e);
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for (int i = bitCount - 1; i >= 0; i--)
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{
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res = Double (res, ctx);
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if (BN_is_bit_set (e, i)) res = Sum (res, p, ctx);
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}
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}
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return res;
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}
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EDDSAPoint MulB (const uint8_t * e, BN_CTX * ctx) const // B*e, e is 32 bytes Little Endian
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{
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BIGNUM * zero = BN_new (), * one = BN_new ();
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BN_zero (zero); BN_one (one);
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EDDSAPoint res {zero, one};
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bool carry = false;
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for (int i = 0; i < 32; i++)
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{
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uint8_t x = e[i];
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if (carry)
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{
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if (x < 255)
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{
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x++;
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carry = false;
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}
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else
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x = 0;
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}
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if (x > 0)
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{
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if (x <= 128)
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res = Sum (res, Bi256[i][x-1], ctx);
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else
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{
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res = Sum (res, -Bi256[i][255-x], ctx); // -Bi[256-x]
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carry = true;
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}
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}
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}
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if (carry) res = Sum (res, Bi256Carry, ctx);
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return res;
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}
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EDDSAPoint Normalize (const EDDSAPoint& p, BN_CTX * ctx) const
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{
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if (p.z)
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{
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BIGNUM * x = BN_new (), * y = BN_new ();
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BN_mod_inverse (y, p.z, q, ctx);
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BN_mod_mul (x, p.x, y, q, ctx); // x = x/z
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BN_mod_mul (y, p.y, y, q, ctx); // y = y/z
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return EDDSAPoint{x, y};
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}
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else
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return EDDSAPoint{BN_dup (p.x), BN_dup (p.y)};
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}
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bool IsOnCurve (const EDDSAPoint& p, BN_CTX * ctx) const
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{
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BIGNUM * x2 = BN_new ();
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BN_sqr (x2, p.x, ctx); // x^2
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BIGNUM * y2 = BN_new ();
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BN_sqr (y2, p.y, ctx); // y^2
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// y^2 - x^2 - 1 - d*x^2*y^2
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BIGNUM * tmp = BN_new ();
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BN_mul (tmp, d, x2, ctx);
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BN_mul (tmp, tmp, y2, ctx);
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BN_sub (tmp, y2, tmp);
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BN_sub (tmp, tmp, x2);
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BN_sub_word (tmp, 1);
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BN_mod (tmp, tmp, q, ctx); // % q
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bool ret = BN_is_zero (tmp);
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BN_free (x2);
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BN_free (y2);
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BN_free (tmp);
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return ret;
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}
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BIGNUM * RecoverX (const BIGNUM * y, BN_CTX * ctx) const
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{
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BIGNUM * y2 = BN_new ();
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BN_sqr (y2, y, ctx); // y^2
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// xx = (y^2 -1)*inv(d*y^2 +1)
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BIGNUM * xx = BN_new ();
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BN_mul (xx, d, y2, ctx);
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BN_add_word (xx, 1);
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BN_mod_inverse (xx, xx, q, ctx);
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BN_sub_word (y2, 1);
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BN_mul (xx, y2, xx, ctx);
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// x = srqt(xx) = xx^(2^252-2)
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BIGNUM * x = BN_new ();
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BN_mod_exp (x, xx, two_252_2, q, ctx);
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// check (x^2 -xx) % q
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BN_sqr (y2, x, ctx);
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BN_mod_sub (y2, y2, xx, q, ctx);
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if (!BN_is_zero (y2))
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BN_mod_mul (x, x, I, q, ctx);
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if (BN_is_odd (x))
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BN_sub (x, q, x);
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BN_free (y2);
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BN_free (xx);
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return x;
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}
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EDDSAPoint DecodePoint (const uint8_t * buf, BN_CTX * ctx) const
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{
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// buf is 32 bytes Little Endian, convert it to Big Endian
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uint8_t buf1[EDDSA25519_PUBLIC_KEY_LENGTH];
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for (size_t i = 0; i < EDDSA25519_PUBLIC_KEY_LENGTH/2; i++) // invert bytes
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{
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buf1[i] = buf[EDDSA25519_PUBLIC_KEY_LENGTH -1 - i];
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buf1[EDDSA25519_PUBLIC_KEY_LENGTH -1 - i] = buf[i];
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}
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bool isHighestBitSet = buf1[0] & 0x80;
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if (isHighestBitSet)
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buf1[0] &= 0x7f; // clear highest bit
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BIGNUM * y = BN_new ();
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BN_bin2bn (buf1, EDDSA25519_PUBLIC_KEY_LENGTH, y);
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auto x = RecoverX (y, ctx);
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if (BN_is_bit_set (x, 0) != isHighestBitSet)
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BN_sub (x, q, x); // x = q - x
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BIGNUM * z = BN_new (), * t = BN_new ();
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BN_one (z); BN_mod_mul (t, x, y, q, ctx); // pre-calculate t
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EDDSAPoint p {x, y, z, t};
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if (!IsOnCurve (p, ctx))
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LogPrint (eLogError, "Decoded point is not on 25519");
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return p;
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}
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void EncodePoint (const EDDSAPoint& p, uint8_t * buf) const
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{
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EncodeBN (p.y, buf,EDDSA25519_PUBLIC_KEY_LENGTH);
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if (BN_is_bit_set (p.x, 0)) // highest bit
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buf[EDDSA25519_PUBLIC_KEY_LENGTH - 1] |= 0x80; // set highest bit
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}
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template<int len>
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BIGNUM * DecodeBN (const uint8_t * buf) const
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{
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// buf is Little Endian convert it to Big Endian
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uint8_t buf1[len];
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for (size_t i = 0; i < len/2; i++) // invert bytes
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{
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buf1[i] = buf[len -1 - i];
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buf1[len -1 - i] = buf[i];
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}
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BIGNUM * res = BN_new ();
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BN_bin2bn (buf1, len, res);
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return res;
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}
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void EncodeBN (const BIGNUM * bn, uint8_t * buf, size_t len) const
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{
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bn2buf (bn, buf, len);
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// To Little Endian
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for (size_t i = 0; i < len/2; i++) // invert bytes
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{
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uint8_t tmp = buf[i];
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buf[i] = buf[len -1 - i];
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buf[len -1 - i] = tmp;
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}
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}
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private:
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BIGNUM * q, * l, * d, * I;
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// transient values
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BIGNUM * two_252_2; // 2^252-2
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EDDSAPoint Bi256[32][128]; // per byte, Bi256[i][j] = (256+j+1)^i*B, we don't store zeroes
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// if j > 128 we use 256 - j and carry 1 to next byte
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// Bi256[0][0] = B, base point
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EDDSAPoint Bi256Carry; // Bi256[32][0]
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};
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static std::unique_ptr<Ed25519> g_Ed25519;
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std::unique_ptr<Ed25519>& GetEd25519 ()
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{
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if (!g_Ed25519)
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g_Ed25519.reset (new Ed25519());
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return g_Ed25519;
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}
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EDDSA25519Verifier::EDDSA25519Verifier (const uint8_t * signingKey)
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{
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memcpy (m_PublicKeyEncoded, signingKey, EDDSA25519_PUBLIC_KEY_LENGTH);
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BN_CTX * ctx = BN_CTX_new ();
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m_PublicKey = GetEd25519 ()->DecodePublicKey (m_PublicKeyEncoded, ctx);
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BN_CTX_free (ctx);
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}
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bool EDDSA25519Verifier::Verify (const uint8_t * buf, size_t len, const uint8_t * signature) const
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{
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uint8_t digest[64];
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SHA512_CTX ctx;
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SHA512_Init (&ctx);
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SHA512_Update (&ctx, signature, EDDSA25519_SIGNATURE_LENGTH/2); // R
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SHA512_Update (&ctx, m_PublicKeyEncoded, EDDSA25519_PUBLIC_KEY_LENGTH); // public key
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SHA512_Update (&ctx, buf, len); // data
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SHA512_Final (digest, &ctx);
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return GetEd25519 ()->Verify (m_PublicKey, digest, signature);
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}
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EDDSA25519Signer::EDDSA25519Signer (const uint8_t * signingPrivateKey)
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{
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// expand key
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SHA512 (signingPrivateKey, EDDSA25519_PRIVATE_KEY_LENGTH, m_ExpandedPrivateKey);
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m_ExpandedPrivateKey[0] &= 0xF8; // drop last 3 bits
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m_ExpandedPrivateKey[EDDSA25519_PRIVATE_KEY_LENGTH - 1] &= 0x1F; // drop first 3 bits
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m_ExpandedPrivateKey[EDDSA25519_PRIVATE_KEY_LENGTH - 1] |= 0x40; // set second bit
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// generate and encode public key
|
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BN_CTX * ctx = BN_CTX_new ();
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auto publicKey = GetEd25519 ()->GeneratePublicKey (m_ExpandedPrivateKey, ctx);
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GetEd25519 ()->EncodePublicKey (publicKey, m_PublicKeyEncoded, ctx);
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BN_CTX_free (ctx);
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}
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void EDDSA25519Signer::Sign (const uint8_t * buf, int len, uint8_t * signature) const
|
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{
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GetEd25519 ()->Sign (m_ExpandedPrivateKey, m_PublicKeyEncoded, buf, len, signature);
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}
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}
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}
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