使用OpenCL为secp256k1从私钥生成公钥

Question

我想从私钥计算公钥。它必须使用OpenCL才能工作。看起来hashcat有一个不错的库，但我不确定如何使用它。

• https://github.com/hashcat/hashcat/blob/master/OpenCL/inc_ecc_secp256k1.h
• https://github.com/hashcat/hashcat/blob/master/OpenCL/inc_ecc_secp256k1.cl

其他库也是可能的。secp256k1 cl似乎很难使用https://github.com/hhanh00/secp256k1-cl/blob/master/secp256k1.cl

请参阅下面的示例，了解它如何基于inc_ecc_secp256k1.cl.工作

我应该在已知基点G上使用parse_public来获得secp256k1_t对象中的坐标吗？然后使用point_mul和我通过k传递的随机秘密以及通过basepoint_precalculated传递的基点G来获得r中的公钥？

// 8+1 to make room for the parity
#define KEY_LENGTH_WITH_PARITY 9
// (32*8 == 256)
#define PRIVATE_KEY_LENGTH 8
// the base point G in compressed form
#define SECP256K1_G0 0x00000002
#define SECP256K1_G1 0x79be667e
#define SECP256K1_G2 0xf9dcbbac
#define SECP256K1_G3 0x55a06295
#define SECP256K1_G4 0xce870b07
#define SECP256K1_G5 0x029bfcdb
#define SECP256K1_G6 0x2dce28d9
#define SECP256K1_G7 0x59f2815b
#define SECP256K1_G8 0x16f81798
__kernel void generateKeysKernel(__global u32 *r, __global const u32 *k)
{
u32 basepoint_g[KEY_LENGTH_WITH_PARITY];
u32 u32r_local[KEY_LENGTH_WITH_PARITY];
u32 u32k_local[PRIVATE_KEY_LENGTH];
secp256k1_t basepoint_precalculated;
basepoint_g[0] = SECP256K1_G0;
basepoint_g[1] = SECP256K1_G1;
basepoint_g[2] = SECP256K1_G2;
basepoint_g[3] = SECP256K1_G3;
basepoint_g[4] = SECP256K1_G4;
basepoint_g[5] = SECP256K1_G5;
basepoint_g[6] = SECP256K1_G6;
basepoint_g[7] = SECP256K1_G7;
basepoint_g[8] = SECP256K1_G8;
// global to local
u32k_local[0] = k[0];
u32k_local[1] = k[1];
u32k_local[2] = k[2];
u32k_local[3] = k[3];
u32k_local[4] = k[4];
u32k_local[5] = k[5];
u32k_local[6] = k[6];
u32k_local[7] = k[7];
parse_public(&basepoint_precalculated, basepoint_g);
point_mul(u32r_local, u32k_local, &basepoint_precalculated);
// local to global
r[0] = u32r_local[0];
r[1] = u32r_local[1];
r[2] = u32r_local[2];
r[3] = u32r_local[3];
r[4] = u32r_local[4];
r[5] = u32r_local[5];
r[6] = u32r_local[6];
r[7] = u32r_local[7];
r[8] = u32r_local[8];
}

Answer 1

我找到了一个有效的解决方案

// finite field Fp
// p = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F
#define SECP256K1_P0 0xfffffc2f
#define SECP256K1_P1 0xfffffffe
#define SECP256K1_P2 0xffffffff
#define SECP256K1_P3 0xffffffff
#define SECP256K1_P4 0xffffffff
#define SECP256K1_P5 0xffffffff
#define SECP256K1_P6 0xffffffff
#define SECP256K1_P7 0xffffffff
// prime order N
// n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141
#define SECP256K1_N0 0xd0364141
#define SECP256K1_N1 0xbfd25e8c
#define SECP256K1_N2 0xaf48a03b
#define SECP256K1_N3 0xbaaedce6
#define SECP256K1_N4 0xfffffffe
#define SECP256K1_N5 0xffffffff
#define SECP256K1_N6 0xffffffff
#define SECP256K1_N7 0xffffffff
// the base point G in compressed form for transform_public
// G = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798
#define SECP256K1_G_PARITY 0x00000002
#define SECP256K1_G0 0x16f81798
#define SECP256K1_G1 0x59f2815b
#define SECP256K1_G2 0x2dce28d9
#define SECP256K1_G3 0x029bfcdb
#define SECP256K1_G4 0xce870b07
#define SECP256K1_G5 0x55a06295
#define SECP256K1_G6 0xf9dcbbac
#define SECP256K1_G7 0x79be667e
// the base point G in compressed form for parse_public
// parity and reversed byte/char (8 bit) byte order
// G = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798
#define SECP256K1_G_STRING0 0x66be7902
#define SECP256K1_G_STRING1 0xbbdcf97e
#define SECP256K1_G_STRING2 0x62a055ac
#define SECP256K1_G_STRING3 0x0b87ce95
#define SECP256K1_G_STRING4 0xfc9b0207
#define SECP256K1_G_STRING5 0x28ce2ddb
#define SECP256K1_G_STRING6 0x81f259d9
#define SECP256K1_G_STRING7 0x17f8165b
#define SECP256K1_G_STRING8 0x00000098
#define SECP256K1_PRE_COMPUTED_XY_SIZE 96
#define SECP256K1_NAF_SIZE 33 // 32+1, we need one extra slot
#define PUBLIC_KEY_LENGTH_WITHOUT_PARITY 8
// 8+1 to make room for the parity
#define PUBLIC_KEY_LENGTH_WITH_PARITY 9
// (32*8 == 256)
#define PRIVATE_KEY_LENGTH 8
__kernel void generateKeysKernel_parse_public(__global u32 *r, __global const u32 *k)
{
u32 g_local[PUBLIC_KEY_LENGTH_WITH_PARITY];
u32 r_local[PUBLIC_KEY_LENGTH_WITH_PARITY];
u32 k_local[PRIVATE_KEY_LENGTH];
secp256k1_t g_xy_local;
g_local[0] = SECP256K1_G_STRING0;
g_local[1] = SECP256K1_G_STRING1;
g_local[2] = SECP256K1_G_STRING2;
g_local[3] = SECP256K1_G_STRING3;
g_local[4] = SECP256K1_G_STRING4;
g_local[5] = SECP256K1_G_STRING5;
g_local[6] = SECP256K1_G_STRING6;
g_local[7] = SECP256K1_G_STRING7;
g_local[8] = SECP256K1_G_STRING8;
// global to local
k_local[0] = k[0];
k_local[1] = k[1];
k_local[2] = k[2];
k_local[3] = k[3];
k_local[4] = k[4];
k_local[5] = k[5];
k_local[6] = k[6];
k_local[7] = k[7];

/*
// example private key (in)
// hex: 68e23530deb6d5011ab56d8ad9f7b4a3b424f1112f08606357497495929f72dc
// decimal: 47440210799387980664936216788675555637818488436833759923669526136462528967388
// WiF
// to generate the public key (out)
// 025d99d81d9e731e0d7eebd1c858b1155da7981b1f0a16d322a361f8b589ad2e3b
// hex:
k_local[7] = 0x68e23530;
k_local[6] = 0xdeb6d501;
k_local[5] = 0x1ab56d8a;
k_local[4] = 0xd9f7b4a3;
k_local[3] = 0xb424f111;
k_local[2] = 0x2f086063;
k_local[1] = 0x57497495;
k_local[0] = 0x929f72dc;
*/
parse_public(&g_xy_local, g_local);
point_mul(r_local, k_local, &g_xy_local);
// local to global
r[0] = r_local[0];
r[1] = r_local[1];
r[2] = r_local[2];
r[3] = r_local[3];
r[4] = r_local[4];
r[5] = r_local[5];
r[6] = r_local[6];
r[7] = r_local[7];
r[8] = r_local[8];
}