/* * Vanitygen, vanity bitcoin address generator * Copyright (C) 2011 * * Vanitygen is free software: you can redistribute it and/or modify * it under the terms of the GNU Affero General Public License as published by * the Free Software Foundation, either version 3 of the License, or * any later version. * * Vanitygen is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU Affero General Public License for more details. * * You should have received a copy of the GNU Affero General Public License * along with Vanitygen. If not, see . */ /* * This file contains an OpenCL kernel for performing certain parts of * the bitcoin address calculation process. * * Kernel: ec_add_grid * * Inputs: * - Row: Array of (sequential) EC points * - Column: Array of column increment EC points (= rowsize * Pgenerator) * * Steps: * - Compute P = Row[x] + Column[y] * P is computed as numerator/denominator components Pxj, Pyj, Pz * Final values are: Px = Pxj / (Pz^2), Py = Pyj / (Pz^3) * * The modular inverse of Pz is required to compute Px and Py, and * can be computed more efficiently in large batches. This is done in * the next kernel heap_invert. * * - Store Pxj, Pyj to intermediate point buffer * - Store Pz to z_heap * * Outputs: * - Intermediate point buffer * - Denominator buffer (z_heap) * * ------------------------------- * Kernel: heap_invert * * Inputs: * - Denominator buffer (z_heap) * - N = Batch size (power of 2) * * Steps: * - Compute the product tree for N values in the denominator buffer * - Compute the modular inverse of the root of the product tree * - Multiply down the tree to compute the modular inverse of each leaf * * Outputs: * - Modular inverse denominator buffer (z_heap) * * ------------------------------- * Kernel: hash_ec_point_get * * Inputs: * - Intermediate point buffer * - Modular inverse denominator buffer (z_heap) * * Steps: * - Compute Px = Pxj * (1/Pz)^2 * - Compute Py = Pyj * (1/Pz)^3 * - Compute H = RIPEMD160(SHA256(0x04 | Px | Py)) * * Output: * - Array of 20-byte address hash values * * ------------------------------- * Kernel: hash_ec_point_search_prefix * * Like hash_ec_point_get, but instead of storing the complete hash * value to an output buffer, it searches a sorted list of ranges, * and if a match is found, writes a flag to an output buffer. */ /* Byte-swapping and endianness */ #define bswap32(v) \ (((v) >> 24) | (((v) >> 8) & 0xff00) | \ (((v) << 8) & 0xff0000) | ((v) << 24)) #if __ENDIAN_LITTLE__ != 1 #define load_le32(v) bswap32(v) #define load_be32(v) (v) #else #define load_le32(v) (v) #define load_be32(v) bswap32(v) #endif /* * Loop unrolling macros * * In most cases, preprocessor unrolling works best. * The exception is NVIDIA's compiler, which seems to take unreasonably * long to compile a loop with a larger iteration count, or a loop with * a body of >50 PTX instructions, with preprocessor unrolling. * However, it does not seem to take as long with pragma unroll, and * produces good output. */ /* Explicit loop unrolling */ #define unroll_5(a) do { a(0) a(1) a(2) a(3) a(4) } while (0) #define unroll_8(a) do { a(0) a(1) a(2) a(3) a(4) a(5) a(6) a(7) } while (0) #define unroll_1_7(a) do { a(1) a(2) a(3) a(4) a(5) a(6) a(7) } while (0) #define unroll_7(a) do { a(0) a(1) a(2) a(3) a(4) a(5) a(6) } while (0) #define unroll_7_0(a) do { a(7) a(6) a(5) a(4) a(3) a(2) a(1) a(0) } while (0) #define unroll_7_1(a) do { a(7) a(6) a(5) a(4) a(3) a(2) a(1) } while (0) #define unroll_16(a) do { \ a(0) a(1) a(2) a(3) a(4) a(5) a(6) a(7) \ a(8) a(9) a(10) a(11) a(12) a(13) a(14) a(15) \ } while (0) #define unroll_64(a) do { \ a(0) a(1) a(2) a(3) a(4) a(5) a(6) a(7) \ a(8) a(9) a(10) a(11) a(12) a(13) a(14) a(15) \ a(16) a(17) a(18) a(19) a(20) a(21) a(22) a(23) \ a(24) a(25) a(26) a(27) a(28) a(29) a(30) a(31) \ a(32) a(33) a(34) a(35) a(36) a(37) a(38) a(39) \ a(40) a(41) a(42) a(43) a(44) a(45) a(46) a(47) \ a(48) a(49) a(50) a(51) a(52) a(53) a(54) a(55) \ a(56) a(57) a(58) a(59) a(60) a(61) a(62) a(63) \ } while (0) /* Conditional loop unrolling */ #if defined(DEEP_PREPROC_UNROLL) #define iter_5(a) unroll_5(a) #define iter_8(a) unroll_8(a) #define iter_16(a) unroll_16(a) #define iter_64(a) unroll_64(a) #else #define iter_5(a) do {int _i; for (_i = 0; _i < 5; _i++) { a(_i) }} while (0) #define iter_8(a) do {int _i; for (_i = 0; _i < 8; _i++) { a(_i) }} while (0) #define iter_16(a) do {int _i; for (_i = 0; _i < 16; _i++) { a(_i) }} while (0) #define iter_64(a) do {int _i; for (_i = 0; _i < 64; _i++) { a(_i) }} while (0) #endif /* * BIGNUM mini-library * This module deals with fixed-size 256-bit bignums. * Where modular arithmetic is performed, the SECP256k1 prime * modulus (below) is assumed. * * Methods include: * - bn_is_zero/bn_is_one/bn_is_odd/bn_is_even/bn_is_bit_set * - bn_rshift[1]/bn_lshift[1] * - bn_neg * - bn_uadd/bn_uadd_p * - bn_usub/bn_usub_p */ typedef uint bn_word; #define BN_NBITS 256 #define BN_WSHIFT 5 #define BN_WBITS (1 << BN_WSHIFT) #define BN_NWORDS ((BN_NBITS/8) / sizeof(bn_word)) #define BN_WORDMAX 0xffffffff #define MODULUS_BYTES \ 0xfffffc2f, 0xfffffffe, 0xffffffff, 0xffffffff, \ 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff typedef struct { bn_word d[BN_NWORDS]; } bignum; __constant bn_word modulus[] = { MODULUS_BYTES }; __constant bignum bn_zero; __constant bn_word mont_rr[BN_NWORDS] = { 0xe90a1, 0x7a2, 0x1, 0, }; __constant bn_word mont_n0[2] = { 0xd2253531, 0xd838091d }; #define bn_is_odd(bn) (bn.d[0] & 1) #define bn_is_even(bn) (!bn_is_odd(bn)) #define bn_is_zero(bn) (!bn.d[0] && !bn.d[1] && !bn.d[2] && \ !bn.d[3] && !bn.d[4] && !bn.d[5] && \ !bn.d[6] && !bn.d[7]) #define bn_is_one(bn) ((bn.d[0] == 1) && !bn.d[1] && !bn.d[2] && \ !bn.d[3] && !bn.d[4] && !bn.d[5] && \ !bn.d[6] && !bn.d[7]) #define bn_is_bit_set(bn, n) \ ((((bn_word*)&bn)[n >> BN_WSHIFT]) & (1 << (n & (BN_WBITS-1)))) #define bn_unroll(e) unroll_8(e) #define bn_unroll_sf(e) unroll_1_7(e) #define bn_unroll_sl(e) unroll_7(e) #define bn_unroll_reverse(e) unroll_7_0(e) #define bn_unroll_reverse_sl(e) unroll_7_1(e) #define bn_unroll_arg(e, arg) \ e(arg, 0) e(arg, 1) e(arg, 2) e(arg, 3) \ e(arg, 4) e(arg, 5) e(arg, 6) e(arg, 7) #define bn_unroll_arg_sf(e, arg) \ e(arg, 1) e(arg, 2) e(arg, 3) \ e(arg, 4) e(arg, 5) e(arg, 6) e(arg, 7) #define bn_iter(e) iter_8(e) /* * Bitwise shift */ void bn_lshift1(bignum *bn) { #define bn_lshift1_inner1(i) \ bn->d[i] = (bn->d[i] << 1) | (bn->d[i-1] >> 31); bn_unroll_reverse_sl(bn_lshift1_inner1); bn->d[0] <<= 1; } void bn_rshift(bignum *bn, int shift) { int wd, iws, iwr; bn_word ihw, ilw; iws = (shift & (BN_WBITS-1)); iwr = BN_WBITS - iws; wd = (shift >> BN_WSHIFT); ihw = (wd < BN_WBITS) ? bn->d[wd] : 0; #define bn_rshift_inner1(i) \ wd++; \ ilw = ihw; \ ihw = (wd < BN_WBITS) ? bn->d[wd] : 0; \ bn->d[i] = (ilw >> iws) | (ihw << iwr); bn_unroll_sl(bn_rshift_inner1); bn->d[BN_NWORDS-1] = (ihw >> iws); } void bn_rshift1(bignum *bn) { #define bn_rshift1_inner1(i) \ bn->d[i] = (bn->d[i+1] << 31) | (bn->d[i] >> 1); bn_unroll_sl(bn_rshift1_inner1); bn->d[BN_NWORDS-1] >>= 1; } void bn_rshift1_2(bignum *bna, bignum *bnb) { #define bn_rshift1_2_inner1(i) \ bna->d[i] = (bna->d[i+1] << 31) | (bna->d[i] >> 1); \ bnb->d[i] = (bnb->d[i+1] << 31) | (bnb->d[i] >> 1); bn_unroll_sl(bn_rshift1_2_inner1); bna->d[BN_NWORDS-1] >>= 1; bnb->d[BN_NWORDS-1] >>= 1; } /* * Unsigned comparison */ int bn_ucmp_ge(bignum *a, bignum *b) { int l = 0, g = 0; #define bn_ucmp_ge_inner1(i) \ if (a->d[i] < b->d[i]) l |= (1 << i); \ if (a->d[i] > b->d[i]) g |= (1 << i); bn_unroll_reverse(bn_ucmp_ge_inner1); return (l > g) ? 0 : 1; } int bn_ucmp_ge_c(bignum *a, __constant bn_word *b) { int l = 0, g = 0; #define bn_ucmp_ge_c_inner1(i) \ if (a->d[i] < b[i]) l |= (1 << i); \ if (a->d[i] > b[i]) g |= (1 << i); bn_unroll_reverse(bn_ucmp_ge_c_inner1); return (l > g) ? 0 : 1; } /* * Negate */ void bn_neg(bignum *n) { int c = 1; #define bn_neg_inner1(i) \ c = (n->d[i] = (~n->d[i]) + c) ? 0 : c; bn_unroll(bn_neg_inner1); } /* * Add/subtract */ #define bn_add_word(r, a, b, t, c) do { \ t = a + b; \ c = (t < a) ? 1 : 0; \ r = t; \ } while (0) #define bn_addc_word(r, a, b, t, c) do { \ t = a + b + c; \ c = (t < a) ? 1 : ((c & (t == a)) ? 1 : 0); \ r = t; \ } while (0) bn_word bn_uadd_words_seq(bn_word *r, bn_word *a, bn_word *b) { bn_word t, c = 0; #define bn_uadd_words_seq_inner1(i) \ bn_addc_word(r[i], a[i], b[i], t, c); bn_add_word(r[0], a[0], b[0], t, c); bn_unroll_sf(bn_uadd_words_seq_inner1); return c; } bn_word bn_uadd_words_c_seq(bn_word *r, bn_word *a, __constant bn_word *b) { bn_word t, c = 0; bn_add_word(r[0], a[0], b[0], t, c); bn_unroll_sf(bn_uadd_words_seq_inner1); return c; } #define bn_sub_word(r, a, b, t, c) do { \ t = a - b; \ c = (a < b) ? 1 : 0; \ r = t; \ } while (0) #define bn_subb_word(r, a, b, t, c) do { \ t = a - (b + c); \ c = (!(a) && c) ? 1 : 0; \ c |= (a < b) ? 1 : 0; \ r = t; \ } while (0) bn_word bn_usub_words_seq(bn_word *r, bn_word *a, bn_word *b) { bn_word t, c = 0; #define bn_usub_words_seq_inner1(i) \ bn_subb_word(r[i], a[i], b[i], t, c); bn_sub_word(r[0], a[0], b[0], t, c); bn_unroll_sf(bn_usub_words_seq_inner1); return c; } bn_word bn_usub_words_c_seq(bn_word *r, bn_word *a, __constant bn_word *b) { bn_word t, c = 0; bn_sub_word(r[0], a[0], b[0], t, c); bn_unroll_sf(bn_usub_words_seq_inner1); return c; } /* * Add/subtract better suited for AMD's VLIW architecture */ bn_word bn_uadd_words_vliw(bn_word *r, bn_word *a, bn_word *b) { bignum x; bn_word c = 0, cp = 0; #define bn_uadd_words_vliw_inner1(i) \ x.d[i] = a[i] + b[i]; #define bn_uadd_words_vliw_inner2(i) \ c |= (a[i] > x.d[i]) ? (1 << i) : 0; \ cp |= (!~x.d[i]) ? (1 << i) : 0; #define bn_uadd_words_vliw_inner3(i) \ r[i] = x.d[i] + ((c >> i) & 1); bn_unroll(bn_uadd_words_vliw_inner1); bn_unroll(bn_uadd_words_vliw_inner2); c = ((cp + (c << 1)) ^ cp); r[0] = x.d[0]; bn_unroll_sf(bn_uadd_words_vliw_inner3); return c >> BN_NWORDS; } bn_word bn_uadd_words_c_vliw(bn_word *r, bn_word *a, __constant bn_word *b) { bignum x; bn_word c = 0, cp = 0; bn_unroll(bn_uadd_words_vliw_inner1); bn_unroll(bn_uadd_words_vliw_inner2); c = ((cp + (c << 1)) ^ cp); r[0] = x.d[0]; bn_unroll_sf(bn_uadd_words_vliw_inner3); return c >> BN_NWORDS; } bn_word bn_usub_words_vliw(bn_word *r, bn_word *a, bn_word *b) { bignum x; bn_word c = 0, cp = 0; #define bn_usub_words_vliw_inner1(i) \ x.d[i] = a[i] - b[i]; #define bn_usub_words_vliw_inner2(i) \ c |= (a[i] < b[i]) ? (1 << i) : 0; \ cp |= (!x.d[i]) ? (1 << i) : 0; #define bn_usub_words_vliw_inner3(i) \ r[i] = x.d[i] - ((c >> i) & 1); bn_unroll(bn_usub_words_vliw_inner1); bn_unroll(bn_usub_words_vliw_inner2); c = ((cp + (c << 1)) ^ cp); r[0] = x.d[0]; bn_unroll_sf(bn_usub_words_vliw_inner3); return c >> BN_NWORDS; } bn_word bn_usub_words_c_vliw(bn_word *r, bn_word *a, __constant bn_word *b) { bignum x; bn_word c = 0, cp = 0; bn_unroll(bn_usub_words_vliw_inner1); bn_unroll(bn_usub_words_vliw_inner2); c = ((cp + (c << 1)) ^ cp); r[0] = x.d[0]; bn_unroll_sf(bn_usub_words_vliw_inner3); return c >> BN_NWORDS; } #if defined(DEEP_VLIW) #define bn_uadd_words bn_uadd_words_vliw #define bn_uadd_words_c bn_uadd_words_c_vliw #define bn_usub_words bn_usub_words_vliw #define bn_usub_words_c bn_usub_words_c_vliw #else #define bn_uadd_words bn_uadd_words_seq #define bn_uadd_words_c bn_uadd_words_c_seq #define bn_usub_words bn_usub_words_seq #define bn_usub_words_c bn_usub_words_c_seq #endif #define bn_uadd(r, a, b) bn_uadd_words((r)->d, (a)->d, (b)->d) #define bn_uadd_c(r, a, b) bn_uadd_words_c((r)->d, (a)->d, b) #define bn_usub(r, a, b) bn_usub_words((r)->d, (a)->d, (b)->d) #define bn_usub_c(r, a, b) bn_usub_words_c((r)->d, (a)->d, b) /* * Modular add/sub */ void bn_mod_add(bignum *r, bignum *a, bignum *b) { if (bn_uadd(r, a, b) || (bn_ucmp_ge_c(r, modulus))) bn_usub_c(r, r, modulus); } void bn_mod_sub(bignum *r, bignum *a, bignum *b) { if (bn_usub(r, a, b)) bn_uadd_c(r, r, modulus); } void bn_mod_lshift1(bignum *bn) { bn_word c = (bn->d[BN_NWORDS-1] & 0x80000000); bn_lshift1(bn); if (c || (bn_ucmp_ge_c(bn, modulus))) bn_usub_c(bn, bn, modulus); } /* * Montgomery multiplication * * This includes normal multiplication of two "Montgomeryized" * bignums, and bn_from_mont for de-Montgomeryizing a bignum. */ #define bn_mul_word(r, a, w, c, p, s) do { \ r = (a * w) + c; \ p = mul_hi(a, w); \ c = (r < c) ? p + 1 : p; \ } while (0) #define bn_mul_add_word(r, a, w, c, p, s) do { \ s = r + c; \ p = mul_hi(a, w); \ r = (a * w) + s; \ c = (s < c) ? p + 1 : p; \ if (r < s) c++; \ } while (0) void bn_mul_mont(bignum *r, bignum *a, bignum *b) { bignum t; bn_word tea, teb, c, p, s, m; #if !defined(VERY_EXPENSIVE_BRANCHES) int q; #endif c = 0; #define bn_mul_mont_inner1(j) \ bn_mul_word(t.d[j], a->d[j], b->d[0], c, p, s); bn_unroll(bn_mul_mont_inner1); tea = c; teb = 0; c = 0; m = t.d[0] * mont_n0[0]; bn_mul_add_word(t.d[0], modulus[0], m, c, p, s); #define bn_mul_mont_inner2(j) \ bn_mul_add_word(t.d[j], modulus[j], m, c, p, s); \ t.d[j-1] = t.d[j]; bn_unroll_sf(bn_mul_mont_inner2); t.d[BN_NWORDS-1] = tea + c; tea = teb + ((t.d[BN_NWORDS-1] < c) ? 1 : 0); #define bn_mul_mont_inner3_1(i, j) \ bn_mul_add_word(t.d[j], a->d[j], b->d[i], c, p, s); #define bn_mul_mont_inner3_2(i, j) \ bn_mul_add_word(t.d[j], modulus[j], m, c, p, s); \ t.d[j-1] = t.d[j]; #define bn_mul_mont_inner3(i) \ c = 0; \ bn_unroll_arg(bn_mul_mont_inner3_1, i); \ tea += c; \ teb = ((tea < c) ? 1 : 0); \ c = 0; \ m = t.d[0] * mont_n0[0]; \ bn_mul_add_word(t.d[0], modulus[0], m, c, p, s); \ bn_unroll_arg_sf(bn_mul_mont_inner3_2, i); \ t.d[BN_NWORDS-1] = tea + c; \ tea = teb + ((t.d[BN_NWORDS-1] < c) ? 1 : 0); /* * The outer loop here is quite long, and we won't unroll it * unless VERY_EXPENSIVE_BRANCHES is set. */ #if defined(VERY_EXPENSIVE_BRANCHES) bn_unroll_sf(bn_mul_mont_inner3); c = tea | !bn_usub_c(r, &t, modulus); if (!c) *r = t; #else for (q = 1; q < BN_NWORDS; q++) { bn_mul_mont_inner3(q); } c = tea || (t.d[BN_NWORDS-1] >= modulus[BN_NWORDS-1]); if (c) { c = tea | !bn_usub_c(r, &t, modulus); if (c) return; } *r = t; #endif } void bn_from_mont(bignum *rb, bignum *b) { #define WORKSIZE ((2*BN_NWORDS) + 1) bn_word r[WORKSIZE]; bn_word m, c, p, s; #if defined(PRAGMA_UNROLL) int i; #endif /* Copy the input to the working area */ /* Zero the upper words */ #define bn_from_mont_inner1(i) \ r[i] = b->d[i]; #define bn_from_mont_inner2(i) \ r[BN_NWORDS+i] = 0; bn_unroll(bn_from_mont_inner1); bn_unroll(bn_from_mont_inner2); r[WORKSIZE-1] = 0; /* Multiply (long) by modulus */ #define bn_from_mont_inner3_1(i, j) \ bn_mul_add_word(r[i+j], modulus[j], m, c, p, s); #if !defined(VERY_EXPENSIVE_BRANCHES) #define bn_from_mont_inner3_2(i) \ if (r[BN_NWORDS + i] < c) \ r[BN_NWORDS + i + 1] += 1; #else #define bn_from_mont_inner3_2(i) \ r[BN_NWORDS + i + 1] += (r[BN_NWORDS + i] < c) ? 1 : 0; #endif #define bn_from_mont_inner3(i) \ m = r[i] * mont_n0[0]; \ c = 0; \ bn_unroll_arg(bn_from_mont_inner3_1, i); \ r[BN_NWORDS + i] += c; \ bn_from_mont_inner3_2(i) /* * The outer loop here is not very long, so we will unroll * it by default. However, it's just complicated enough to * cause NVIDIA's compiler to take unreasonably long to compile * it, unless we use pragma unroll. */ #if !defined(PRAGMA_UNROLL) bn_iter(bn_from_mont_inner3); #else #pragma unroll 8 for (i = 0; i < BN_NWORDS; i++) { bn_from_mont_inner3(i) } #endif /* * Make sure the result is less than the modulus. * Subtracting is not much more expensive than compare, so * subtract always and assign based on the carry out value. */ c = bn_usub_words_c(rb->d, &r[BN_NWORDS], modulus); if (c) { #define bn_from_mont_inner4(i) \ rb->d[i] = r[BN_NWORDS + i]; bn_unroll(bn_from_mont_inner4); } } /* * Modular inversion */ void bn_mod_inverse(bignum *r, bignum *n) { bignum a, b, x, y; int shift; bn_word xc, yc; for (shift = 0; shift < BN_NWORDS; shift++) { a.d[shift] = modulus[shift]; x.d[shift] = 0; y.d[shift] = 0; } b = *n; x.d[0] = 1; xc = 0; yc = 0; while (!bn_is_zero(b)) { shift = 0; while (!bn_is_odd(b)) { if (bn_is_odd(x)) xc += bn_uadd_c(&x, &x, modulus); bn_rshift1_2(&x, &b); x.d[7] |= (xc << 31); xc >>= 1; } while (!bn_is_odd(a)) { if (bn_is_odd(y)) yc += bn_uadd_c(&y, &y, modulus); bn_rshift1_2(&y, &a); y.d[7] |= (yc << 31); yc >>= 1; } if (bn_ucmp_ge(&b, &a)) { xc += yc + bn_uadd(&x, &x, &y); bn_usub(&b, &b, &a); } else { yc += xc + bn_uadd(&y, &y, &x); bn_usub(&a, &a, &b); } } if (!bn_is_one(a)) { /* no modular inverse */ *r = bn_zero; } else { /* Compute y % m as cheaply as possible */ while (yc < 0x80000000) yc -= bn_usub_c(&y, &y, modulus); bn_neg(&y); *r = y; } } /* * HASH FUNCTIONS * * BYTE ORDER NOTE: None of the hash functions below deal with byte * order. The caller is expected to be aware of this when it stuffs * data into in the native integer. * * NOTE #2: Endianness of the OpenCL device makes no difference here. */ #define hash256_unroll(a) unroll_8(a) #define hash160_unroll(a) unroll_5(a) #define hash256_iter(a) iter_8(a) #define hash160_iter(a) iter_5(a) /* * SHA-2 256 * * CAUTION: Input buffer will be overwritten/mangled. * Data expected in big-endian format. * This implementation is designed for space efficiency more than * raw speed. */ __constant uint sha2_init[8] = { 0x6a09e667, 0xbb67ae85, 0x3c6ef372, 0xa54ff53a, 0x510e527f, 0x9b05688c, 0x1f83d9ab, 0x5be0cd19 }; __constant uint sha2_k[64] = { 0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5, 0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174, 0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da, 0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967, 0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85, 0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070, 0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3, 0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2 }; void sha2_256_init(uint *out) { #define sha2_256_init_inner_1(i) \ out[i] = sha2_init[i]; hash256_unroll(sha2_256_init_inner_1); } /* The state variable remapping is really contorted */ #define sha2_stvar(vals, i, v) vals[(64+v-i) % 8] #define sha2_s0(a) (rotate(a, 30U) ^ rotate(a, 19U) ^ rotate(a, 10U)) #define sha2_s1(a) (rotate(a, 26U) ^ rotate(a, 21U) ^ rotate(a, 7U)) #if defined(AMD_BFI_INT) #pragma OPENCL EXTENSION cl_amd_media_ops : enable #define sha2_ch(a, b, c) amd_bytealign(a, b, c) #define sha2_ma(a, b, c) amd_bytealign((a^c), b, a) #else #define sha2_ch(a, b, c) (c ^ (a & (b ^ c))) #define sha2_ma(a, b, c) ((a & c) | (b & (a | c))) #endif void sha2_256_block(uint *out, uint *in) { uint state[8], t1, t2; #if defined(PRAGMA_UNROLL) int i; #endif #define sha2_256_block_inner_1(i) \ state[i] = out[i]; hash256_unroll(sha2_256_block_inner_1); #define sha2_256_block_inner_2(i) \ if (i >= 16) { \ t1 = in[(i + 1) % 16]; \ t2 = in[(i + 14) % 16]; \ in[i % 16] += (in[(i + 9) % 16] + \ (rotate(t1, 25U) ^ rotate(t1, 14U) ^ (t1 >> 3)) + \ (rotate(t2, 15U) ^ rotate(t2, 13U) ^ (t2 >> 10))); \ } \ t1 = (sha2_stvar(state, i, 7) + \ sha2_s1(sha2_stvar(state, i, 4)) + \ sha2_ch(sha2_stvar(state, i, 4), \ sha2_stvar(state, i, 5), \ sha2_stvar(state, i, 6)) + \ sha2_k[i] + \ in[i % 16]); \ t2 = (sha2_s0(sha2_stvar(state, i, 0)) + \ sha2_ma(sha2_stvar(state, i, 0), \ sha2_stvar(state, i, 1), \ sha2_stvar(state, i, 2))); \ sha2_stvar(state, i, 3) += t1; \ sha2_stvar(state, i, 7) = t1 + t2; \ #if !defined(PRAGMA_UNROLL) iter_64(sha2_256_block_inner_2); #else #pragma unroll 64 for (i = 0; i < 64; i++) { sha2_256_block_inner_2(i) } #endif #define sha2_256_block_inner_3(i) \ out[i] += state[i]; hash256_unroll(sha2_256_block_inner_3); } /* * RIPEMD160 * * Data expected in little-endian format. */ __constant uint ripemd160_iv[] = { 0x67452301, 0xEFCDAB89, 0x98BADCFE, 0x10325476, 0xC3D2E1F0 }; __constant uint ripemd160_k[] = { 0x00000000, 0x5A827999, 0x6ED9EBA1, 0x8F1BBCDC, 0xA953FD4E }; __constant uint ripemd160_kp[] = { 0x50A28BE6, 0x5C4DD124, 0x6D703EF3, 0x7A6D76E9, 0x00000000 }; __constant uchar ripemd160_ws[] = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 7, 4, 13, 1, 10, 6, 15, 3, 12, 0, 9, 5, 2, 14, 11, 8, 3, 10, 14, 4, 9, 15, 8, 1, 2, 7, 0, 6, 13, 11, 5, 12, 1, 9, 11, 10, 0, 8, 12, 4, 13, 3, 7, 15, 14, 5, 6, 2, 4, 0, 5, 9, 7, 12, 2, 10, 14, 1, 3, 8, 11, 6, 15, 13, }; __constant uchar ripemd160_wsp[] = { 5, 14, 7, 0, 9, 2, 11, 4, 13, 6, 15, 8, 1, 10, 3, 12, 6, 11, 3, 7, 0, 13, 5, 10, 14, 15, 8, 12, 4, 9, 1, 2, 15, 5, 1, 3, 7, 14, 6, 9, 11, 8, 12, 2, 10, 0, 4, 13, 8, 6, 4, 1, 3, 11, 15, 0, 5, 12, 2, 13, 9, 7, 10, 14, 12, 15, 10, 4, 1, 5, 8, 7, 6, 2, 13, 14, 0, 3, 9, 11 }; __constant uchar ripemd160_rl[] = { 11, 14, 15, 12, 5, 8, 7, 9, 11, 13, 14, 15, 6, 7, 9, 8, 7, 6, 8, 13, 11, 9, 7, 15, 7, 12, 15, 9, 11, 7, 13, 12, 11, 13, 6, 7, 14, 9, 13, 15, 14, 8, 13, 6, 5, 12, 7, 5, 11, 12, 14, 15, 14, 15, 9, 8, 9, 14, 5, 6, 8, 6, 5, 12, 9, 15, 5, 11, 6, 8, 13, 12, 5, 12, 13, 14, 11, 8, 5, 6, }; __constant uchar ripemd160_rlp[] = { 8, 9, 9, 11, 13, 15, 15, 5, 7, 7, 8, 11, 14, 14, 12, 6, 9, 13, 15, 7, 12, 8, 9, 11, 7, 7, 12, 7, 6, 15, 13, 11, 9, 7, 15, 11, 8, 6, 6, 14, 12, 13, 5, 14, 13, 13, 7, 5, 15, 5, 8, 11, 14, 14, 6, 14, 6, 9, 12, 9, 12, 5, 15, 8, 8, 5, 12, 9, 12, 5, 14, 6, 8, 13, 6, 5, 15, 13, 11, 11 }; #define ripemd160_val(v, i, n) (v)[(80+(n)-(i)) % 5] #define ripemd160_valp(v, i, n) (v)[5 + ((80+(n)-(i)) % 5)] #if defined(AMD_BFI_INT) #define ripemd160_f0(x, y, z) (x ^ y ^ z) #define ripemd160_f1(x, y, z) amd_bytealign(x, y, z) #define ripemd160_f2(x, y, z) (z ^ (x | ~y)) #define ripemd160_f3(x, y, z) amd_bytealign(z, x, y) #define ripemd160_f4(x, y, z) (x ^ (y | ~z)) #else #define ripemd160_f0(x, y, z) (x ^ y ^ z) #define ripemd160_f1(x, y, z) ((x & y) | (~x & z)) #define ripemd160_f2(x, y, z) (z ^ (x | ~y)) #define ripemd160_f3(x, y, z) ((x & z) | (y & ~z)) #define ripemd160_f4(x, y, z) (x ^ (y | ~z)) #endif #define ripemd160_round(i, in, vals, f, fp, t) do { \ ripemd160_val(vals, i, 0) = \ rotate(ripemd160_val(vals, i, 0) + \ f(ripemd160_val(vals, i, 1), \ ripemd160_val(vals, i, 2), \ ripemd160_val(vals, i, 3)) + \ in[ripemd160_ws[i]] + \ ripemd160_k[i / 16], \ (uint)ripemd160_rl[i]) + \ ripemd160_val(vals, i, 4); \ ripemd160_val(vals, i, 2) = \ rotate(ripemd160_val(vals, i, 2), 10U); \ ripemd160_valp(vals, i, 0) = \ rotate(ripemd160_valp(vals, i, 0) + \ fp(ripemd160_valp(vals, i, 1), \ ripemd160_valp(vals, i, 2), \ ripemd160_valp(vals, i, 3)) + \ in[ripemd160_wsp[i]] + \ ripemd160_kp[i / 16], \ (uint)ripemd160_rlp[i]) + \ ripemd160_valp(vals, i, 4); \ ripemd160_valp(vals, i, 2) = \ rotate(ripemd160_valp(vals, i, 2), 10U); \ } while (0) void ripemd160_init(uint *out) { #define ripemd160_init_inner_1(i) \ out[i] = ripemd160_iv[i]; hash160_unroll(ripemd160_init_inner_1); } void ripemd160_block(uint *out, uint *in) { uint vals[10], t; #if defined(PRAGMA_UNROLL) int i; #endif #define ripemd160_block_inner_1(i) \ vals[i] = vals[i + 5] = out[i]; hash160_unroll(ripemd160_block_inner_1); #define ripemd160_block_inner_p0(i) \ ripemd160_round(i, in, vals, \ ripemd160_f0, ripemd160_f4, t); #define ripemd160_block_inner_p1(i) \ ripemd160_round((16 + i), in, vals, \ ripemd160_f1, ripemd160_f3, t); #define ripemd160_block_inner_p2(i) \ ripemd160_round((32 + i), in, vals, \ ripemd160_f2, ripemd160_f2, t); #define ripemd160_block_inner_p3(i) \ ripemd160_round((48 + i), in, vals, \ ripemd160_f3, ripemd160_f1, t); #define ripemd160_block_inner_p4(i) \ ripemd160_round((64 + i), in, vals, \ ripemd160_f4, ripemd160_f0, t); #if !defined(PRAGMA_UNROLL) iter_16(ripemd160_block_inner_p0); iter_16(ripemd160_block_inner_p1); iter_16(ripemd160_block_inner_p2); iter_16(ripemd160_block_inner_p3); iter_16(ripemd160_block_inner_p4); #else #pragma unroll 16 for (i = 0; i < 16; i++) { ripemd160_block_inner_p0(i); } #pragma unroll 16 for (i = 0; i < 16; i++) { ripemd160_block_inner_p1(i); } #pragma unroll 16 for (i = 0; i < 16; i++) { ripemd160_block_inner_p2(i); } #pragma unroll 16 for (i = 0; i < 16; i++) { ripemd160_block_inner_p3(i); } #pragma unroll 16 for (i = 0; i < 16; i++) { ripemd160_block_inner_p4(i); } #endif t = out[1] + vals[2] + vals[8]; out[1] = out[2] + vals[3] + vals[9]; out[2] = out[3] + vals[4] + vals[5]; out[3] = out[4] + vals[0] + vals[6]; out[4] = out[0] + vals[1] + vals[7]; out[0] = t; } #ifdef TEST_KERNELS /* * Test kernels */ /* Montgomery multiplication test kernel */ __kernel void test_mul_mont(__global bignum *products_out, __global bignum *nums_in) { bignum a, b, c; int o; o = get_global_id(0); nums_in += (2*o); a = nums_in[0]; b = nums_in[1]; bn_mul_mont(&c, &a, &b); products_out[o] = c; } /* modular inversion test kernel */ __kernel void test_mod_inverse(__global bignum *inv_out, __global bignum *nums_in, int count) { bignum x, xp; int i, o; o = get_global_id(0) * count; for (i = 0; i < count; i++) { x = nums_in[o]; bn_mod_inverse(&xp, &x); inv_out[o++] = xp; } } #endif /* TEST_KERNELS */ #define ACCESS_BUNDLE 1024 #define ACCESS_STRIDE (ACCESS_BUNDLE/BN_NWORDS) __kernel void ec_add_grid(__global bn_word *points_out, __global bn_word *z_heap, __global bn_word *row_in, __global bignum *col_in) { bignum rx, ry; bignum x1, y1, a, b, c, d, e, z; bn_word cy; int i, cell, start; /* Load the row increment point */ i = 2 * get_global_id(1); rx = col_in[i]; ry = col_in[i+1]; cell = get_global_id(0); start = ((((2 * cell) / ACCESS_STRIDE) * ACCESS_BUNDLE) + (cell % (ACCESS_STRIDE/2))); #define ec_add_grid_inner_1(i) \ x1.d[i] = row_in[start + (i*ACCESS_STRIDE)]; bn_unroll(ec_add_grid_inner_1); start += (ACCESS_STRIDE/2); #define ec_add_grid_inner_2(i) \ y1.d[i] = row_in[start + (i*ACCESS_STRIDE)]; bn_unroll(ec_add_grid_inner_2); bn_mod_sub(&z, &x1, &rx); cell += (get_global_id(1) * get_global_size(0)); start = (((cell / ACCESS_STRIDE) * ACCESS_BUNDLE) + (cell % ACCESS_STRIDE)); #define ec_add_grid_inner_3(i) \ z_heap[start + (i*ACCESS_STRIDE)] = z.d[i]; bn_unroll(ec_add_grid_inner_3); bn_mod_sub(&b, &y1, &ry); bn_mod_add(&c, &x1, &rx); bn_mod_add(&d, &y1, &ry); bn_mul_mont(&y1, &b, &b); bn_mul_mont(&x1, &z, &z); bn_mul_mont(&e, &c, &x1); bn_mod_sub(&y1, &y1, &e); /* * This disgusting code caters to the global memory unit on * various GPUs, by giving it a nice contiguous patch to write * per warp/wavefront. */ start = ((((2 * cell) / ACCESS_STRIDE) * ACCESS_BUNDLE) + (cell % (ACCESS_STRIDE/2))); #define ec_add_grid_inner_4(i) \ points_out[start + (i*ACCESS_STRIDE)] = y1.d[i]; bn_unroll(ec_add_grid_inner_4); bn_mod_lshift1(&y1); bn_mod_sub(&y1, &e, &y1); bn_mul_mont(&y1, &y1, &b); bn_mul_mont(&a, &x1, &z); bn_mul_mont(&c, &d, &a); bn_mod_sub(&y1, &y1, &c); cy = 0; if (bn_is_odd(y1)) cy = bn_uadd_c(&y1, &y1, modulus); bn_rshift1(&y1); y1.d[BN_NWORDS-1] |= (cy ? 0x80000000 : 0); start += (ACCESS_STRIDE/2); bn_unroll(ec_add_grid_inner_4); } __kernel void heap_invert(__global bn_word *z_heap, int batch) { bignum a, b, c, z; int i, off, lcell, hcell, start; #define heap_invert_inner_load_a(j) \ a.d[j] = z_heap[start + j*ACCESS_STRIDE]; #define heap_invert_inner_load_b(j) \ b.d[j] = z_heap[start + j*ACCESS_STRIDE]; #define heap_invert_inner_load_z(j) \ z.d[j] = z_heap[start + j*ACCESS_STRIDE]; #define heap_invert_inner_store_z(j) \ z_heap[start + j*ACCESS_STRIDE] = z.d[j]; #define heap_invert_inner_store_c(j) \ z_heap[start + j*ACCESS_STRIDE] = c.d[j]; off = get_global_size(0); lcell = get_global_id(0); hcell = (off * batch) + lcell; for (i = 0; i < (batch-1); i++) { start = (((lcell / ACCESS_STRIDE) * ACCESS_BUNDLE) + (lcell % ACCESS_STRIDE)); bn_unroll(heap_invert_inner_load_a); lcell += off; start = (((lcell / ACCESS_STRIDE) * ACCESS_BUNDLE) + (lcell % ACCESS_STRIDE)); bn_unroll(heap_invert_inner_load_b); bn_mul_mont(&z, &a, &b); start = (((hcell / ACCESS_STRIDE) * ACCESS_BUNDLE) + (hcell % ACCESS_STRIDE)); bn_unroll(heap_invert_inner_store_z); lcell += off; hcell += off; } /* Invert the root, fix up 1/ZR -> R/Z */ bn_mod_inverse(&z, &z); #define heap_invert_inner_1(i) \ a.d[i] = mont_rr[i]; bn_unroll(heap_invert_inner_1); bn_mul_mont(&z, &z, &a); bn_mul_mont(&z, &z, &a); /* Unroll the first iteration to avoid a load/store on the root */ lcell -= (off << 1); hcell -= (off << 1); start = (((lcell / ACCESS_STRIDE) * ACCESS_BUNDLE) + (lcell % ACCESS_STRIDE)); bn_unroll(heap_invert_inner_load_a); lcell += off; start = (((lcell / ACCESS_STRIDE) * ACCESS_BUNDLE) + (lcell % ACCESS_STRIDE)); bn_unroll(heap_invert_inner_load_b); bn_mul_mont(&c, &a, &z); bn_unroll(heap_invert_inner_store_c); bn_mul_mont(&c, &b, &z); lcell -= off; start = (((lcell / ACCESS_STRIDE) * ACCESS_BUNDLE) + (lcell % ACCESS_STRIDE)); bn_unroll(heap_invert_inner_store_c); lcell -= (off << 1); for (i = 0; i < (batch-2); i++) { start = (((hcell / ACCESS_STRIDE) * ACCESS_BUNDLE) + (hcell % ACCESS_STRIDE)); bn_unroll(heap_invert_inner_load_z); start = (((lcell / ACCESS_STRIDE) * ACCESS_BUNDLE) + (lcell % ACCESS_STRIDE)); bn_unroll(heap_invert_inner_load_a); lcell += off; start = (((lcell / ACCESS_STRIDE) * ACCESS_BUNDLE) + (lcell % ACCESS_STRIDE)); bn_unroll(heap_invert_inner_load_b); bn_mul_mont(&c, &a, &z); bn_unroll(heap_invert_inner_store_c); bn_mul_mont(&c, &b, &z); lcell -= off; start = (((lcell / ACCESS_STRIDE) * ACCESS_BUNDLE) + (lcell % ACCESS_STRIDE)); bn_unroll(heap_invert_inner_store_c); lcell -= (off << 1); hcell -= off; } } void hash_ec_point(uint *hash_out, __global bn_word *xy, __global bn_word *zip) { uint hash1[16], hash2[16]; bignum c, zi, zzi; bn_word wh, wl; /* * Multiply the coordinates by the inverted Z values. * Stash the coordinates in the hash buffer. * SHA-2 requires big endian, and our intended hash input * is big-endian, so swapping is unnecessary, but * inserting the format byte in front causes a headache. */ #define hash_ec_point_inner_1(i) \ zi.d[i] = zip[i*ACCESS_STRIDE]; bn_unroll(hash_ec_point_inner_1); bn_mul_mont(&zzi, &zi, &zi); /* 1 / Z^2 */ #define hash_ec_point_inner_2(i) \ c.d[i] = xy[i*ACCESS_STRIDE]; bn_unroll(hash_ec_point_inner_2); bn_mul_mont(&c, &c, &zzi); /* X / Z^2 */ bn_from_mont(&c, &c); wh = 0x00000004; /* POINT_CONVERSION_UNCOMPRESSED */ #define hash_ec_point_inner_3(i) \ wl = wh; \ wh = c.d[(BN_NWORDS - 1) - i]; \ hash1[i] = (wl << 24) | (wh >> 8); bn_unroll(hash_ec_point_inner_3); bn_mul_mont(&zzi, &zzi, &zi); /* 1 / Z^3 */ #define hash_ec_point_inner_4(i) \ c.d[i] = xy[(ACCESS_STRIDE/2) + i*ACCESS_STRIDE]; bn_unroll(hash_ec_point_inner_4); bn_mul_mont(&c, &c, &zzi); /* Y / Z^3 */ bn_from_mont(&c, &c); #define hash_ec_point_inner_5(i) \ wl = wh; \ wh = c.d[(BN_NWORDS - 1) - i]; \ hash1[BN_NWORDS + i] = (wl << 24) | (wh >> 8); bn_unroll(hash_ec_point_inner_5); /* * Hash the first 64 bytes of the buffer */ sha2_256_init(hash2); sha2_256_block(hash2, hash1); /* * Hash the last byte of the buffer + SHA-2 padding */ hash1[0] = wh << 24 | 0x800000; hash1[1] = 0; hash1[2] = 0; hash1[3] = 0; hash1[4] = 0; hash1[5] = 0; hash1[6] = 0; hash1[7] = 0; hash1[8] = 0; hash1[9] = 0; hash1[10] = 0; hash1[11] = 0; hash1[12] = 0; hash1[13] = 0; hash1[14] = 0; hash1[15] = 65 * 8; sha2_256_block(hash2, hash1); /* * Hash the SHA-2 result with RIPEMD160 * Unfortunately, SHA-2 outputs big-endian, but * RIPEMD160 expects little-endian. Need to swap! */ #define hash_ec_point_inner_6(i) \ hash2[i] = bswap32(hash2[i]); hash256_unroll(hash_ec_point_inner_6); hash2[8] = bswap32(0x80000000); hash2[9] = 0; hash2[10] = 0; hash2[11] = 0; hash2[12] = 0; hash2[13] = 0; hash2[14] = 32 * 8; hash2[15] = 0; ripemd160_init(hash_out); ripemd160_block(hash_out, hash2); } __kernel void hash_ec_point_get(__global uint *hashes_out, __global bn_word *points_in, __global bn_word *z_heap) { uint hash[5]; int i, p, cell, start; cell = ((get_global_id(1) * get_global_size(0)) + get_global_id(0)); start = (((cell / ACCESS_STRIDE) * ACCESS_BUNDLE) + (cell % ACCESS_STRIDE)); z_heap += start; start = ((((2 * cell) / ACCESS_STRIDE) * ACCESS_BUNDLE) + (cell % (ACCESS_STRIDE/2))); points_in += start; /* Complete the coordinates and hash */ hash_ec_point(hash, points_in, z_heap); p = get_global_size(0); i = p * get_global_id(1); hashes_out += 5 * (i + get_global_id(0)); /* Output the hash in proper byte-order */ #define hash_ec_point_get_inner_1(i) \ hashes_out[i] = load_le32(hash[i]); hash160_unroll(hash_ec_point_get_inner_1); } /* * Normally this would be one function that compared two hash160s. * This one compares a hash160 with an upper and lower bound in one * function to work around a problem with AMD's OpenCL compiler. */ int hash160_ucmp_g(uint *a, __global uint *bound) { uint gv; #define hash160_ucmp_g_inner_1(i) \ gv = load_be32(bound[i]); \ if (a[i] < gv) return -1; \ if (a[i] > gv) break; hash160_iter(hash160_ucmp_g_inner_1); #define hash160_ucmp_g_inner_2(i) \ gv = load_be32(bound[5+i]); \ if (a[i] < gv) return 0; \ if (a[i] > gv) return 1; hash160_iter(hash160_ucmp_g_inner_2); return 0; } __kernel void hash_ec_point_search_prefix(__global uint *found, __global bn_word *points_in, __global bn_word *z_heap, __global uint *target_table, int ntargets) { uint hash[5]; int i, high, low, p, cell, start; cell = ((get_global_id(1) * get_global_size(0)) + get_global_id(0)); start = (((cell / ACCESS_STRIDE) * ACCESS_BUNDLE) + (cell % ACCESS_STRIDE)); z_heap += start; start = ((((2 * cell) / ACCESS_STRIDE) * ACCESS_BUNDLE) + (cell % (ACCESS_STRIDE/2))); points_in += start; /* Complete the coordinates and hash */ hash_ec_point(hash, points_in, z_heap); /* * Unconditionally byteswap the hash result, because: * - The byte-level convention of RIPEMD160 is little-endian * - We are comparing it in big-endian order */ #define hash_ec_point_search_prefix_inner_1(i) \ hash[i] = bswap32(hash[i]); hash160_unroll(hash_ec_point_search_prefix_inner_1); /* Binary-search the target table for the hash we just computed */ for (high = ntargets - 1, low = 0, i = high >> 1; high >= low; i = low + ((high - low) >> 1)) { p = hash160_ucmp_g(hash, &target_table[10*i]); low = (p > 0) ? (i + 1) : low; high = (p < 0) ? (i - 1) : high; if (p == 0) { /* For debugging purposes, write the hash value */ found[0] = ((get_global_id(1) * get_global_size(0)) + get_global_id(0)); found[1] = i; #define hash_ec_point_search_prefix_inner_2(i) \ found[i+2] = load_be32(hash[i]); hash160_unroll(hash_ec_point_search_prefix_inner_2); high = -1; } } }