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| 1 | +#include "third_party/crypto/bignum.h" |
| 2 | + |
| 3 | +namespace bignum { |
| 4 | + |
| 5 | +void BigNum::trim() { |
| 6 | + while (limbs.size() > 1 && limbs.back() == 0) { |
| 7 | + limbs.pop_back(); |
| 8 | + } |
| 9 | +} |
| 10 | + |
| 11 | +BigNum BigNum::from_bytes_be(const uint8_t* data, size_t len) { |
| 12 | + BigNum r; |
| 13 | + // Number of 8-byte limbs, rounding up |
| 14 | + size_t n = (len + 7) / 8; |
| 15 | + r.limbs.resize(n, 0); |
| 16 | + |
| 17 | + // Read bytes big-endian into little-endian limbs |
| 18 | + for (size_t i = 0; i < len; i++) { |
| 19 | + size_t byte_pos = len - 1 - i; // position from LSB |
| 20 | + r.limbs[byte_pos / 8] |= static_cast<uint64_t>(data[i]) |
| 21 | + << (8 * (byte_pos % 8)); |
| 22 | + } |
| 23 | + |
| 24 | + r.trim(); |
| 25 | + return r; |
| 26 | +} |
| 27 | + |
| 28 | +void BigNum::to_bytes_be(uint8_t* out, size_t len) const { |
| 29 | + std::memset(out, 0, len); |
| 30 | + for (size_t i = 0; i < len; i++) { |
| 31 | + size_t byte_pos = len - 1 - i; // position from LSB |
| 32 | + size_t li = byte_pos / 8; |
| 33 | + if (li < limbs.size()) { |
| 34 | + out[i] = static_cast<uint8_t>(limbs[li] >> (8 * (byte_pos % 8))); |
| 35 | + } |
| 36 | + } |
| 37 | +} |
| 38 | + |
| 39 | +int BigNum::compare(const BigNum& a, const BigNum& b) { |
| 40 | + size_t an = a.limbs.size(), bn = b.limbs.size(); |
| 41 | + size_t n = std::max(an, bn); |
| 42 | + for (size_t i = n; i > 0; i--) { |
| 43 | + uint64_t al = (i - 1 < an) ? a.limbs[i - 1] : 0; |
| 44 | + uint64_t bl = (i - 1 < bn) ? b.limbs[i - 1] : 0; |
| 45 | + if (al < bl) return -1; |
| 46 | + if (al > bl) return 1; |
| 47 | + } |
| 48 | + return 0; |
| 49 | +} |
| 50 | + |
| 51 | +BigNum BigNum::sub(const BigNum& a, const BigNum& b) { |
| 52 | + // Assumes a >= b |
| 53 | + BigNum r; |
| 54 | + size_t n = a.limbs.size(); |
| 55 | + r.limbs.resize(n, 0); |
| 56 | + uint64_t borrow = 0; |
| 57 | + for (size_t i = 0; i < n; i++) { |
| 58 | + uint64_t bl = (i < b.limbs.size()) ? b.limbs[i] : 0; |
| 59 | + __uint128_t diff = |
| 60 | + static_cast<__uint128_t>(a.limbs[i]) - bl - borrow; |
| 61 | + r.limbs[i] = static_cast<uint64_t>(diff); |
| 62 | + borrow = (diff >> 127) ? 1 : 0; // Check if underflow (high bit set) |
| 63 | + } |
| 64 | + r.trim(); |
| 65 | + return r; |
| 66 | +} |
| 67 | + |
| 68 | +BigNum BigNum::mul(const BigNum& a, const BigNum& b) { |
| 69 | + size_t an = a.limbs.size(), bn = b.limbs.size(); |
| 70 | + BigNum r; |
| 71 | + r.limbs.resize(an + bn, 0); |
| 72 | + |
| 73 | + for (size_t i = 0; i < an; i++) { |
| 74 | + uint64_t carry = 0; |
| 75 | + for (size_t j = 0; j < bn; j++) { |
| 76 | + __uint128_t prod = static_cast<__uint128_t>(a.limbs[i]) * b.limbs[j] + |
| 77 | + r.limbs[i + j] + carry; |
| 78 | + r.limbs[i + j] = static_cast<uint64_t>(prod); |
| 79 | + carry = static_cast<uint64_t>(prod >> 64); |
| 80 | + } |
| 81 | + r.limbs[i + bn] += carry; |
| 82 | + } |
| 83 | + |
| 84 | + r.trim(); |
| 85 | + return r; |
| 86 | +} |
| 87 | + |
| 88 | +// Knuth Algorithm D: multi-precision division, returns remainder |
| 89 | +BigNum BigNum::mod(const BigNum& a, const BigNum& m) { |
| 90 | + if (compare(a, m) < 0) return a; |
| 91 | + |
| 92 | + size_t n = m.limbs.size(); |
| 93 | + size_t total = a.limbs.size(); |
| 94 | + |
| 95 | + if (n == 0 || (n == 1 && m.limbs[0] == 0)) { |
| 96 | + return BigNum(); // division by zero guard |
| 97 | + } |
| 98 | + |
| 99 | + // Single-limb divisor fast path |
| 100 | + if (n == 1) { |
| 101 | + uint64_t d = m.limbs[0]; |
| 102 | + uint64_t rem = 0; |
| 103 | + for (size_t i = total; i > 0; i--) { |
| 104 | + __uint128_t cur = (static_cast<__uint128_t>(rem) << 64) | a.limbs[i - 1]; |
| 105 | + rem = static_cast<uint64_t>(cur % d); |
| 106 | + } |
| 107 | + BigNum r; |
| 108 | + r.limbs = {rem}; |
| 109 | + r.trim(); |
| 110 | + return r; |
| 111 | + } |
| 112 | + |
| 113 | + // Normalize: shift so that the MSB of the divisor's top limb is set |
| 114 | + int shift = 0; |
| 115 | + uint64_t top = m.limbs[n - 1]; |
| 116 | + if (top != 0) { |
| 117 | + shift = __builtin_clzll(top); |
| 118 | + } |
| 119 | + |
| 120 | + // Create normalized copies |
| 121 | + BigNum u, v; |
| 122 | + // u = a << shift, with one extra limb |
| 123 | + u.limbs.resize(total + 1, 0); |
| 124 | + if (shift > 0) { |
| 125 | + uint64_t carry = 0; |
| 126 | + for (size_t i = 0; i < total; i++) { |
| 127 | + __uint128_t val = (static_cast<__uint128_t>(a.limbs[i]) << shift) | carry; |
| 128 | + u.limbs[i] = static_cast<uint64_t>(val); |
| 129 | + carry = static_cast<uint64_t>(val >> 64); |
| 130 | + } |
| 131 | + u.limbs[total] = carry; |
| 132 | + } else { |
| 133 | + for (size_t i = 0; i < total; i++) u.limbs[i] = a.limbs[i]; |
| 134 | + u.limbs[total] = 0; |
| 135 | + } |
| 136 | + |
| 137 | + v.limbs.resize(n, 0); |
| 138 | + if (shift > 0) { |
| 139 | + uint64_t carry = 0; |
| 140 | + for (size_t i = 0; i < n; i++) { |
| 141 | + __uint128_t val = (static_cast<__uint128_t>(m.limbs[i]) << shift) | carry; |
| 142 | + v.limbs[i] = static_cast<uint64_t>(val); |
| 143 | + carry = static_cast<uint64_t>(val >> 64); |
| 144 | + } |
| 145 | + } else { |
| 146 | + v.limbs = m.limbs; |
| 147 | + } |
| 148 | + |
| 149 | + uint64_t vn_1 = v.limbs[n - 1]; |
| 150 | + uint64_t vn_2 = (n >= 2) ? v.limbs[n - 2] : 0; |
| 151 | + |
| 152 | + // Main loop: for each quotient digit position |
| 153 | + for (size_t j = total; j >= n; j--) { |
| 154 | + // Estimate quotient digit |
| 155 | + __uint128_t num_top = |
| 156 | + (static_cast<__uint128_t>(u.limbs[j]) << 64) | u.limbs[j - 1]; |
| 157 | + __uint128_t qhat = num_top / vn_1; |
| 158 | + __uint128_t rhat = num_top % vn_1; |
| 159 | + |
| 160 | + // Refine estimate |
| 161 | + while (qhat > 0xFFFFFFFFFFFFFFFFULL || |
| 162 | + qhat * vn_2 > |
| 163 | + ((rhat << 64) | u.limbs[j - 2])) { |
| 164 | + qhat--; |
| 165 | + rhat += vn_1; |
| 166 | + if (rhat > 0xFFFFFFFFFFFFFFFFULL) break; |
| 167 | + } |
| 168 | + |
| 169 | + // Multiply and subtract: u[j-n..j] -= qhat * v[0..n-1] |
| 170 | + uint64_t carry = 0; |
| 171 | + for (size_t i = 0; i < n; i++) { |
| 172 | + __uint128_t prod = |
| 173 | + static_cast<__uint128_t>(static_cast<uint64_t>(qhat)) * v.limbs[i] + |
| 174 | + carry; |
| 175 | + uint64_t prod_lo = static_cast<uint64_t>(prod); |
| 176 | + carry = static_cast<uint64_t>(prod >> 64); |
| 177 | + uint64_t u_val = u.limbs[j - n + i]; |
| 178 | + u.limbs[j - n + i] = u_val - prod_lo; |
| 179 | + if (u_val < prod_lo) carry++; |
| 180 | + } |
| 181 | + int64_t final_diff = |
| 182 | + static_cast<int64_t>(u.limbs[j]) - static_cast<int64_t>(carry); |
| 183 | + u.limbs[j] = static_cast<uint64_t>(final_diff); |
| 184 | + |
| 185 | + // If we subtracted too much, add back |
| 186 | + if (final_diff < 0) { |
| 187 | + uint64_t carry = 0; |
| 188 | + for (size_t i = 0; i < n; i++) { |
| 189 | + __uint128_t sum = static_cast<__uint128_t>(u.limbs[j - n + i]) + |
| 190 | + v.limbs[i] + carry; |
| 191 | + u.limbs[j - n + i] = static_cast<uint64_t>(sum); |
| 192 | + carry = static_cast<uint64_t>(sum >> 64); |
| 193 | + } |
| 194 | + u.limbs[j] += carry; |
| 195 | + } |
| 196 | + } |
| 197 | + |
| 198 | + // Remainder is u[0..n-1] >> shift (un-normalize) |
| 199 | + BigNum r; |
| 200 | + r.limbs.resize(n, 0); |
| 201 | + if (shift > 0) { |
| 202 | + uint64_t carry = 0; |
| 203 | + for (size_t i = n; i > 0; i--) { |
| 204 | + __uint128_t val = |
| 205 | + (static_cast<__uint128_t>(carry) << 64) | u.limbs[i - 1]; |
| 206 | + r.limbs[i - 1] = static_cast<uint64_t>(val >> shift); |
| 207 | + carry = u.limbs[i - 1] & ((1ULL << shift) - 1); |
| 208 | + } |
| 209 | + } else { |
| 210 | + for (size_t i = 0; i < n; i++) r.limbs[i] = u.limbs[i]; |
| 211 | + } |
| 212 | + |
| 213 | + r.trim(); |
| 214 | + return r; |
| 215 | +} |
| 216 | + |
| 217 | +BigNum BigNum::modexp(const BigNum& base, uint32_t exp, const BigNum& mod_val) { |
| 218 | + // Left-to-right binary square-and-multiply |
| 219 | + BigNum result; |
| 220 | + result.limbs = {1}; |
| 221 | + |
| 222 | + // Find highest set bit |
| 223 | + if (exp == 0) { |
| 224 | + return mod(result, mod_val); |
| 225 | + } |
| 226 | + |
| 227 | + int highest_bit = 31 - __builtin_clz(exp); |
| 228 | + |
| 229 | + BigNum b = mod(base, mod_val); |
| 230 | + |
| 231 | + for (int i = highest_bit; i >= 0; i--) { |
| 232 | + result = mod(mul(result, result), mod_val); |
| 233 | + if ((exp >> i) & 1) { |
| 234 | + result = mod(mul(result, b), mod_val); |
| 235 | + } |
| 236 | + } |
| 237 | + |
| 238 | + return result; |
| 239 | +} |
| 240 | + |
| 241 | +} // namespace bignum |
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