Daniel Erat | 59c5f4b | 2015-08-24 12:50:25 -0600 | [diff] [blame] | 1 | // Copyright (c) 2012 The Chromium Authors. All rights reserved. |
| 2 | // Use of this source code is governed by a BSD-style license that can be |
| 3 | // found in the LICENSE file. |
| 4 | |
| 5 | #include "crypto/ghash.h" |
| 6 | |
| 7 | #include <algorithm> |
| 8 | |
| 9 | #include "base/logging.h" |
| 10 | #include "base/sys_byteorder.h" |
| 11 | |
| 12 | namespace crypto { |
| 13 | |
| 14 | // GaloisHash is a polynomial authenticator that works in GF(2^128). |
| 15 | // |
| 16 | // Elements of the field are represented in `little-endian' order (which |
| 17 | // matches the description in the paper[1]), thus the most significant bit is |
| 18 | // the right-most bit. (This is backwards from the way that everybody else does |
| 19 | // it.) |
| 20 | // |
| 21 | // We store field elements in a pair of such `little-endian' uint64s. So the |
| 22 | // value one is represented by {low = 2**63, high = 0} and doubling a value |
| 23 | // involves a *right* shift. |
| 24 | // |
| 25 | // [1] http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/proposedmodes/gcm/gcm-revised-spec.pdf |
| 26 | |
| 27 | namespace { |
| 28 | |
| 29 | // Get64 reads a 64-bit, big-endian number from |bytes|. |
| 30 | uint64 Get64(const uint8 bytes[8]) { |
| 31 | uint64 t; |
| 32 | memcpy(&t, bytes, sizeof(t)); |
| 33 | return base::NetToHost64(t); |
| 34 | } |
| 35 | |
| 36 | // Put64 writes |x| to |bytes| as a 64-bit, big-endian number. |
| 37 | void Put64(uint8 bytes[8], uint64 x) { |
| 38 | x = base::HostToNet64(x); |
| 39 | memcpy(bytes, &x, sizeof(x)); |
| 40 | } |
| 41 | |
| 42 | // Reverse reverses the order of the bits of 4-bit number in |i|. |
| 43 | int Reverse(int i) { |
| 44 | i = ((i << 2) & 0xc) | ((i >> 2) & 0x3); |
| 45 | i = ((i << 1) & 0xa) | ((i >> 1) & 0x5); |
| 46 | return i; |
| 47 | } |
| 48 | |
| 49 | } // namespace |
| 50 | |
| 51 | GaloisHash::GaloisHash(const uint8 key[16]) { |
| 52 | Reset(); |
| 53 | |
| 54 | // We precompute 16 multiples of |key|. However, when we do lookups into this |
| 55 | // table we'll be using bits from a field element and therefore the bits will |
| 56 | // be in the reverse order. So normally one would expect, say, 4*key to be in |
| 57 | // index 4 of the table but due to this bit ordering it will actually be in |
| 58 | // index 0010 (base 2) = 2. |
| 59 | FieldElement x = {Get64(key), Get64(key+8)}; |
| 60 | product_table_[0].low = 0; |
| 61 | product_table_[0].hi = 0; |
| 62 | product_table_[Reverse(1)] = x; |
| 63 | |
| 64 | for (int i = 0; i < 16; i += 2) { |
| 65 | product_table_[Reverse(i)] = Double(product_table_[Reverse(i/2)]); |
| 66 | product_table_[Reverse(i+1)] = Add(product_table_[Reverse(i)], x); |
| 67 | } |
| 68 | } |
| 69 | |
| 70 | void GaloisHash::Reset() { |
| 71 | state_ = kHashingAdditionalData; |
| 72 | additional_bytes_ = 0; |
| 73 | ciphertext_bytes_ = 0; |
| 74 | buf_used_ = 0; |
| 75 | y_.low = 0; |
| 76 | y_.hi = 0; |
| 77 | } |
| 78 | |
| 79 | void GaloisHash::UpdateAdditional(const uint8* data, size_t length) { |
| 80 | DCHECK_EQ(state_, kHashingAdditionalData); |
| 81 | additional_bytes_ += length; |
| 82 | Update(data, length); |
| 83 | } |
| 84 | |
| 85 | void GaloisHash::UpdateCiphertext(const uint8* data, size_t length) { |
| 86 | if (state_ == kHashingAdditionalData) { |
| 87 | // If there's any remaining additional data it's zero padded to the next |
| 88 | // full block. |
| 89 | if (buf_used_ > 0) { |
| 90 | memset(&buf_[buf_used_], 0, sizeof(buf_)-buf_used_); |
| 91 | UpdateBlocks(buf_, 1); |
| 92 | buf_used_ = 0; |
| 93 | } |
| 94 | state_ = kHashingCiphertext; |
| 95 | } |
| 96 | |
| 97 | DCHECK_EQ(state_, kHashingCiphertext); |
| 98 | ciphertext_bytes_ += length; |
| 99 | Update(data, length); |
| 100 | } |
| 101 | |
| 102 | void GaloisHash::Finish(void* output, size_t len) { |
| 103 | DCHECK(state_ != kComplete); |
| 104 | |
| 105 | if (buf_used_ > 0) { |
| 106 | // If there's any remaining data (additional data or ciphertext), it's zero |
| 107 | // padded to the next full block. |
| 108 | memset(&buf_[buf_used_], 0, sizeof(buf_)-buf_used_); |
| 109 | UpdateBlocks(buf_, 1); |
| 110 | buf_used_ = 0; |
| 111 | } |
| 112 | |
| 113 | state_ = kComplete; |
| 114 | |
| 115 | // The lengths of the additional data and ciphertext are included as the last |
| 116 | // block. The lengths are the number of bits. |
| 117 | y_.low ^= additional_bytes_*8; |
| 118 | y_.hi ^= ciphertext_bytes_*8; |
| 119 | MulAfterPrecomputation(product_table_, &y_); |
| 120 | |
| 121 | uint8 *result, result_tmp[16]; |
| 122 | if (len >= 16) { |
| 123 | result = reinterpret_cast<uint8*>(output); |
| 124 | } else { |
| 125 | result = result_tmp; |
| 126 | } |
| 127 | |
| 128 | Put64(result, y_.low); |
| 129 | Put64(result + 8, y_.hi); |
| 130 | |
| 131 | if (len < 16) |
| 132 | memcpy(output, result_tmp, len); |
| 133 | } |
| 134 | |
| 135 | // static |
| 136 | GaloisHash::FieldElement GaloisHash::Add( |
| 137 | const FieldElement& x, |
| 138 | const FieldElement& y) { |
| 139 | // Addition in a characteristic 2 field is just XOR. |
| 140 | FieldElement z = {x.low^y.low, x.hi^y.hi}; |
| 141 | return z; |
| 142 | } |
| 143 | |
| 144 | // static |
| 145 | GaloisHash::FieldElement GaloisHash::Double(const FieldElement& x) { |
| 146 | const bool msb_set = x.hi & 1; |
| 147 | |
| 148 | FieldElement xx; |
| 149 | // Because of the bit-ordering, doubling is actually a right shift. |
| 150 | xx.hi = x.hi >> 1; |
| 151 | xx.hi |= x.low << 63; |
| 152 | xx.low = x.low >> 1; |
| 153 | |
| 154 | // If the most-significant bit was set before shifting then it, conceptually, |
| 155 | // becomes a term of x^128. This is greater than the irreducible polynomial |
| 156 | // so the result has to be reduced. The irreducible polynomial is |
| 157 | // 1+x+x^2+x^7+x^128. We can subtract that to eliminate the term at x^128 |
| 158 | // which also means subtracting the other four terms. In characteristic 2 |
| 159 | // fields, subtraction == addition == XOR. |
| 160 | if (msb_set) |
| 161 | xx.low ^= 0xe100000000000000ULL; |
| 162 | |
| 163 | return xx; |
| 164 | } |
| 165 | |
| 166 | void GaloisHash::MulAfterPrecomputation(const FieldElement* table, |
| 167 | FieldElement* x) { |
| 168 | FieldElement z = {0, 0}; |
| 169 | |
| 170 | // In order to efficiently multiply, we use the precomputed table of i*key, |
| 171 | // for i in 0..15, to handle four bits at a time. We could obviously use |
| 172 | // larger tables for greater speedups but the next convenient table size is |
| 173 | // 4K, which is a little large. |
| 174 | // |
| 175 | // In other fields one would use bit positions spread out across the field in |
| 176 | // order to reduce the number of doublings required. However, in |
| 177 | // characteristic 2 fields, repeated doublings are exceptionally cheap and |
| 178 | // it's not worth spending more precomputation time to eliminate them. |
| 179 | for (unsigned i = 0; i < 2; i++) { |
| 180 | uint64 word; |
| 181 | if (i == 0) { |
| 182 | word = x->hi; |
| 183 | } else { |
| 184 | word = x->low; |
| 185 | } |
| 186 | |
| 187 | for (unsigned j = 0; j < 64; j += 4) { |
| 188 | Mul16(&z); |
| 189 | // the values in |table| are ordered for little-endian bit positions. See |
| 190 | // the comment in the constructor. |
| 191 | const FieldElement& t = table[word & 0xf]; |
| 192 | z.low ^= t.low; |
| 193 | z.hi ^= t.hi; |
| 194 | word >>= 4; |
| 195 | } |
| 196 | } |
| 197 | |
| 198 | *x = z; |
| 199 | } |
| 200 | |
| 201 | // kReductionTable allows for rapid multiplications by 16. A multiplication by |
| 202 | // 16 is a right shift by four bits, which results in four bits at 2**128. |
| 203 | // These terms have to be eliminated by dividing by the irreducible polynomial. |
| 204 | // In GHASH, the polynomial is such that all the terms occur in the |
| 205 | // least-significant 8 bits, save for the term at x^128. Therefore we can |
| 206 | // precompute the value to be added to the field element for each of the 16 bit |
| 207 | // patterns at 2**128 and the values fit within 12 bits. |
| 208 | static const uint16 kReductionTable[16] = { |
| 209 | 0x0000, 0x1c20, 0x3840, 0x2460, 0x7080, 0x6ca0, 0x48c0, 0x54e0, |
| 210 | 0xe100, 0xfd20, 0xd940, 0xc560, 0x9180, 0x8da0, 0xa9c0, 0xb5e0, |
| 211 | }; |
| 212 | |
| 213 | // static |
| 214 | void GaloisHash::Mul16(FieldElement* x) { |
| 215 | const unsigned msw = x->hi & 0xf; |
| 216 | x->hi >>= 4; |
| 217 | x->hi |= x->low << 60; |
| 218 | x->low >>= 4; |
| 219 | x->low ^= static_cast<uint64>(kReductionTable[msw]) << 48; |
| 220 | } |
| 221 | |
| 222 | void GaloisHash::UpdateBlocks(const uint8* bytes, size_t num_blocks) { |
| 223 | for (size_t i = 0; i < num_blocks; i++) { |
| 224 | y_.low ^= Get64(bytes); |
| 225 | bytes += 8; |
| 226 | y_.hi ^= Get64(bytes); |
| 227 | bytes += 8; |
| 228 | MulAfterPrecomputation(product_table_, &y_); |
| 229 | } |
| 230 | } |
| 231 | |
| 232 | void GaloisHash::Update(const uint8* data, size_t length) { |
| 233 | if (buf_used_ > 0) { |
| 234 | const size_t n = std::min(length, sizeof(buf_) - buf_used_); |
| 235 | memcpy(&buf_[buf_used_], data, n); |
| 236 | buf_used_ += n; |
| 237 | length -= n; |
| 238 | data += n; |
| 239 | |
| 240 | if (buf_used_ == sizeof(buf_)) { |
| 241 | UpdateBlocks(buf_, 1); |
| 242 | buf_used_ = 0; |
| 243 | } |
| 244 | } |
| 245 | |
| 246 | if (length >= 16) { |
| 247 | const size_t n = length / 16; |
| 248 | UpdateBlocks(data, n); |
| 249 | length -= n*16; |
| 250 | data += n*16; |
| 251 | } |
| 252 | |
| 253 | if (length > 0) { |
| 254 | memcpy(buf_, data, length); |
| 255 | buf_used_ = length; |
| 256 | } |
| 257 | } |
| 258 | |
| 259 | } // namespace crypto |