crypto/ghash.cc

   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