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