crypto: add GHASH implementation.

crypto/ghash.cc

+// Copyright (c) 2012 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#include "crypto/ghash.h"
+
+#include "base/logging.h"
+#include "base/sys_byteorder.h"
+
+namespace crypto {
+
+// GaliosHash is a polynomial authenticator that works in GF(2^128).
+//
+// Elements of the field are represented in `little-endian' order (which
+// matches the description in the paper[1]), thus the most significant bit is
+// the right-most bit. (This is backwards from the way that everybody else does
+// it.)
+//
+// We store field elements in a pair of such `little-endian' uint64s. So the
+// value one is represented by {low = 2**63, high = 0} and doubling a value
+// involves a *right* shift.
+//
+// [1] http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/proposedmodes/gcm/gcm-revised-spec.pdf
+
+namespace {
+
+// Get64 reads a 64-bit, big-endian number from |bytes|.
+uint64 Get64(const uint8 bytes[8]) {
+  uint64 t;
+  memcpy(&t, bytes, sizeof(t));
+  return base::NetToHost64(t);
+}
+
+// Put64 writes |x| to |bytes| as a 64-bit, big-endian number.
+void Put64(uint8 bytes[8], uint64 x) {
+  x = base::HostToNet64(x);
+  memcpy(bytes, &x, 8);

[wtc, 2012/10/19 21:35:22]

Nit: 8 => sizeof(x) ?

(You use sizeof(t) on line 30.)

[agl, 2012/10/22 21:50:56]

Done.

+}
+
+// Reverse reverses the order of the bits of 4-bit number in |i|.
+int Reverse(int i) {
+  i = ((i << 2)&0xc) | ((i >> 2)&0x3);
+  i = ((i << 1)&0xa) | ((i >> 1)&0x5);

[wtc, 2012/10/19 21:35:22]

Nit: add spaces around the & operators.

[agl, 2012/10/22 21:50:56]

Done.

+  return i;
+}
+
+}  // anonymous namespace
+
+GaliosHash::GaliosHash(const uint8 key[16]) {
+  Reset();
+
+  // We precompute 16 multiples of |key|. However, when we do lookups into this
+  // table we'll be using bits from a field element and therefore the bits will
+  // be in the reverse order. So normally one would expect, say, 4*key to be in
+  // index 4 of the table but due to this bit ordering it will actually be in
+  // index 0010b = 2.

[wtc, 2012/10/19 21:35:22]

Nit: your use of the 'b' suffix confused me for a bit
because 'b' is also a hexadecimal digit. I wonder if we
should be more verbose: 0010 (base 2) = 2.

[agl, 2012/10/22 21:50:56]

Done.

+  FieldElement x = {Get64(key), Get64(key+8)};
+  productTable[0].low = 0;
+  productTable[0].hi = 0;
+  productTable[Reverse(1)] = x;
+
+  for (int i = 0; i < 16; i += 2) {
+    productTable[Reverse(i)] = Double(productTable[Reverse(i/2)]);
+    productTable[Reverse(i+1)] = Add(productTable[Reverse(i)], x);

[wtc, 2012/10/19 21:35:22]

In Reverse(i+1), you are relying on the fact that
Reverse(16) is the same as Reverse(0), right?

[agl, 2012/10/22 21:50:56]

Reverse(16) should never be called, I believe. The for loop is advancing by two
each time, so the maximum value for i is 14.

+  }
+}
+
+void GaliosHash::Reset() {
+  state_ = kHashingAdditionalData;
+  additional_bytes_ = 0;
+  ciphertext_bytes_ = 0;
+  buf_used_ = 0;
+  y_.low = 0;
+  y_.hi = 0;
+}
+
+void GaliosHash::UpdateAdditional(const uint8* data, size_t length) {
+  DCHECK_EQ(state_, kHashingAdditionalData);
+  additional_bytes_ += length;
+  Update(data, length);
+}
+
+void GaliosHash::UpdateCiphertext(const uint8* data, size_t length) {
+  if (state_ == kHashingAdditionalData) {
+    // If there's any remaining additional data it's zero padded to the next
+    // full block.
+    if (buf_used_ > 0) {
+      memset(&buf_[buf_used_], 0, sizeof(buf_)-buf_used_);
+      UpdateBlocks(buf_, 1);
+      buf_used_ = 0;
+    }
+    state_ = kHashingCiphertext;
+  }
+
+  DCHECK_EQ(state_, kHashingCiphertext);
+  ciphertext_bytes_ += length;
+  Update(data, length);
+}
+
+void GaliosHash::Digest(uint8 result[16]) {
+  DCHECK(state_ != kComplete);
+
+  if (buf_used_ > 0) {
+    // If there's any remaining data (additional data or ciphertext), it's zero
+    // padded to the next full block.
+    memset(&buf_[buf_used_], 0, sizeof(buf_)-buf_used_);
+    UpdateBlocks(buf_, 1);
+    buf_used_ = 0;
+  }
+
+  state_ = kComplete;
+
+  // The lengths of the additional data and ciphertext are included as the last
+  // block. The lengths are the number of bits.

[wtc, 2012/10/19 21:35:22]

This shows you implemented the original GHASH.

+  y_.low ^= additional_bytes_*8;
+  y_.hi ^= ciphertext_bytes_*8;
+  MulAfterPrecomputation(productTable, &y_);
+
+  Put64(result, y_.low);
+  Put64(result+8, y_.hi);

[wtc, 2012/10/19 21:35:22]

I suggest adding spaces around the operators in this function.

[agl, 2012/10/22 21:50:56]

Done.

+}
+
+// static
+GaliosHash::FieldElement GaliosHash::Add(
+    const FieldElement& x,
+    const FieldElement& y) {
+  // Addition in a characteristic 2 field is just XOR.
+  FieldElement z = {x.low^y.low, x.hi^y.hi};
+  return z;
+}
+
+// static
+GaliosHash::FieldElement GaliosHash::Double(const FieldElement& x) {
+  const bool msbSet = x.hi & 1;

[wtc, 2012/10/19 21:35:22]

msbSet => msb_set

[agl, 2012/10/22 21:50:56]

Done.

+
+  FieldElement xx;
+  // Because of the bit-ordering, doubling is actually a right shift.
+  xx.hi = x.hi >> 1;
+  xx.hi |= x.low << 63;
+  xx.low = x.low >> 1;
+
+  // If the most-significant bit was set before shifting then it, conceptually,
+  // becomes a term of x^128. This is greater than the irreducible polynomial
+  // so the result has to be reduced. The irreducible polynomial is
+  // 1+x+x^2+x^7+x^128. We can subtract that to eliminate the term at x^128
+  // which also means subtracting the other four terms. In characteristic 2
+  // fields, subtraction == addition == XOR.
+  if (msbSet) {
+    xx.low ^= 0xe100000000000000;

[wtc, 2012/10/19 21:35:22]

You may need to add a ULL suffix to the constant to
avoid a compiler warning.

Nit: omit the curly braces.

[agl, 2012/10/22 21:50:56]

Done.

+  }
+
+  return xx;
+}
+
+void GaliosHash::MulAfterPrecomputation(const FieldElement* table,
+                                        FieldElement* x) {
+  FieldElement z = {0, 0};
+
+  // In order to efficiently multiply, we use the precomputed table of i*key,
+  // for i in 0..15, to handle four bits at a time. We could obviously use
+  // larger tables for greater speedups but the next convenient table size is
+  // 4K, which is a little large.
+  //
+  // In other fields one would use bit positions spread out across the field in
+  // order to reduce the number of doublings required. However, in
+  // characteristic 2 fields, repeated doublings are exceptionally cheap and
+  // it's not worth spending more precomputation time to eliminate them.
+  for (unsigned i = 0; i < 2; i++) {
+    uint64 word;
+    if (i == 0) {
+      word = x->hi;
+    } else {
+      word = x->low;
+    }
+
+    for (unsigned j = 0; j < 64; j += 4) {
+      Mul16(&z);
+      // the values in |table| are ordered for little-endian bit positions. See
+      // the comment in the constructor.
+      const FieldElement& t = table[word & 0xf];
+      z.low ^= t.low;
+      z.hi ^= t.hi;
+      word >>= 4;
+    }
+  }
+
+  *x = z;
+}
+
+// kReductionTable allows for rapid multiplications by 16. A multiplication by
+// 16 is a right shift by four bits, which results in four bits at 2**128.
+// These terms have to be eliminated by dividing by the irreducible polynomial.
+// In GHASH, the polynomial is such that all the terms occur in the
+// least-significant 8 bits, save for the term at x^128. Therefore we can
+// precompute the value to be added to the field element for each of the 16 bit
+// patterns at 2**128 and the values fit within 12 bits.
+static const uint16 kReductionTable[16] = {
+  0x0000, 0x1c20, 0x3840, 0x2460, 0x7080, 0x6ca0, 0x48c0, 0x54e0,
+  0xe100, 0xfd20, 0xd940, 0xc560, 0x9180, 0x8da0, 0xa9c0, 0xb5e0,
+};
+
+// static
+void GaliosHash::Mul16(FieldElement* x) {
+  const unsigned msw = x->hi & 0xf;
+  x->hi >>= 4;
+  x->hi |= x->low << 60;
+  x->low >>= 4;
+  x->low ^= static_cast<uint64>(kReductionTable[msw]) << 48;
+}
+
+void GaliosHash::UpdateBlocks(const uint8* bytes, size_t num_blocks) {
+  for (size_t i = 0; i < num_blocks; i++) {
+    y_.low ^= Get64(bytes);
+    bytes += 8;
+    y_.hi ^= Get64(bytes);
+    bytes += 8;
+    MulAfterPrecomputation(productTable, &y_);
+  }
+}
+
+void GaliosHash::Update(const uint8* data, size_t length) {
+  if (buf_used_ > 0) {
+    const size_t n = std::min(length, buf_used_);
+    memcpy(&buf_[buf_used_], data, n);
+    buf_used_ += n;
+    length -= n;
+    data += n;
+
+    if (buf_used_ == sizeof(buf_)) {
+      UpdateBlocks(buf_, 1);
+      buf_used_ = 0;
+    }
+  }
+
+  if (length >= 16) {
+    const size_t n = length / 16;
+    UpdateBlocks(data, n);
+    length -= n*16;
+    data += n*16;
+  }
+
+  if (length > 0) {
+    memcpy(buf_, data, length);
+    buf_used_ = length;
+  }
+}
+
+}  // namespace crypto