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 // 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 #include "base/logging.h" #include "base/sys_byteorder.h" namespace crypto { // GaloisHash 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, sizeof(x)); } // 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); return i; } } // namespace GaloisHash::GaloisHash(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 0010 (base 2) = 2. FieldElement x = {Get64(key), Get64(key+8)}; product_table_[0].low = 0; product_table_[0].hi = 0; product_table_[Reverse(1)] = x; for (int i = 0; i < 16; i += 2) { product_table_[Reverse(i)] = Double(product_table_[Reverse(i/2)]); product_table_[Reverse(i+1)] = Add(product_table_[Reverse(i)], x); } } void GaloisHash::Reset() { state_ = kHashingAdditionalData; additional_bytes_ = 0; ciphertext_bytes_ = 0; buf_used_ = 0; y_.low = 0; y_.hi = 0; } void GaloisHash::UpdateAdditional(const uint8* data, size_t length) { DCHECK_EQ(state_, kHashingAdditionalData); additional_bytes_ += length; Update(data, length); } void GaloisHash::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 GaloisHash::Finish(void* output, size_t len) { 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. y_.low ^= additional_bytes_*8; y_.hi ^= ciphertext_bytes_*8; MulAfterPrecomputation(product_table_, &y_); uint8 *result, result_tmp[16]; if (len >= 16) { result = reinterpret_cast(output); } else { result = result_tmp; } Put64(result, y_.low); Put64(result + 8, y_.hi); if (len < 16) memcpy(output, result_tmp, len); } // static GaloisHash::FieldElement GaloisHash::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 GaloisHash::FieldElement GaloisHash::Double(const FieldElement& x) { const bool msb_set = x.hi & 1; 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 (msb_set) xx.low ^= 0xe100000000000000ULL; return xx; } void GaloisHash::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 GaloisHash::Mul16(FieldElement* x) { const unsigned msw = x->hi & 0xf; x->hi >>= 4; x->hi |= x->low << 60; x->low >>= 4; x->low ^= static_cast(kReductionTable[msw]) << 48; } void GaloisHash::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(product_table_, &y_); } } void GaloisHash::Update(const uint8* data, size_t length) { if (buf_used_ > 0) { const size_t n = std::min(length, sizeof(buf_) - 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