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/*
* Copyright (C) 2019 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include <HadamardUtils.h>
#include <android-base/logging.h>
namespace aidl {
namespace android {
namespace hardware {
namespace rebootescrow {
namespace hadamard {
static inline uint8_t read_bit(const std::vector<uint8_t>& input, size_t bit) {
return (input[bit >> 3] >> (bit & 7)) & 1u;
}
// Use a simple LCG which is easy to run in reverse.
// https://www.johndcook.com/blog/2017/07/05/simple-random-number-generator/
constexpr uint64_t RNG_MODULUS = 0x7fffffff;
constexpr uint64_t RNG_MUL = 742938285;
constexpr uint64_t RNG_SEED = 20170705;
constexpr uint64_t RNG_INV_MUL = 1413043504; // (mul * inv_mul) % modulus == 1
constexpr uint64_t RNG_INV_SEED = 1173538311; // (seed * mul**65534) % modulus
// Apply an error correcting encoding.
//
// The error correcting code used is an augmented Hadamard code with
// k=15, so it takes a 16-bit input and produces a 2^15-bit output.
// We break the 32-byte key into 16 16-bit codewords and encode
// each codeword to a 2^15-bit output.
//
// To better defend against clustered errors, we stripe together the encoded
// codewords. Thus if a single 512-byte DRAM line is lost, instead of losing
// 2^11 bits from the encoding of a single code word, we lose 2^7 bits
// from the encoding of each of the 16 codewords.
// In addition we apply a Fisher-Yates shuffle to the bytes of the encoding;
// Hadamard encoding recovers much better from random errors than systematic
// ones, and this ensures that errors will be random.
std::vector<uint8_t> EncodeKey(const std::vector<uint8_t>& input) {
CHECK_EQ(input.size(), KEY_SIZE_IN_BYTES);
std::vector<uint8_t> result(OUTPUT_SIZE_BYTES, 0);
static_assert(OUTPUT_SIZE_BYTES == 64 * 1024);
// Transpose the key so that each row contains one bit from each codeword
uint16_t wordmatrix[CODEWORD_BITS];
for (size_t i = 0; i < CODEWORD_BITS; i++) {
uint16_t word = 0;
for (size_t j = 0; j < KEY_CODEWORDS; j++) {
word |= read_bit(input, i + j * CODEWORD_BITS) << j;
}
wordmatrix[i] = word;
}
// Fill in the encodings in Gray code order for speed.
uint16_t val = wordmatrix[CODEWORD_BITS - 1];
size_t ix = 0;
for (size_t i = 0; i < ENCODE_LENGTH; i++) {
for (size_t b = 0; b < CODEWORD_BITS; b++) {
if (i & (1 << b)) {
ix ^= (1 << b);
val ^= wordmatrix[b];
break;
}
}
result[ix * KEY_CODEWORD_BYTES] = val & 0xffu;
result[ix * KEY_CODEWORD_BYTES + 1] = val >> 8u;
}
// Apply the inverse shuffle here; we apply the forward shuffle in decoding.
uint64_t rng_state = RNG_INV_SEED;
for (size_t i = OUTPUT_SIZE_BYTES - 1; i > 0; i--) {
auto j = rng_state % (i + 1);
auto t = result[i];
result[i] = result[j];
result[j] = t;
rng_state *= RNG_INV_MUL;
rng_state %= RNG_MODULUS;
}
return result;
}
// Constant-time conditional copy, to fix b/146520538
// ctl must be 0 or 1; we do the copy if it's 1.
static void CondCopy(uint32_t ctl, void* dest, const void* src, size_t len) {
const auto cdest = reinterpret_cast<uint8_t*>(dest);
const auto csrc = reinterpret_cast<const uint8_t*>(src);
for (size_t i = 0; i < len; i++) {
const uint32_t d = cdest[i];
const uint32_t s = csrc[i];
cdest[i] = d ^ (-ctl & (s ^ d));
}
}
struct CodewordWinner {
uint16_t codeword;
int32_t score;
};
// Replace dest with src if it has a higher score
static void CopyWinner(CodewordWinner* dest, const CodewordWinner& src) {
// Scores are between - 2^15 and 2^15, so taking the difference won't
// overflow; we use the sign bit of the difference here.
CondCopy(static_cast<uint32_t>(dest->score - src.score) >> 31, dest, &src,
sizeof(CodewordWinner));
}
// Decode a single codeword. Because of the way codewords are striped together
// this takes the entire input, plus an offset telling it which word to decode.
static uint16_t DecodeWord(size_t word, const std::vector<uint8_t>& encoded) {
std::vector<int32_t> scores;
scores.reserve(ENCODE_LENGTH);
// Convert x -> -1^x in the encoded bits. e.g [1, 0, 0, 1] -> [-1, 1, 1, -1]
for (uint32_t i = 0; i < ENCODE_LENGTH; i++) {
scores.push_back(1 - 2 * read_bit(encoded, i * KEY_CODEWORDS + word));
}
// Multiply the hadamard matrix by the transformed input.
// |1 1 1 1| |-1| | 0|
// |1 -1 1 -1| * | 1| = | 0|
// |1 1 -1 -1| | 1| | 0|
// |1 -1 -1 1| |-1| |-4|
for (uint32_t i = 0; i < CODE_K; i++) {
uint16_t step = 1u << i;
for (uint32_t j = 0; j < ENCODE_LENGTH; j += 2 * step) {
for (uint32_t k = j; k < j + step; k++) {
auto a0 = scores[k];
auto a1 = scores[k + step];
scores[k] = a0 + a1;
scores[k + step] = a0 - a1;
}
}
}
// -ENCODE_LENGTH is least possible score, so start one less than that
auto best = CodewordWinner{0, -static_cast<int32_t>(ENCODE_LENGTH + 1)};
// For every possible codeword value, look at its score, and replace best if it's higher,
// in constant time.
for (size_t i = 0; i < ENCODE_LENGTH; i++) {
CopyWinner(&best, CodewordWinner{static_cast<uint16_t>(i), scores[i]});
CopyWinner(&best, CodewordWinner{static_cast<uint16_t>(i | (1 << CODE_K)), -scores[i]});
}
return best.codeword;
}
std::vector<uint8_t> DecodeKey(const std::vector<uint8_t>& shuffled) {
CHECK_EQ(OUTPUT_SIZE_BYTES, shuffled.size());
// Apply the forward Fisher-Yates shuffle.
std::vector<uint8_t> encoded(OUTPUT_SIZE_BYTES, 0);
encoded[0] = shuffled[0];
uint64_t rng_state = RNG_SEED;
for (size_t i = 1; i < OUTPUT_SIZE_BYTES; i++) {
auto j = rng_state % (i + 1);
encoded[i] = encoded[j];
encoded[j] = shuffled[i];
rng_state *= RNG_MUL;
rng_state %= RNG_MODULUS;
}
std::vector<uint8_t> result(KEY_SIZE_IN_BYTES, 0);
for (size_t i = 0; i < KEY_CODEWORDS; i++) {
uint16_t val = DecodeWord(i, encoded);
result[i * CODEWORD_BYTES] = val & 0xffu;
result[i * CODEWORD_BYTES + 1] = val >> 8u;
}
return result;
}
} // namespace hadamard
} // namespace rebootescrow
} // namespace hardware
} // namespace android
} // namespace aidl
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