Merge "Transpose the encoding matrix" (b6ed52a1) · Commits · e / os / android_hardware_interfaces

rebootescrow/aidl/default/HadamardUtils.cpp

+60 −93

Original line number	Diff line number	Diff line
		@@ -16,6 +16,8 @@

		#include <HadamardUtils.h>

		#include <limits>

		#include <android-base/logging.h>

		namespace aidl {
		@@ -24,99 +26,52 @@ namespace hardware {
		namespace rebootescrow {
		namespace hadamard {

		constexpr auto BYTE_LENGTH = 8u;

		std::vector<uint8_t> BitsetToBytes(const std::bitset<ENCODE_LENGTH>& encoded_bits) {
		CHECK_EQ(0, (encoded_bits.size() % BYTE_LENGTH));
		std::vector<uint8_t> result;
		for (size_t i = 0; i < encoded_bits.size(); i += 8) {
		uint8_t current = 0;
		// Set each byte starting from the LSB.
		for (size_t j = 0; j < BYTE_LENGTH; j++) {
		CHECK_LE(i + j, encoded_bits.size());
		if (encoded_bits[i + j]) {
		current \|= (1u << j);
		}
		}
		result.push_back(current);
		}
		return result;
		}

		std::bitset<ENCODE_LENGTH> BytesToBitset(const std::vector<uint8_t>& encoded) {
		CHECK_EQ(ENCODE_LENGTH, encoded.size() * BYTE_LENGTH);

		std::bitset<ENCODE_LENGTH> result;
		size_t offset = 0;
		for (const auto& byte : encoded) {
		// Set each byte starting from the LSB.
		for (size_t j = 0; j < BYTE_LENGTH; j++) {
		result[offset + j] = byte & (1u << j);
		}
		offset += BYTE_LENGTH;
		}
		return result;
		}

		// The encoding is equivalent to multiply the word with the generator matrix (and take the module
		// of 2). Here is an example of encoding a number with 3 bits. The encoded length is thus
		// 2^(3-1) = 4 bits.
		// \|1 1 1 1\| \|0\|
		// \|0 1 1\| * \|0 0 1 1\| = \|1\|
		// \|0 1 0 1\| \|1\|
		// \|0\|
		std::bitset<ENCODE_LENGTH> EncodeWord(uint16_t word) {
		std::bitset<ENCODE_LENGTH> result;
		for (uint64_t i = ENCODE_LENGTH; i < 2 * ENCODE_LENGTH; i++) {
		uint32_t wi = word & i;
		static inline void or_bit(std::vector<uint8_t>* input, size_t bit, uint8_t val) {
		(*input)[bit >> 3] \|= (val & 1u) << (bit & 7);
		}

		static inline uint8_t read_bit(const std::vector<uint8_t>& input, size_t bit) {
		return (input[bit >> 3] >> (bit & 7)) & 1u;
		}

		// 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.
		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);
		for (size_t i = 0; i < KEY_CODEWORDS; i++) {
		uint16_t word = input[i * 2 + 1] << 8 \| input[i * 2];
		for (size_t j = 0; j < ENCODE_LENGTH; j++) {
		uint16_t wi = word & (j + ENCODE_LENGTH);
		// Sum all the bits in the word and check its parity.
		wi ^= wi >> 8u;
		wi ^= wi >> 4u;
		wi ^= wi >> 2u;
		wi ^= wi >> 1u;
		result[i - ENCODE_LENGTH] = wi & 1u;
		or_bit(&result, (j * KEY_CODEWORDS) + i, wi & 1);
		}
		return result;
		}

		std::vector<uint8_t> EncodeKey(const std::vector<uint8_t>& key) {
		CHECK_EQ(KEY_SIZE_IN_BYTES, key.size());

		std::vector<uint8_t> result;
		for (size_t i = 0; i < key.size(); i += 2) {
		uint16_t word = static_cast<uint16_t>(key[i + 1]) << BYTE_LENGTH \| key[i];
		auto encoded_bits = EncodeWord(word);
		auto byte_array = BitsetToBytes(encoded_bits);
		std::move(byte_array.begin(), byte_array.end(), std::back_inserter(result));
		}
		return result;
		}

		std::vector<uint8_t> DecodeKey(const std::vector<uint8_t>& encoded) {
		CHECK_EQ(0, (encoded.size() * 8) % ENCODE_LENGTH);
		std::vector<uint8_t> result;
		for (size_t i = 0; i < encoded.size(); i += ENCODE_LENGTH / 8) {
		auto current =
		std::vector<uint8_t>{encoded.begin() + i, encoded.begin() + i + ENCODE_LENGTH / 8};
		auto bits = BytesToBitset(current);
		auto candidates = DecodeWord(bits);
		CHECK(!candidates.empty());
		// TODO(xunchang) Do we want to try other candidates?
		uint16_t val = candidates.top().second;
		result.push_back(val & 0xffu);
		result.push_back(val >> BYTE_LENGTH);
		}

		return result;
		}

		std::priority_queue<std::pair<int32_t, uint16_t>> DecodeWord(
		const std::bitset<ENCODE_LENGTH>& encoded) {
		// 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 0 -> -1 in the encoded bits. e.g [0, 1, 1, 0] -> [-1, 1, 1, -1]
		// 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(2 * encoded[i] - 1);
		scores.push_back(1 - 2 * read_bit(encoded, i * KEY_CODEWORDS + word));
		}

		// Multiply the hadamard matrix by the transformed input.
		@@ -135,19 +90,31 @@ std::priority_queue<std::pair<int32_t, uint16_t>> DecodeWord(
		}
		}
		}
		auto hiscore = std::numeric_limits<int32_t>::min();
		uint16_t winner;
		// TODO(b/146520538): this needs to be constant time
		for (size_t i = 0; i < ENCODE_LENGTH; i++) {
		if (scores[i] > hiscore) {
		winner = i;
		hiscore = scores[i];

		// Assign the corresponding score to each index; larger score indicates higher probability. e.g.
		// value 3, encoding [0, 1, 1, 0] -> score: 4
		// value 7, encoding [1, 0, 0, 1] (3's complement) -> score: -4
		std::priority_queue<std::pair<int32_t, uint16_t>> candidates;
		// TODO(xunchang) limit the candidate size since we don't need all of them?
		for (uint32_t i = 0; i < scores.size(); i++) {
		candidates.emplace(-scores[i], i);
		candidates.emplace(scores[i], (1u << CODE_K) \| i);
		} else if (-scores[i] > hiscore) {
		winner = i \| (1 << CODE_K);
		hiscore = -scores[i];
		}
		}
		return winner;
		}

		CHECK_EQ(2 * ENCODE_LENGTH, candidates.size());
		return candidates;
		std::vector<uint8_t> DecodeKey(const std::vector<uint8_t>& encoded) {
		CHECK_EQ(OUTPUT_SIZE_BYTES, encoded.size());
		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

rebootescrow/aidl/default/HadamardUtils.h

+7 −20

Original line number	Diff line number	Diff line
		@@ -18,9 +18,6 @@

		#include <stdint.h>

		#include <bitset>
		#include <queue>
		#include <utility>
		#include <vector>

		namespace aidl {
		@@ -29,18 +26,14 @@ namespace hardware {
		namespace rebootescrow {
		namespace hadamard {

		constexpr uint32_t CODE_K = 15;
		constexpr auto BYTE_LENGTH = 8u;
		constexpr auto CODEWORD_BYTES = 2u; // uint16_t
		constexpr auto CODEWORD_BITS = CODEWORD_BYTES * BYTE_LENGTH;
		constexpr uint32_t CODE_K = CODEWORD_BITS - 1;
		constexpr uint32_t ENCODE_LENGTH = 1u << CODE_K;
		constexpr auto KEY_SIZE_IN_BYTES = 32u;

		// Encodes a 2 bytes word with hadamard code. The encoding expands a word of k+1 bits to a 2^k
		// bitset. Returns the encoded bitset.
		std::bitset<ENCODE_LENGTH> EncodeWord(uint16_t word);

		// Decodes the input bitset, and returns a sorted list of pair with (score, value). The value with
		// a higher score indicates a greater likehood.
		std::priority_queue<std::pair<int32_t, uint16_t>> DecodeWord(
		const std::bitset<ENCODE_LENGTH>& encoded);
		constexpr auto KEY_CODEWORDS = 16u;
		constexpr auto KEY_SIZE_IN_BYTES = KEY_CODEWORDS * CODEWORD_BYTES;
		constexpr auto OUTPUT_SIZE_BYTES = KEY_CODEWORDS * ENCODE_LENGTH / BYTE_LENGTH;

		// Encodes a key that has a size of KEY_SIZE_IN_BYTES. Returns a byte array representation of the
		// encoded bitset. So a 32 bytes key will expand to 16*(2^15) bits = 64KiB.
		@@ -49,12 +42,6 @@ std::vector<uint8_t> EncodeKey(const std::vector<uint8_t>& input);
		// Given a byte array representation of the encoded keys, decodes it and return the result.
		std::vector<uint8_t> DecodeKey(const std::vector<uint8_t>& encoded);

		// Converts a bitset of length \|ENCODE_LENGTH\| to a byte array.
		std::vector<uint8_t> BitsetToBytes(const std::bitset<ENCODE_LENGTH>& encoded_bits);

		// Converts a byte array of encoded words back to the bitset.
		std::bitset<ENCODE_LENGTH> BytesToBitset(const std::vector<uint8_t>& encoded);

		} // namespace hadamard
		} // namespace rebootescrow
		} // namespace hardware

rebootescrow/aidl/default/HadamardUtilsTest.cpp

+16 −91

Original line number	Diff line number	Diff line
		@@ -17,110 +17,35 @@
		#include <stdint.h>
		#include <random>

		#include <bitset>
		#include <utility>
		#include <vector>

		#include <gtest/gtest.h>

		#include <HadamardUtils.h>

		using namespace aidl::android::hardware::rebootescrow::hadamard;

		class HadamardTest : public testing::Test {
		protected:
		void SetUp() override {
		auto ones = std::bitset<ENCODE_LENGTH>{}.set();
		// Expects 0x4000 to encode as top half as ones, and lower half as zeros. i.e.
		// [1, 1 .. 1, 0, 0 .. 0]
		expected_half_size_ = ones << half_size_;

		// Expects 0x1 to encode as interleaved 1 and 0s i.e. [1, 0, 1, 0 ..]
		expected_one_ = ones;
		for (uint32_t i = ENCODE_LENGTH / 2; i >= 1; i /= 2) {
		expected_one_ ^= (expected_one_ >> i);
		}
		}
		class HadamardTest : public testing::Test {};

		uint16_t half_size_ = ENCODE_LENGTH / 2;
		std::bitset<ENCODE_LENGTH> expected_one_;
		std::bitset<ENCODE_LENGTH> expected_half_size_;
		};

		static void AddError(std::bitset<ENCODE_LENGTH>* corrupted_bits) {
		// The hadamard code has a hamming distance of ENCODE_LENGTH/2. So we should always be able to
		// correct the data if less than a quarter of the encoded bits are corrupted.
		auto corrupted_max = 0.24f * corrupted_bits->size();
		auto corrupted_num = 0;
		for (size_t i = 0; i < corrupted_bits->size() && corrupted_num < corrupted_max; i++) {
		if (random() % 2 == 0) {
		(corrupted_bits)[i] = !(corrupted_bits)[i];
		corrupted_num += 1;
		}
		}
		static void AddError(std::vector<uint8_t>* data) {
		for (size_t i = 0; i < data->size(); i++) {
		for (size_t j = 0; j < BYTE_LENGTH; j++) {
		if (random() % 100 < 47) {
		(*data)[i] ^= (1 << j);
		}

		static void EncodeAndDecodeKeys(const std::vector<uint8_t>& key) {
		auto encoded = EncodeKey(key);
		ASSERT_EQ(64 * 1024, encoded.size());
		auto decoded = DecodeKey(encoded);
		ASSERT_EQ(key, std::vector<uint8_t>(decoded.begin(), decoded.begin() + key.size()));
		}

		TEST_F(HadamardTest, Encode_smoke) {
		ASSERT_EQ(expected_half_size_, EncodeWord(half_size_));
		ASSERT_EQ(expected_one_, EncodeWord(1));
		// Check the complement of 1.
		ASSERT_EQ(~expected_one_, EncodeWord(1u << CODE_K \| 1u));
		}

		TEST_F(HadamardTest, Decode_smoke) {
		auto candidate = DecodeWord(expected_half_size_);
		auto expected = std::pair<int32_t, uint16_t>{ENCODE_LENGTH, half_size_};
		ASSERT_EQ(expected, candidate.top());

		candidate = DecodeWord(expected_one_);
		expected = std::pair<int32_t, uint16_t>{ENCODE_LENGTH, 1};
		ASSERT_EQ(expected, candidate.top());
		}

		TEST_F(HadamardTest, Decode_error_correction) {
		constexpr auto iteration = 10;
		for (int i = 0; i < iteration; i++) {
		uint16_t word = random() % (ENCODE_LENGTH * 2);
		auto corrupted_bits = EncodeWord(word);
		AddError(&corrupted_bits);

		auto candidate = DecodeWord(corrupted_bits);
		ASSERT_EQ(word, candidate.top().second);
		}
		std::vector<uint8_t> key;
		for (int j = 0; j < KEY_SIZE_IN_BYTES; j++) {
		key.emplace_back(random() & 0xff);
		}

		TEST_F(HadamardTest, BytesToBitset_smoke) {
		auto bytes = BitsetToBytes(expected_one_);

		auto read_back = BytesToBitset(bytes);
		ASSERT_EQ(expected_one_, read_back);
		auto encoded = EncodeKey(key);
		ASSERT_EQ(64 * 1024, encoded.size());
		AddError(&encoded);
		auto decoded = DecodeKey(encoded);
		ASSERT_EQ(key, std::vector<uint8_t>(decoded.begin(), decoded.begin() + key.size()));
		}

		TEST_F(HadamardTest, EncodeAndDecodeKey) {
		std::vector<uint8_t> KEY_1{
		0xA5, 0x00, 0xFF, 0x01, 0xA5, 0x5a, 0xAA, 0x55, 0x00, 0xD3, 0x2A,
		0x8C, 0x2E, 0x83, 0x0E, 0x65, 0x9E, 0x8D, 0xC6, 0xAC, 0x1E, 0x83,
		0x21, 0xB3, 0x95, 0x02, 0x89, 0x64, 0x64, 0x92, 0x12, 0x1F,
		};
		std::vector<uint8_t> KEY_2{
		0xFF, 0x00, 0x00, 0xAA, 0x5A, 0x19, 0x20, 0x71, 0x9F, 0xFB, 0xDA,
		0xB6, 0x2D, 0x06, 0xD5, 0x49, 0x7E, 0xEF, 0x63, 0xAC, 0x18, 0xFF,
		0x5A, 0xA3, 0x40, 0xBB, 0x64, 0xFA, 0x67, 0xC1, 0x10, 0x18,
		};

		EncodeAndDecodeKeys(KEY_1);
		EncodeAndDecodeKeys(KEY_2);

		std::vector<uint8_t> key;
		for (uint8_t i = 0; i < KEY_SIZE_IN_BYTES; i++) {
		key.push_back(i);
		};
		EncodeAndDecodeKeys(key);
		}