Merge "Shuffle the encoding to prevent systematic errors"

    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

// 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);

            or_bit(&result, (j * KEY_CODEWORDS) + i, wi & 1);

        }

    }

    // 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;

}

    return winner;

}

std::vector<uint8_t> DecodeKey(const std::vector<uint8_t>& encoded) {

    CHECK_EQ(OUTPUT_SIZE_BYTES, encoded.size());

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);