matrix_mul.cpp

// Compile with: clang++ -std=c++17 -O3 matrix_mul.cpp -o matrix_mul
// Run with:     ./matrix_mul
// Produces:
// result: [
// 	1, 0, 0, 0,
// 	0, 1, 0, 0,
// 	0, 0, 1, 0,
// 	0, 0, 0, 1,
// ]

#include <stdint.h>

#include <array>
#include <functional>
#include <iomanip>
#include <iostream>
#include <string>

template <unsigned I, typename T>
constexpr T bit_get(T input) noexcept {
  return (input & (1 << I)) >> I;
}

template <unsigned I, typename T>
constexpr void bit_set(T& input, T value) noexcept {
  input |= (value & 1) << I;
}

// Von Aufgabe 5b)
constexpr uint8_t mul2(uint8_t i) noexcept {
  uint8_t ret = 0;

  bit_set<7>(ret, bit_get<6>(i));
  bit_set<6>(ret, bit_get<5>(i));
  bit_set<5>(ret, bit_get<4>(i));
  bit_set<4>(ret, (uint8_t)(bit_get<3>(i) ^ bit_get<7>(i)));
  bit_set<3>(ret, (uint8_t)(bit_get<2>(i) ^ bit_get<7>(i)));
  bit_set<2>(ret, bit_get<1>(i));
  bit_set<1>(ret, (uint8_t)(bit_get<0>(i) ^ bit_get<7>(i)));
  bit_set<0>(ret, bit_get<7>(i));

  return ret;
}

// Von Aufgabe 5c)
constexpr uint8_t mul3(uint8_t i) noexcept {
  uint8_t ret = 0;

  bit_set<7>(ret, (uint8_t)(bit_get<6>(i) ^ bit_get<7>(i)));
  bit_set<6>(ret, (uint8_t)(bit_get<5>(i) ^ bit_get<6>(i)));
  bit_set<5>(ret, (uint8_t)(bit_get<4>(i) ^ bit_get<5>(i)));
  bit_set<4>(ret, (uint8_t)(bit_get<3>(i) ^ bit_get<4>(i) ^ bit_get<7>(i)));
  bit_set<3>(ret, (uint8_t)(bit_get<2>(i) ^ bit_get<3>(i) ^ bit_get<7>(i)));
  bit_set<2>(ret, (uint8_t)(bit_get<1>(i) ^ bit_get<2>(i)));
  bit_set<1>(ret, (uint8_t)(bit_get<0>(i) ^ bit_get<1>(i) ^ bit_get<7>(i)));
  bit_set<0>(ret, (uint8_t)(bit_get<0>(i) ^ bit_get<7>(i)));

  return ret;
}

// * 1 mod P(x)
constexpr uint8_t identity(uint8_t x) noexcept { return x; }

// clang-format off
// Matrix M, partially applied functions.
static std::array<std::function<uint8_t(uint8_t)>, 16> M = {
  mul2, mul3, identity, identity, 
  identity, mul2, mul3, identity, 
  identity, identity, mul2, mul3,
  mul3, identity, identity, mul2
};

static std::array<uint8_t, 16> M_inv = {
  0xE, 0xB, 0xD, 0x9,
  0x9, 0xE, 0xB, 0xD,
  0xD, 0x9, 0xE, 0xB,
  0xB, 0xD, 0x9, 0xE
};

// clang-format on

constexpr uint8_t mul_row_column(int row, int column) noexcept {
  uint8_t ret = 0;

  for (auto i = 0; i < 4; ++i) {
    ret ^= M[row * 4 + i](M_inv[i * 4 + column]);
  }

  return ret;
}

// M * M^{-1}
std::array<uint8_t, 16> matrix_mul() noexcept {
  std::array<uint8_t, 16> ret = {0};

  for (auto i = 0; i < 16; ++i) {
    ret[i] = mul_row_column(i / 4, i % 4);
  }

  return ret;
}

int main() {
  auto result = matrix_mul();

  std::cout << "result: [\n";

  for (auto j = 0; j < 4; ++j) {
    std::cout << "\t";
    for (auto i = 0; i < 4; ++i) {
      std::cout << (unsigned)result[j * 4 + i] << ", ";
    }
    std::cout << '\n';
  }

  std::cout << "]" << std::endl;

  return 0;
}