-- The AES128 and AES256 block ciphers.
--
-- Ref:
-- - https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.197-upd1.pdf

local lib = {}

local sBox do
  local substitutionTable = {
    [0] = 0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5,
    0x30, 0x01, 0x67, 0x2b, 0xfe, 0xd7, 0xab, 0x76,
    0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59, 0x47, 0xf0,
    0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0,
    0xb7, 0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc,
    0x34, 0xa5, 0xe5, 0xf1, 0x71, 0xd8, 0x31, 0x15,
    0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05, 0x9a,
    0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75,
    0x09, 0x83, 0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0,
    0x52, 0x3b, 0xd6, 0xb3, 0x29, 0xe3, 0x2f, 0x84,
    0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b,
    0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf,
    0xd0, 0xef, 0xaa, 0xfb, 0x43, 0x4d, 0x33, 0x85,
    0x45, 0xf9, 0x02, 0x7f, 0x50, 0x3c, 0x9f, 0xa8,
    0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5,
    0xbc, 0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2,
    0xcd, 0x0c, 0x13, 0xec, 0x5f, 0x97, 0x44, 0x17,
    0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19, 0x73,
    0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88,
    0x46, 0xee, 0xb8, 0x14, 0xde, 0x5e, 0x0b, 0xdb,
    0xe0, 0x32, 0x3a, 0x0a, 0x49, 0x06, 0x24, 0x5c,
    0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79,
    0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9,
    0x6c, 0x56, 0xf4, 0xea, 0x65, 0x7a, 0xae, 0x08,
    0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6, 0xb4, 0xc6,
    0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x8a,
    0x70, 0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e,
    0x61, 0x35, 0x57, 0xb9, 0x86, 0xc1, 0x1d, 0x9e,
    0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e, 0x94,
    0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf,
    0x8c, 0xa1, 0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68,
    0x41, 0x99, 0x2d, 0x0f, 0xb0, 0x54, 0xbb, 0x16,
  }

  function sBox(x)
    return substitutionTable[x]
  end
end

local invSBox do
  local substitutionTable = {
    [0] = 0x52, 0x09, 0x6a, 0xd5, 0x30, 0x36, 0xa5, 0x38,
    0xbf, 0x40, 0xa3, 0x9e, 0x81, 0xf3, 0xd7, 0xfb,
    0x7c, 0xe3, 0x39, 0x82, 0x9b, 0x2f, 0xff, 0x87,
    0x34, 0x8e, 0x43, 0x44, 0xc4, 0xde, 0xe9, 0xcb,
    0x54, 0x7b, 0x94, 0x32, 0xa6, 0xc2, 0x23, 0x3d,
    0xee, 0x4c, 0x95, 0x0b, 0x42, 0xfa, 0xc3, 0x4e,
    0x08, 0x2e, 0xa1, 0x66, 0x28, 0xd9, 0x24, 0xb2,
    0x76, 0x5b, 0xa2, 0x49, 0x6d, 0x8b, 0xd1, 0x25,
    0x72, 0xf8, 0xf6, 0x64, 0x86, 0x68, 0x98, 0x16,
    0xd4, 0xa4, 0x5c, 0xcc, 0x5d, 0x65, 0xb6, 0x92,
    0x6c, 0x70, 0x48, 0x50, 0xfd, 0xed, 0xb9, 0xda,
    0x5e, 0x15, 0x46, 0x57, 0xa7, 0x8d, 0x9d, 0x84,
    0x90, 0xd8, 0xab, 0x00, 0x8c, 0xbc, 0xd3, 0x0a,
    0xf7, 0xe4, 0x58, 0x05, 0xb8, 0xb3, 0x45, 0x06,
    0xd0, 0x2c, 0x1e, 0x8f, 0xca, 0x3f, 0x0f, 0x02,
    0xc1, 0xaf, 0xbd, 0x03, 0x01, 0x13, 0x8a, 0x6b,
    0x3a, 0x91, 0x11, 0x41, 0x4f, 0x67, 0xdc, 0xea,
    0x97, 0xf2, 0xcf, 0xce, 0xf0, 0xb4, 0xe6, 0x73,
    0x96, 0xac, 0x74, 0x22, 0xe7, 0xad, 0x35, 0x85,
    0xe2, 0xf9, 0x37, 0xe8, 0x1c, 0x75, 0xdf, 0x6e,
    0x47, 0xf1, 0x1a, 0x71, 0x1d, 0x29, 0xc5, 0x89,
    0x6f, 0xb7, 0x62, 0x0e, 0xaa, 0x18, 0xbe, 0x1b,
    0xfc, 0x56, 0x3e, 0x4b, 0xc6, 0xd2, 0x79, 0x20,
    0x9a, 0xdb, 0xc0, 0xfe, 0x78, 0xcd, 0x5a, 0xf4,
    0x1f, 0xdd, 0xa8, 0x33, 0x88, 0x07, 0xc7, 0x31,
    0xb1, 0x12, 0x10, 0x59, 0x27, 0x80, 0xec, 0x5f,
    0x60, 0x51, 0x7f, 0xa9, 0x19, 0xb5, 0x4a, 0x0d,
    0x2d, 0xe5, 0x7a, 0x9f, 0x93, 0xc9, 0x9c, 0xef,
    0xa0, 0xe0, 0x3b, 0x4d, 0xae, 0x2a, 0xf5, 0xb0,
    0xc8, 0xeb, 0xbb, 0x3c, 0x83, 0x53, 0x99, 0x61,
    0x17, 0x2b, 0x04, 0x7e, 0xba, 0x77, 0xd6, 0x26,
    0xe1, 0x69, 0x14, 0x63, 0x55, 0x21, 0x0c, 0x7d,
  }

  function invSBox(x)
    return substitutionTable[x]
  end
end

local function subBytes(state)
  for i = 1, 16, 1 do
    state[i] = sBox(state[i])
  end
end

local function invSubBytes(state)
  for i = 1, 16, 1 do
    state[i] = invSBox(state[i])
  end
end

local function shiftRows(state)
  state[2], state[3], state[4],
    state[6], state[7], state[8],
    state[10], state[11], state[12],
    state[14], state[15], state[16] =
      state[6], state[11], state[16],
      state[10], state[15], state[4],
      state[14], state[3], state[8],
      state[2], state[7], state[12]
end

local function invShiftRows(state)
  state[2], state[3], state[4],
    state[6], state[7], state[8],
    state[10], state[11], state[12],
    state[14], state[15], state[16] =
      state[14], state[11], state[8],
      state[2], state[15], state[12],
      state[6], state[3], state[16],
      state[10], state[7], state[4]
end

local mixColumns, invMixColumns do
  -- lookup tables for multiplication in
  --   GF(2⁸) = (ℤ/2ℤ)[x]/(x⁸ + x⁴ + x³ + x + 1)
  local lutMul2 = {}
  local lutMul3 = {}
  local lutMul9 = {}
  local lutMul11 = {}
  local lutMul13 = {}
  local lutMul14 = {}

  for byte = 0, 255, 1 do
    local mul2 = byte << 1

    if mul2 > 0xff then
      -- subtract the generating polynomial
      -- this could be written branchlessly but I'm not sure it'd be faster
      mul2 = mul2 ~ 0x11b
    end

    local mul4 = mul2 << 1
    if mul4 > 0xff then mul4 = mul4 ~ 0x11b end

    local mul8 = mul4 << 1
    if mul8 > 0xff then mul8 = mul8 ~ 0x11b end

    lutMul2[byte] = mul2
    lutMul3[byte] = mul2 ~ byte
    lutMul9[byte] = mul8 ~ byte
    lutMul11[byte] = mul8 ~ mul2 ~ byte
    lutMul13[byte] = mul8 ~ mul4 ~ byte
    lutMul14[byte] = mul8 ~ mul4 ~ mul2
  end

  -- matrix multiplication in GF(2⁸)
  function mixColumns(state)
    local
      s00, s10, s20, s30,
      s01, s11, s21, s31,
      s02, s12, s22, s32,
      s03, s13, s23, s33 = table.unpack(state)

    state[1] = lutMul2[s00] ~ lutMul3[s10] ~ s20 ~ s30
    state[2] = s00 ~ lutMul2[s10] ~ lutMul3[s20] ~ s30
    state[3] = s00 ~ s10 ~ lutMul2[s20] ~ lutMul3[s30]
    state[4] = lutMul3[s00] ~ s10 ~ s20 ~ lutMul2[s30]

    state[5] = lutMul2[s01] ~ lutMul3[s11] ~ s21 ~ s31
    state[6] = s01 ~ lutMul2[s11] ~ lutMul3[s21] ~ s31
    state[7] = s01 ~ s11 ~ lutMul2[s21] ~ lutMul3[s31]
    state[8] = lutMul3[s01] ~ s11 ~ s21 ~ lutMul2[s31]

    state[9] = lutMul2[s02] ~ lutMul3[s12] ~ s22 ~ s32
    state[10] = s02 ~ lutMul2[s12] ~ lutMul3[s22] ~ s32
    state[11] = s02 ~ s12 ~ lutMul2[s22] ~ lutMul3[s32]
    state[12] = lutMul3[s02] ~ s12 ~ s22 ~ lutMul2[s32]

    state[13] = lutMul2[s03] ~ lutMul3[s13] ~ s23 ~ s33
    state[14] = s03 ~ lutMul2[s13] ~ lutMul3[s23] ~ s33
    state[15] = s03 ~ s13 ~ lutMul2[s23] ~ lutMul3[s33]
    state[16] = lutMul3[s03] ~ s13 ~ s23 ~ lutMul2[s33]
  end

  function invMixColumns(state)
    local
      s00, s10, s20, s30,
      s01, s11, s21, s31,
      s02, s12, s22, s32,
      s03, s13, s23, s33 = table.unpack(state)

    state[1] = lutMul14[s00] ~ lutMul11[s10] ~ lutMul13[s20] ~ lutMul9[s30]
    state[2] = lutMul9[s00] ~ lutMul14[s10] ~ lutMul11[s20] ~ lutMul13[s30]
    state[3] = lutMul13[s00] ~ lutMul9[s10] ~ lutMul14[s20] ~ lutMul11[s30]
    state[4] = lutMul11[s00] ~ lutMul13[s10] ~ lutMul9[s20] ~ lutMul14[s30]

    state[5] = lutMul14[s01] ~ lutMul11[s11] ~ lutMul13[s21] ~ lutMul9[s31]
    state[6] = lutMul9[s01] ~ lutMul14[s11] ~ lutMul11[s21] ~ lutMul13[s31]
    state[7] = lutMul13[s01] ~ lutMul9[s11] ~ lutMul14[s21] ~ lutMul11[s31]
    state[8] = lutMul11[s01] ~ lutMul13[s11] ~ lutMul9[s21] ~ lutMul14[s31]

    state[9] = lutMul14[s02] ~ lutMul11[s12] ~ lutMul13[s22] ~ lutMul9[s32]
    state[10] = lutMul9[s02] ~ lutMul14[s12] ~ lutMul11[s22] ~ lutMul13[s32]
    state[11] = lutMul13[s02] ~ lutMul9[s12] ~ lutMul14[s22] ~ lutMul11[s32]
    state[12] = lutMul11[s02] ~ lutMul13[s12] ~ lutMul9[s22] ~ lutMul14[s32]

    state[13] = lutMul14[s03] ~ lutMul11[s13] ~ lutMul13[s23] ~ lutMul9[s33]
    state[14] = lutMul9[s03] ~ lutMul14[s13] ~ lutMul11[s23] ~ lutMul13[s33]
    state[15] = lutMul13[s03] ~ lutMul9[s13] ~ lutMul14[s23] ~ lutMul11[s33]
    state[16] = lutMul11[s03] ~ lutMul13[s13] ~ lutMul9[s23] ~ lutMul14[s33]
  end
end

local function addRoundKey(state, keySchedule, roundNumber)
  local startIndex = roundNumber * 4 + 1

  for column = 0, 3, 1 do
    local keyWord = keySchedule[startIndex + column]

    state[column * 4 + 1] = state[column * 4 + 1] ~ (keyWord >> 24)
    state[column * 4 + 2] = state[column * 4 + 2] ~ (keyWord >> 16) & 0xff
    state[column * 4 + 3] = state[column * 4 + 3] ~ (keyWord >> 8) & 0xff
    state[column * 4 + 4] = state[column * 4 + 4] ~ keyWord & 0xff
  end
end

local function cipher(plaintext, rounds, keySchedule)
  local state = {("B"):rep(16):unpack(plaintext)}
  addRoundKey(state, keySchedule, 0)

  for roundNumber = 1, rounds - 1, 1 do
    subBytes(state)
    shiftRows(state)
    mixColumns(state)
    addRoundKey(state, keySchedule, roundNumber)
  end

  subBytes(state)
  shiftRows(state)
  addRoundKey(state, keySchedule, rounds)

  return state
end

local keyExpansion do
  local roundConstants = {
    0x01000000,
    0x02000000,
    0x04000000,
    0x08000000,
    0x10000000,
    0x20000000,
    0x40000000,
    0x80000000,
    0x1b000000,
    0x36000000,
  }

  local function subWord(word)
    return
      sBox(word >> 24) << 24
      | sBox((word >> 16) & 0xff) << 16
      | sBox((word >> 8) & 0xff) << 8
      | sBox(word & 0xff)
  end

  local function subRotWord(word)
    return
      sBox((word >> 16) & 0xff) << 24
      | sBox((word >> 8) & 0xff) << 16
      | sBox(word & 0xff) << 8
      | sBox(word >> 24)
  end

  function keyExpansion(key, keyWordCount, rounds)
    assert(
      keyWordCount & (keyWordCount - 1) == 0,
      "keyWordCount must be a power of two"
    )

    local keySchedule = {(">I4"):rep(keyWordCount):unpack(key)}
    local keyWordCountMask = keyWordCount - 1
    local roundWord = 1

    for i = keyWordCount + 1, 4 * (rounds + 1), 1 do
      if i & keyWordCountMask == 1 then
        keySchedule[i] =
          keySchedule[i - keyWordCount]
          ~ subRotWord(keySchedule[i - 1])
          ~ roundConstants[roundWord]
        roundWord = roundWord + 1
      elseif keyWordCount > 6 and i & keyWordCountMask == 5 then
        keySchedule[i] =
          keySchedule[i - keyWordCount]
          ~ subWord(keySchedule[i - 1])
      else
        keySchedule[i] =
          keySchedule[i - keyWordCount]
          ~ keySchedule[i - 1]
      end
    end

    return keySchedule
  end

  lib.keyExpansion = keyExpansion
end

local function invCipher(ciphertext, rounds, keySchedule)
  local state = {("B"):rep(16):unpack(ciphertext)}
  addRoundKey(state, keySchedule, rounds)

  for roundNumber = rounds - 1, 1, -1 do
    invShiftRows(state)
    invSubBytes(state)
    addRoundKey(state, keySchedule, roundNumber)
    invMixColumns(state)
  end

  invShiftRows(state)
  invSubBytes(state)
  addRoundKey(state, keySchedule, 0)

  return state
end

local function concatState(state)
  return ("B"):rep(16):pack(table.unpack(state))
end

local function makeAes(args)
  local keySize = args.keySize
  local rounds = args.rounds
  local keyWordCount = keySize // 4

  return {
    BLOCK_SIZE = 16,
    KEY_SIZE = keySize,

    encrypt = function(self, block, key)
      assert(#block == 16, "block must be 16 bytes long")
      assert(#key == keySize, "key must be " .. keySize .. " bytes long")

      return concatState(
        cipher(block, rounds, keyExpansion(key, keyWordCount, rounds))
      )
    end,

    decrypt = function(self, block, key)
      assert(#block == 16, "block must be 16 bytes long")
      assert(#key == keySize, "key must be " .. keySize .. " bytes long")

      return concatState(
        invCipher(block, rounds, keyExpansion(key, keyWordCount, rounds))
      )
    end,
  }
end

lib.aes128 = makeAes {
  keySize = 16,
  rounds = 10,
}

lib.aes256 = makeAes {
  keySize = 32,
  rounds = 14,
}

return lib
