// Cryptol AES Implementation // Copyright (c) 2010-2013, Galois Inc. // www.cryptol.net // You can freely use this source code for educational purposes. // This is a fairly close implementation of the FIPS-197 standard: // http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf // Nk: Number of blocks in the key // Must be one of 4 (AES128), 6 (AES192), or 8 (AES256) // Aside from this line, no other code below needs to change for // implementing AES128, AES192, or AES256 module AES where type AES128 = 4 type AES192 = 6 type AES256 = 8 type Nk = AES128 // For Cryptol 2.x | x > 0 // NkValid: `Nk -> Bit // property NkValid k = (k == `AES128) || (k == `AES192) || (k == `AES256) // Number of blocks and Number of rounds type Nb = 4 type Nr = 6 + Nk type AESKeySize = (Nk*32) // Helper type definitions type GF28 = [8] type State = [4][Nb]GF28 type RoundKey = State type KeySchedule = (RoundKey, [Nr-1]RoundKey, RoundKey) // GF28 operations gf28Add : {n} (fin n) => [n]GF28 -> GF28 gf28Add ps = sums ! 0 where sums = [zero] # [ p ^ s | p <- ps | s <- sums ] irreducible = <| x^^8 + x^^4 + x^^3 + x + 1 |> gf28Mult : (GF28, GF28) -> GF28 gf28Mult (x, y) = pmod(pmult x y) irreducible gf28Pow : (GF28, [8]) -> GF28 gf28Pow (n, k) = pow k where sq x = gf28Mult (x, x) odd x = x ! 0 pow i = if i == 0 then 1 else if odd i then gf28Mult(n, sq (pow (i >> 1))) else sq (pow (i >> 1)) gf28Inverse : GF28 -> GF28 gf28Inverse x = gf28Pow (x, 254) gf28DotProduct : {n} (fin n) => ([n]GF28, [n]GF28) -> GF28 gf28DotProduct (xs, ys) = gf28Add [ gf28Mult (x, y) | x <- xs | y <- ys ] gf28VectorMult : {n, m} (fin n) => ([n]GF28, [m][n]GF28) -> [m]GF28 gf28VectorMult (v, ms) = [ gf28DotProduct(v, m) | m <- ms ] gf28MatrixMult : {n, m, k} (fin m) => ([n][m]GF28, [m][k]GF28) -> [n][k]GF28 gf28MatrixMult (xss, yss) = [ gf28VectorMult(xs, yss') | xs <- xss ] where yss' = transpose yss // The affine transform and its inverse xformByte : GF28 -> GF28 xformByte b = gf28Add [b, (b >>> 4), (b >>> 5), (b >>> 6), (b >>> 7), c] where c = 0x63 xformByte' : GF28 -> GF28 xformByte' b = gf28Add [(b >>> 2), (b >>> 5), (b >>> 7), d] where d = 0x05 // The SubBytes transform and its inverse SubByte : GF28 -> GF28 SubByte b = xformByte (gf28Inverse b) SubByte' : GF28 -> GF28 SubByte' b = sbox@b SubBytes : State -> State SubBytes state = [ [ SubByte' b | b <- row ] | row <- state ] InvSubByte : GF28 -> GF28 InvSubByte b = gf28Inverse (xformByte' b) InvSubBytes : State -> State InvSubBytes state =[ [ InvSubByte b | b <- row ] | row <- state ] // The ShiftRows transform and its inverse ShiftRows : State -> State ShiftRows state = [ row <<< shiftAmount | row <- state | shiftAmount <- [0 .. 3] ] InvShiftRows : State -> State InvShiftRows state = [ row >>> shiftAmount | row <- state | shiftAmount <- [0 .. 3] ] // The MixColumns transform and its inverse MixColumns : State -> State MixColumns state = gf28MatrixMult (m, state) where m = [[2, 3, 1, 1], [1, 2, 3, 1], [1, 1, 2, 3], [3, 1, 1, 2]] InvMixColumns : State -> State InvMixColumns state = gf28MatrixMult (m, state) where m = [[0x0e, 0x0b, 0x0d, 0x09], [0x09, 0x0e, 0x0b, 0x0d], [0x0d, 0x09, 0x0e, 0x0b], [0x0b, 0x0d, 0x09, 0x0e]] // The AddRoundKey transform AddRoundKey : (RoundKey, State) -> State AddRoundKey (rk, s) = rk ^ s // Key expansion Rcon : [8] -> [4]GF28 Rcon i = [(gf28Pow (<| x |>, i-1)), 0, 0, 0] SubWord : [4]GF28 -> [4]GF28 SubWord bs = [ SubByte b | b <- bs ] RotWord : [4]GF28 -> [4]GF28 RotWord [a0, a1, a2, a3] = [a1, a2, a3, a0] NextWord : ([8],[4][8],[4][8]) -> [4][8] NextWord(i, prev, old) = old ^ mask where mask = if i % `Nk == 0 then SubWord(RotWord(prev)) ^ Rcon (i / `Nk) else if (`Nk > 6) && (i % `Nk == 4) then SubWord(prev) else prev ExpandKeyForever : [Nk][4][8] -> [inf]RoundKey ExpandKeyForever seed = [ transpose g | g <- groupBy`{4} (keyWS seed) ] keyWS : [Nk][4][8] -> [inf][4][8] keyWS seed = xs where xs = seed # [ NextWord(i, prev, old) | i <- [ `Nk ... ] | prev <- drop`{Nk-1} xs | old <- xs ] checkKey = take`{16} (drop`{8} (keyWS ["abcd", "defg", "1234", "5678"])) checkKey2 = [transpose g | g <- groupBy`{4}checkKey] ExpandKey : [AESKeySize] -> KeySchedule ExpandKey key = (keys @ 0, keys @@ [1 .. (Nr - 1)], keys @ `Nr) where seed : [Nk][4][8] seed = split (split key) keys = ExpandKeyForever seed fromKS : KeySchedule -> [Nr+1][4][32] fromKS (f, ms, l) = [ formKeyWords (transpose k) | k <- [f] # ms # [l] ] where formKeyWords bbs = [ join bs | bs <- bbs ] // AES rounds and inverses AESRound : (RoundKey, State) -> State AESRound (rk, s) = AddRoundKey (rk, MixColumns (ShiftRows (SubBytes s))) AESFinalRound : (RoundKey, State) -> State AESFinalRound (rk, s) = AddRoundKey (rk, ShiftRows (SubBytes s)) AESInvRound : (RoundKey, State) -> State AESInvRound (rk, s) = InvMixColumns (AddRoundKey (rk, InvSubBytes (InvShiftRows s))) AESFinalInvRound : (RoundKey, State) -> State AESFinalInvRound (rk, s) = AddRoundKey (rk, InvSubBytes (InvShiftRows s)) // Converting a 128 bit message to a State and back msgToState : [128] -> State msgToState msg = transpose (split (split msg)) stateToMsg : State -> [128] stateToMsg st = join (join (transpose st)) // AES Encryption aesEncrypt : ([128], [AESKeySize]) -> [128] aesEncrypt (pt, key) = stateToMsg (AESFinalRound (kFinal, rounds ! 0)) where (kInit, ks, kFinal) = ExpandKey key state0 = AddRoundKey(kInit, msgToState pt) rounds = [state0] # [ AESRound (rk, s) | rk <- ks | s <- rounds ] // AES Decryption aesDecrypt : ([128], [AESKeySize]) -> [128] aesDecrypt (ct, key) = stateToMsg (AESFinalInvRound (kFinal, rounds ! 0)) where (kFinal, ks, kInit) = ExpandKey key state0 = AddRoundKey(kInit, msgToState ct) rounds = [state0] # [ AESInvRound (rk, s) | rk <- reverse ks | s <- rounds ] sbox : [256]GF28 sbox = [ 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] // Test runs: // cryptol> aesEncrypt (0x3243f6a8885a308d313198a2e0370734, \ // 0x2b7e151628aed2a6abf7158809cf4f3c) // 0x3925841d02dc09fbdc118597196a0b32 // cryptol> aesEncrypt (0x00112233445566778899aabbccddeeff, \ // 0x000102030405060708090a0b0c0d0e0f) // 0x69c4e0d86a7b0430d8cdb78070b4c55a property AESCorrect msg key = aesDecrypt (aesEncrypt (msg, key), key) == msg // Benchmark: type nblocks = 128 bench_data : [128 * nblocks] bench_data = random 0 bench : [128 * nblocks] -> [128 * nblocks] bench data = join [ aesEncrypt (block, key) | block <- split data ] where key = 0x3243f6a8885a308d313198a2e0370734