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237 lines
8.3 KiB
Plaintext
237 lines
8.3 KiB
Plaintext
// Cryptol AES Implementation
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// Copyright (c) 2010-2013, Galois Inc.
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// www.cryptol.net
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// You can freely use this source code for educational purposes.
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// This is a fairly close implementation of the FIPS-197 standard:
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// http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf
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// Nk: Number of blocks in the key
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// Must be one of 4 (AES128), 6 (AES192), or 8 (AES256)
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// Aside from this line, no other code below needs to change for
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// implementing AES128, AES192, or AES256
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module AES where
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type AES128 = 4
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type AES192 = 6
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type AES256 = 8
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type Nk = AES128
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// For Cryptol 2.x | x > 0
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// NkValid: `Nk -> Bit
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// property NkValid k = (k == `AES128) || (k == `AES192) || (k == `AES256)
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// Number of blocks and Number of rounds
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type Nb = 4
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type Nr = 6 + Nk
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type AESKeySize = (Nk*32)
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// Helper type definitions
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type GF28 = [8]
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type State = [4][Nb]GF28
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type RoundKey = State
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type KeySchedule = (RoundKey, [Nr-1]RoundKey, RoundKey)
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// GF28 operations
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gf28Add : {n} (fin n) => [n]GF28 -> GF28
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gf28Add ps = sums ! 0
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where sums = [zero] # [ p ^ s | p <- ps | s <- sums ]
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irreducible = <| x^^8 + x^^4 + x^^3 + x + 1 |>
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gf28Mult : (GF28, GF28) -> GF28
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gf28Mult (x, y) = pmod(pmult x y) irreducible
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gf28Pow : (GF28, [8]) -> GF28
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gf28Pow (n, k) = pow k
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where sq x = gf28Mult (x, x)
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odd x = x ! 0
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pow i = if i == 0 then 1
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else if odd i
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then gf28Mult(n, sq (pow (i >> 1)))
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else sq (pow (i >> 1))
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gf28Inverse : GF28 -> GF28
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gf28Inverse x = gf28Pow (x, 254)
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gf28DotProduct : {n} (fin n) => ([n]GF28, [n]GF28) -> GF28
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gf28DotProduct (xs, ys) = gf28Add [ gf28Mult (x, y) | x <- xs
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| y <- ys ]
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gf28VectorMult : {n, m} (fin n) => ([n]GF28, [m][n]GF28) -> [m]GF28
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gf28VectorMult (v, ms) = [ gf28DotProduct(v, m) | m <- ms ]
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gf28MatrixMult : {n, m, k} (fin m) => ([n][m]GF28, [m][k]GF28) -> [n][k]GF28
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gf28MatrixMult (xss, yss) = [ gf28VectorMult(xs, yss') | xs <- xss ]
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where yss' = transpose yss
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// The affine transform and its inverse
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xformByte : GF28 -> GF28
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xformByte b = gf28Add [b, (b >>> 4), (b >>> 5), (b >>> 6), (b >>> 7), c]
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where c = 0x63
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xformByte' : GF28 -> GF28
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xformByte' b = gf28Add [(b >>> 2), (b >>> 5), (b >>> 7), d] where d = 0x05
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// The SubBytes transform and its inverse
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SubByte : GF28 -> GF28
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SubByte b = xformByte (gf28Inverse b)
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SubByte' : GF28 -> GF28
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SubByte' b = sbox@b
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SubBytes : State -> State
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SubBytes state = [ [ SubByte' b | b <- row ] | row <- state ]
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InvSubByte : GF28 -> GF28
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InvSubByte b = gf28Inverse (xformByte' b)
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InvSubBytes : State -> State
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InvSubBytes state = [ [ InvSubByte b | b <- row ] | row <- state ]
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// The ShiftRows transform and its inverse
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ShiftRows : State -> State
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ShiftRows state = [ row <<< shiftAmount | row <- state
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| shiftAmount <- [0 .. 3]
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]
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InvShiftRows : State -> State
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InvShiftRows state = [ row >>> shiftAmount | row <- state
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| shiftAmount <- [0 .. 3]
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]
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// The MixColumns transform and its inverse
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MixColumns : State -> State
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MixColumns state = gf28MatrixMult (m, state)
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where m = [[2, 3, 1, 1],
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[1, 2, 3, 1],
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[1, 1, 2, 3],
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[3, 1, 1, 2]]
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InvMixColumns : State -> State
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InvMixColumns state = gf28MatrixMult (m, state)
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where m = [[0x0e, 0x0b, 0x0d, 0x09],
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[0x09, 0x0e, 0x0b, 0x0d],
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[0x0d, 0x09, 0x0e, 0x0b],
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[0x0b, 0x0d, 0x09, 0x0e]]
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// The AddRoundKey transform
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AddRoundKey : (RoundKey, State) -> State
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AddRoundKey (rk, s) = rk ^ s
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// Key expansion
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Rcon : [8] -> [4]GF28
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Rcon i = [(gf28Pow (<| x |>, i-1)), 0, 0, 0]
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SubWord : [4]GF28 -> [4]GF28
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SubWord bs = [ SubByte' b | b <- bs ]
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RotWord : [4]GF28 -> [4]GF28
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RotWord [a0, a1, a2, a3] = [a1, a2, a3, a0]
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NextWord : ([8],[4][8],[4][8]) -> [4][8]
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NextWord(i, prev, old) = old ^ mask
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where mask = if i % `Nk == 0
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then SubWord(RotWord(prev)) ^ Rcon (i / `Nk)
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else if (`Nk > 6) && (i % `Nk == 4)
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then SubWord(prev)
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else prev
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ExpandKeyForever : [Nk][4][8] -> [inf]RoundKey
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ExpandKeyForever seed = [ transpose g | g <- groupBy`{4} (keyWS seed) ]
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keyWS : [Nk][4][8] -> [inf][4][8]
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keyWS seed = xs
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where xs = seed # [ NextWord(i, prev, old)
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| i <- [ `Nk ... ]
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| prev <- drop`{Nk-1} xs
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| old <- xs
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]
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ExpandKey : [AESKeySize] -> KeySchedule
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ExpandKey key = (keys @ 0, keys @@ [1 .. (Nr - 1)], keys @ `Nr)
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where seed : [Nk][4][8]
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seed = split (split key)
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keys = ExpandKeyForever seed
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fromKS : KeySchedule -> [Nr+1][4][32]
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fromKS (f, ms, l) = [ formKeyWords (transpose k) | k <- [f] # ms # [l] ]
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where formKeyWords bbs = [ join bs | bs <- bbs ]
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// AES rounds and inverses
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AESRound : (RoundKey, State) -> State
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AESRound (rk, s) = AddRoundKey (rk, MixColumns (ShiftRows (SubBytes s)))
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AESFinalRound : (RoundKey, State) -> State
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AESFinalRound (rk, s) = AddRoundKey (rk, ShiftRows (SubBytes s))
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AESInvRound : (RoundKey, State) -> State
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AESInvRound (rk, s) =
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InvMixColumns (AddRoundKey (rk, InvSubBytes (InvShiftRows s)))
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AESFinalInvRound : (RoundKey, State) -> State
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AESFinalInvRound (rk, s) = AddRoundKey (rk, InvSubBytes (InvShiftRows s))
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// Converting a 128 bit message to a State and back
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msgToState : [128] -> State
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msgToState msg = transpose (split (split msg))
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stateToMsg : State -> [128]
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stateToMsg st = join (join (transpose st))
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// AES Encryption
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aesEncrypt : ([128], [AESKeySize]) -> [128]
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aesEncrypt (pt, key) = stateToMsg (AESFinalRound (kFinal, rounds ! 0))
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where (kInit, ks, kFinal) = ExpandKey key
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state0 = AddRoundKey(kInit, msgToState pt)
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rounds = [state0] # [ AESRound (rk, s) | rk <- ks
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| s <- rounds
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]
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// AES Decryption
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aesDecrypt : ([128], [AESKeySize]) -> [128]
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aesDecrypt (ct, key) = stateToMsg (AESFinalInvRound (kFinal, rounds ! 0))
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where (kFinal, ks, kInit) = ExpandKey key
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state0 = AddRoundKey(kInit, msgToState ct)
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rounds = [state0] # [ AESInvRound (rk, s)
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| rk <- reverse ks
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| s <- rounds
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]
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sbox : [256]GF28
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sbox = [
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0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5, 0x30, 0x01, 0x67,
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0x2b, 0xfe, 0xd7, 0xab, 0x76, 0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59,
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0x47, 0xf0, 0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0, 0xb7,
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0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc, 0x34, 0xa5, 0xe5, 0xf1,
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0x71, 0xd8, 0x31, 0x15, 0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05,
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0x9a, 0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75, 0x09, 0x83,
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0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0, 0x52, 0x3b, 0xd6, 0xb3, 0x29,
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0xe3, 0x2f, 0x84, 0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b,
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0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf, 0xd0, 0xef, 0xaa,
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0xfb, 0x43, 0x4d, 0x33, 0x85, 0x45, 0xf9, 0x02, 0x7f, 0x50, 0x3c,
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0x9f, 0xa8, 0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5, 0xbc,
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0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2, 0xcd, 0x0c, 0x13, 0xec,
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0x5f, 0x97, 0x44, 0x17, 0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19,
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0x73, 0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88, 0x46, 0xee,
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0xb8, 0x14, 0xde, 0x5e, 0x0b, 0xdb, 0xe0, 0x32, 0x3a, 0x0a, 0x49,
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0x06, 0x24, 0x5c, 0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79,
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0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9, 0x6c, 0x56, 0xf4,
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0xea, 0x65, 0x7a, 0xae, 0x08, 0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6,
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0xb4, 0xc6, 0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x8a, 0x70,
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0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e, 0x61, 0x35, 0x57, 0xb9,
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0x86, 0xc1, 0x1d, 0x9e, 0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e,
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0x94, 0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf, 0x8c, 0xa1,
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0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68, 0x41, 0x99, 0x2d, 0x0f, 0xb0,
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0x54, 0xbb, 0x16]
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// Test runs:
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// cryptol> aesEncrypt (0x3243f6a8885a308d313198a2e0370734, \
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// 0x2b7e151628aed2a6abf7158809cf4f3c)
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// 0x3925841d02dc09fbdc118597196a0b32
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// cryptol> aesEncrypt (0x00112233445566778899aabbccddeeff, \
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// 0x000102030405060708090a0b0c0d0e0f)
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// 0x69c4e0d86a7b0430d8cdb78070b4c55a
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property AESCorrect msg key = aesDecrypt (aesEncrypt (msg, key), key) == msg
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