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cryptol/notebook/AES.ipynb
Adam C. Foltzer ba0a0e8576 Initial import from internal repo
2014-04-17 15:34:25 -07:00

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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Cryptol AES Implementation ##\n",
"Copyright (c) 2010-2013, Galois Inc. \n",
"[www.cryptol.net](http://www.cryptol.net) \n",
"You can freely use this source code for educational purposes. \n",
"\n",
"This is a fairly close implementation of the [FIPS-197 standard](http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Key size ###\n",
"\n",
"Let `Nk` be the number of blocks in the key. This must be one of `4` (AES128), `6` (AES192), or `8` (AES256).\n",
"\n",
"Aside from this line, no other code below needs to change for implementing AES128, AES192, or AES256."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"type Nk = 4\n",
"type AESKeySize = (Nk*32)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Number of blocks and rounds"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"type Nb = 4\n",
"type Nr = 6 + Nk"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Helper type definitions"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"type GF28 = [8]\n",
"type State = [4][Nb]GF28\n",
"type RoundKey = State\n",
"type KeySchedule = (RoundKey, [Nr-1]RoundKey, RoundKey) "
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$GF(2^8)$ operations"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"gf28Add : {n} (fin n) => [n]GF28 -> GF28\n",
"gf28Add ps = sums ! 0\n",
" where sums = [zero] # [ p ^ s | p <- ps | s <- sums ]\n",
"\n",
"irreducible = <| x^^8 + x^^4 + x^^3 + x + 1 |>\n",
"\n",
"gf28Mult : (GF28, GF28) -> GF28\n",
"gf28Mult (x, y) = pmod(pmult x y) irreducible\n",
"\n",
"gf28Pow : (GF28, [8]) -> GF28\n",
"gf28Pow (n, k) = pow k\n",
" where sq x = gf28Mult (x, x)\n",
" odd x = x ! 0\n",
" pow i = if i == 0 then 1\n",
" else if odd i\n",
" then gf28Mult(n, sq (pow (i >> 1)))\n",
" else sq (pow (i >> 1))\n",
"\n",
"gf28Inverse : GF28 -> GF28\n",
"gf28Inverse x = gf28Pow (x, 254)\n",
"\n",
"gf28DotProduct : {n} (fin n) => ([n]GF28, [n]GF28) -> GF28\n",
"gf28DotProduct (xs, ys) = gf28Add [ gf28Mult (x, y) | x <- xs\n",
" | y <- ys ]\n",
"\n",
"gf28VectorMult : {n, m} (fin n) => ([n]GF28, [m][n]GF28) -> [m]GF28\n",
"gf28VectorMult (v, ms) = [ gf28DotProduct(v, m) | m <- ms ]\n",
"\n",
"gf28MatrixMult : {n, m, k} (fin m) => ([n][m]GF28, [m][k]GF28) -> [n][k]GF28\n",
"gf28MatrixMult (xss, yss) = [ gf28VectorMult(xs, yss') | xs <- xss ]\n",
" where yss' = transpose yss"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:16:52--16:54\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:17:40--17:42\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:13:21--13:22\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--3:57:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:19--2:20\r\n",
" to 0\r\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The affine transform and its inverse"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"xformByte : GF28 -> GF28\n",
"xformByte b = gf28Add [b, (b >>> 4), (b >>> 5), (b >>> 6), (b >>> 7), c]\n",
" where c = 0x63\n",
"\n",
"xformByte' : GF28 -> GF28\n",
"xformByte' b = gf28Add [(b >>> 2), (b >>> 5), (b >>> 7), d] where d = 0x05"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:28--6:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:39--6:42\r\n",
" to 3\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:50--6:53\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:30--2:33\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:41--2:44\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:52--2:55\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:63--2:66\r\n",
" to 3\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:16:52--16:54\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:17:40--17:42\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:13:21--13:22\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--3:57:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:19--2:20\r\n",
" to 0\r\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The S-box"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sbox : [256]GF28\n",
"sbox = [\n",
" 0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5, 0x30, 0x01, 0x67, 0x2b, 0xfe, 0xd7, 0xab, 0x76,\n",
" 0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59, 0x47, 0xf0, 0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0,\n",
" 0xb7, 0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc, 0x34, 0xa5, 0xe5, 0xf1, 0x71, 0xd8, 0x31, 0x15,\n",
" 0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05, 0x9a, 0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75,\n",
" 0x09, 0x83, 0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0, 0x52, 0x3b, 0xd6, 0xb3, 0x29, 0xe3, 0x2f, 0x84,\n",
" 0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b, 0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf,\n",
" 0xd0, 0xef, 0xaa, 0xfb, 0x43, 0x4d, 0x33, 0x85, 0x45, 0xf9, 0x02, 0x7f, 0x50, 0x3c, 0x9f, 0xa8,\n",
" 0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5, 0xbc, 0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2,\n",
" 0xcd, 0x0c, 0x13, 0xec, 0x5f, 0x97, 0x44, 0x17, 0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19, 0x73,\n",
" 0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88, 0x46, 0xee, 0xb8, 0x14, 0xde, 0x5e, 0x0b, 0xdb,\n",
" 0xe0, 0x32, 0x3a, 0x0a, 0x49, 0x06, 0x24, 0x5c, 0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79,\n",
" 0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9, 0x6c, 0x56, 0xf4, 0xea, 0x65, 0x7a, 0xae, 0x08,\n",
" 0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6, 0xb4, 0xc6, 0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x8a,\n",
" 0x70, 0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e, 0x61, 0x35, 0x57, 0xb9, 0x86, 0xc1, 0x1d, 0x9e,\n",
" 0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e, 0x94, 0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf,\n",
" 0x8c, 0xa1, 0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68, 0x41, 0x99, 0x2d, 0x0f, 0xb0, 0x54, 0xbb, 0x16\n",
" ]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:28--6:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:39--6:42\r\n",
" to 3\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:50--6:53\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:30--2:33\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:41--2:44\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:52--2:55\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:63--2:66\r\n",
" to 3\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:16:52--16:54\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:17:40--17:42\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:13:21--13:22\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--3:57:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:19--2:20\r\n",
" to 0\r\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The SubBytes transform and its inverse"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"SubByte : GF28 -> GF28\n",
"SubByte b = xformByte (gf28Inverse b)\n",
"\n",
"SubByte' : GF28 -> GF28\n",
"SubByte' b = sbox@b\n",
"\n",
"SubBytes : State -> State\n",
"SubBytes state = [ [ SubByte' b | b <- row ] | row <- state ]\n",
"\n",
"\n",
"InvSubByte : GF28 -> GF28\n",
"InvSubByte b = gf28Inverse (xformByte' b)\n",
"\n",
"InvSubBytes : State -> State\n",
"InvSubBytes state =[ [ InvSubByte b | b <- row ] | row <- state ]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:28--6:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:39--6:42\r\n",
" to 3\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:50--6:53\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:30--2:33\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:41--2:44\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:52--2:55\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:63--2:66\r\n",
" to 3\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:16:52--16:54\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:17:40--17:42\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:13:21--13:22\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--3:57:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:19--2:20\r\n",
" to 0\r\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The ShiftRows transform and its inverse"
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"ShiftRows : State -> State\n",
"ShiftRows state = [ row <<< shiftAmount | row <- state\n",
" | shiftAmount <- [0 .. 3]\n",
" ]\n",
"\n",
"InvShiftRows : State -> State\n",
"InvShiftRows state = [ row >>> shiftAmount | row <- state\n",
" | shiftAmount <- [0 .. 3]\n",
" ]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n",
"[warning] at <notebook>:7:1--9:23:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:7:28--7:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:2:1--4:20:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (<<<)\r\n",
" at <notebook>:2:25--2:28\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:28--6:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:39--6:42\r\n",
" to 3\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:50--6:53\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:30--2:33\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:41--2:44\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:52--2:55\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:63--2:66\r\n",
" to 3\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:16:52--16:54\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:17:40--17:42\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:13:21--13:22\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--3:57:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:19--2:20\r\n",
" to 0\r\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The MixColumns transform and its inverse"
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"MixColumns : State -> State\n",
"MixColumns state = gf28MatrixMult (m, state)\n",
" where m = [[2, 3, 1, 1],\n",
" [1, 2, 3, 1],\n",
" [1, 1, 2, 3],\n",
" [3, 1, 1, 2]]\n",
"\n",
"InvMixColumns : State -> State\n",
"InvMixColumns state = gf28MatrixMult (m, state)\n",
" where m = [[0x0e, 0x0b, 0x0d, 0x09],\n",
" [0x09, 0x0e, 0x0b, 0x0d],\n",
" [0x0d, 0x09, 0x0e, 0x0b],\n",
" [0x0b, 0x0d, 0x09, 0x0e]]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n",
"[warning] at <notebook>:7:1--9:23:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:7:28--7:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:2:1--4:20:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (<<<)\r\n",
" at <notebook>:2:25--2:28\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:28--6:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:39--6:42\r\n",
" to 3\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:50--6:53\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:30--2:33\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:41--2:44\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:52--2:55\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:63--2:66\r\n",
" to 3\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:16:52--16:54\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:17:40--17:42\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:13:21--13:22\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--3:57:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:19--2:20\r\n",
" to 0\r\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The AddRoundKey transform"
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"AddRoundKey : (RoundKey, State) -> State\n",
"AddRoundKey (rk, s) = rk ^ s"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n",
"[warning] at <notebook>:7:1--9:23:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:7:28--7:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:2:1--4:20:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (<<<)\r\n",
" at <notebook>:2:25--2:28\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:28--6:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:39--6:42\r\n",
" to 3\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:50--6:53\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:30--2:33\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:41--2:44\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:52--2:55\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:63--2:66\r\n",
" to 3\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:16:52--16:54\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:17:40--17:42\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:13:21--13:22\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--3:57:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:19--2:20\r\n",
" to 0\r\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Key expansion"
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"Rcon : [8] -> [4]GF28\n",
"Rcon i = [(gf28Pow (<| x |>, i-1)), 0, 0, 0]\n",
"\n",
"SubWord : [4]GF28 -> [4]GF28\n",
"SubWord bs = [ SubByte b | b <- bs ]\n",
"\n",
"RotWord : [4]GF28 -> [4]GF28\n",
"RotWord [a0, a1, a2, a3] = [a1, a2, a3, a0]\n",
"\n",
"NextWord : ([8],[4][8],[4][8]) -> [4][8]\n",
"NextWord(i, prev, old) = old ^ mask\n",
" where mask = if i % `Nk == 0\n",
" then SubWord(RotWord(prev)) ^ Rcon (i / `Nk)\n",
" else if (`Nk > 6) && (i % `Nk == 4)\n",
" then SubWord(prev)\n",
" else prev\n",
"\n",
"\n",
"ExpandKeyForever : [Nk][4][8] -> [inf]RoundKey\n",
"ExpandKeyForever seed = [ transpose g | g <- groupBy`{4} (keyWS seed) ]\n",
"\n",
"keyWS : [Nk][4][8] -> [inf][4][8]\n",
"keyWS seed = ret where \n",
" ret = seed # [ NextWord(i, prev, old)\n",
" | i <- [ `Nk ... ]\n",
" | prev <- drop`{Nk-1} ret\n",
" | old <- ret\n",
" ]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n",
"[warning] at <notebook>:11:26--16:31:\r\n",
" Defaulting type parameter 'bits'\r\n",
" of literal or demoted expression\r\n",
" at <notebook>:14:26--14:29\r\n",
" to 3\r\n",
"[warning] at <notebook>:7:1--9:23:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:7:28--7:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:2:1--4:20:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (<<<)\r\n",
" at <notebook>:2:25--2:28\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:28--6:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:39--6:42\r\n",
" to 3\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:50--6:53\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:30--2:33\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:41--2:44\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:52--2:55\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:63--2:66\r\n",
" to 3\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:16:52--16:54\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:17:40--17:42\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:13:21--13:22\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--3:57:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:19--2:20\r\n",
" to 0\r\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"checkKey = take`{16} (drop`{8} (keyWS [\"abcd\", \"defg\", \"1234\", \"5678\"]))\n",
"checkKey2 = [transpose g | g <- groupBy`{4}checkKey]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n",
"[warning] at <notebook>:11:26--16:31:\r\n",
" Defaulting type parameter 'bits'\r\n",
" of literal or demoted expression\r\n",
" at <notebook>:14:26--14:29\r\n",
" to 3\r\n",
"[warning] at <notebook>:7:1--9:23:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:7:28--7:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:2:1--4:20:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (<<<)\r\n",
" at <notebook>:2:25--2:28\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:28--6:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:39--6:42\r\n",
" to 3\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:50--6:53\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:30--2:33\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:41--2:44\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:52--2:55\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:63--2:66\r\n",
" to 3\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:16:52--16:54\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:17:40--17:42\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:13:21--13:22\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--3:57:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:19--2:20\r\n",
" to 0\r\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"checkKey\n",
"checkKey2"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"[[137, 151, 138, 153], [136, 10, 136, 12], [184, 165, 185, 173],\r\n",
" [189, 60, 191, 52], [102, 159, 146, 227], [238, 149, 26, 239],\r\n",
" [86, 48, 163, 66], [235, 12, 28, 118], [144, 3, 170, 10],\r\n",
" [126, 150, 176, 229], [40, 166, 19, 167], [195, 170, 15, 209],\r\n",
" [44, 117, 148, 36], [82, 227, 36, 193], [122, 69, 55, 102],\r\n",
" [185, 239, 56, 183]]\r\n",
"[[[137, 136, 184, 189], [151, 10, 165, 60], [138, 136, 185, 191],\r\n",
" [153, 12, 173, 52]],\r\n",
" [[102, 238, 86, 235], [159, 149, 48, 12], [146, 26, 163, 28],\r\n",
" [227, 239, 66, 118]],\r\n",
" [[144, 126, 40, 195], [3, 150, 166, 170], [170, 176, 19, 15],\r\n",
" [10, 229, 167, 209]],\r\n",
" [[44, 82, 122, 185], [117, 227, 69, 239], [148, 36, 55, 56],\r\n",
" [36, 193, 102, 183]]]\r\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"ExpandKey : [AESKeySize] -> KeySchedule\n",
"ExpandKey key = (keys @ 0, keys @@ [1 .. (Nr - 1)], keys @ `Nr)\n",
" where seed : [Nk][4][8]\n",
" seed = split (split key)\n",
" keys = ExpandKeyForever seed\n",
"\n",
"fromKS : KeySchedule -> [Nr+1][4][32]\n",
"fromKS (f, ms, l) = [ formKeyWords (transpose k) | k <- [f] # ms # [l] ]\n",
" where formKeyWords bbs = [ join bs | bs <- bbs ]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (@)\r\n",
" at <notebook>:2:23--2:24\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 4th type parameter\r\n",
" of expression (@@)\r\n",
" at <notebook>:2:33--2:35\r\n",
" to 4\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (@)\r\n",
" at <notebook>:2:58--2:59\r\n",
" to 4\r\n",
"[warning] at <notebook>:11:26--16:31:\r\n",
" Defaulting type parameter 'bits'\r\n",
" of literal or demoted expression\r\n",
" at <notebook>:14:26--14:29\r\n",
" to 3\r\n",
"[warning] at <notebook>:7:1--9:23:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:7:28--7:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:2:1--4:20:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (<<<)\r\n",
" at <notebook>:2:25--2:28\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:28--6:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:39--6:42\r\n",
" to 3\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:50--6:53\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:30--2:33\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:41--2:44\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:52--2:55\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:63--2:66\r\n",
" to 3\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:16:52--16:54\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:17:40--17:42\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:13:21--13:22\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--3:57:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:19--2:20\r\n",
" to 0\r\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"AES rounds and inverses"
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"AESRound : (RoundKey, State) -> State\n",
"AESRound (rk, s) = AddRoundKey (rk, MixColumns (ShiftRows (SubBytes s)))\n",
"\n",
"AESFinalRound : (RoundKey, State) -> State\n",
"AESFinalRound (rk, s) = AddRoundKey (rk, ShiftRows (SubBytes s))\n",
"\n",
"AESInvRound : (RoundKey, State) -> State\n",
"AESInvRound (rk, s) =\n",
" InvMixColumns (AddRoundKey (rk, InvSubBytes (InvShiftRows s)))\n",
"AESFinalInvRound : (RoundKey, State) -> State\n",
"AESFinalInvRound (rk, s) = AddRoundKey (rk, InvSubBytes (InvShiftRows s))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (@)\r\n",
" at <notebook>:2:23--2:24\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 4th type parameter\r\n",
" of expression (@@)\r\n",
" at <notebook>:2:33--2:35\r\n",
" to 4\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (@)\r\n",
" at <notebook>:2:58--2:59\r\n",
" to 4\r\n",
"[warning] at <notebook>:11:26--16:31:\r\n",
" Defaulting type parameter 'bits'\r\n",
" of literal or demoted expression\r\n",
" at <notebook>:14:26--14:29\r\n",
" to 3\r\n",
"[warning] at <notebook>:7:1--9:23:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:7:28--7:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:2:1--4:20:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (<<<)\r\n",
" at <notebook>:2:25--2:28\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:28--6:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:39--6:42\r\n",
" to 3\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:50--6:53\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:30--2:33\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:41--2:44\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:52--2:55\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:63--2:66\r\n",
" to 3\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:16:52--16:54\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:17:40--17:42\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:13:21--13:22\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--3:57:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:19--2:20\r\n",
" to 0\r\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Converting a 128 bit message to a `State` and then back"
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"msgToState : [128] -> State\n",
"msgToState msg = transpose (split (split msg))\n",
"\n",
"stateToMsg : State -> [128]\n",
"stateToMsg st = join (join (transpose st))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (@)\r\n",
" at <notebook>:2:23--2:24\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 4th type parameter\r\n",
" of expression (@@)\r\n",
" at <notebook>:2:33--2:35\r\n",
" to 4\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (@)\r\n",
" at <notebook>:2:58--2:59\r\n",
" to 4\r\n",
"[warning] at <notebook>:11:26--16:31:\r\n",
" Defaulting type parameter 'bits'\r\n",
" of literal or demoted expression\r\n",
" at <notebook>:14:26--14:29\r\n",
" to 3\r\n",
"[warning] at <notebook>:7:1--9:23:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:7:28--7:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:2:1--4:20:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (<<<)\r\n",
" at <notebook>:2:25--2:28\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:28--6:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:39--6:42\r\n",
" to 3\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:50--6:53\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:30--2:33\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:41--2:44\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:52--2:55\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:63--2:66\r\n",
" to 3\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:16:52--16:54\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:17:40--17:42\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:13:21--13:22\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--3:57:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:19--2:20\r\n",
" to 0\r\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"AES Encryption"
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"aesEncrypt : ([128], [AESKeySize]) -> [128]\n",
"aesEncrypt (pt, key) = stateToMsg (AESFinalRound (kFinal, rounds ! 0))\n",
" where (kInit, ks, kFinal) = ExpandKey key\n",
" state0 = AddRoundKey(kInit, msgToState pt)\n",
" rounds = [state0] # [ AESRound (rk, s) | rk <- ks\n",
" | s <- rounds\n",
" ]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n",
"[warning] at <notebook>:2:1--2:11:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:66--2:67\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (@)\r\n",
" at <notebook>:2:23--2:24\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 4th type parameter\r\n",
" of expression (@@)\r\n",
" at <notebook>:2:33--2:35\r\n",
" to 4\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (@)\r\n",
" at <notebook>:2:58--2:59\r\n",
" to 4\r\n",
"[warning] at <notebook>:11:26--16:31:\r\n",
" Defaulting type parameter 'bits'\r\n",
" of literal or demoted expression\r\n",
" at <notebook>:14:26--14:29\r\n",
" to 3\r\n",
"[warning] at <notebook>:7:1--9:23:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:7:28--7:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:2:1--4:20:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (<<<)\r\n",
" at <notebook>:2:25--2:28\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:28--6:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:39--6:42\r\n",
" to 3\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:50--6:53\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:30--2:33\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:41--2:44\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:52--2:55\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:63--2:66\r\n",
" to 3\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:16:52--16:54\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:17:40--17:42\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:13:21--13:22\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--3:57:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:19--2:20\r\n",
" to 0\r\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"AES Decryption"
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"aesDecrypt : ([128], [AESKeySize]) -> [128]\n",
"aesDecrypt (ct, key) = stateToMsg (AESFinalInvRound (kFinal, rounds ! 0))\n",
" where (kFinal, ks, kInit) = ExpandKey key\n",
" state0 = AddRoundKey(kInit, msgToState ct)\n",
" rounds = [state0] # [ AESInvRound (rk, s) | rk <- reverse ks\n",
" | s <- rounds\n",
" ]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"Loading module Prelude\r\n",
"Loading module Notebook\r\n",
"[warning] at <notebook>:2:1--2:11:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:69--2:70\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--2:11:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:66--2:67\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (@)\r\n",
" at <notebook>:2:23--2:24\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 4th type parameter\r\n",
" of expression (@@)\r\n",
" at <notebook>:2:33--2:35\r\n",
" to 4\r\n",
"[warning] at <notebook>:2:1--5:39:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (@)\r\n",
" at <notebook>:2:58--2:59\r\n",
" to 4\r\n",
"[warning] at <notebook>:11:26--16:31:\r\n",
" Defaulting type parameter 'bits'\r\n",
" of literal or demoted expression\r\n",
" at <notebook>:14:26--14:29\r\n",
" to 3\r\n",
"[warning] at <notebook>:7:1--9:23:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:7:28--7:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:2:1--4:20:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (<<<)\r\n",
" at <notebook>:2:25--2:28\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:28--6:31\r\n",
" to 2\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:39--6:42\r\n",
" to 3\r\n",
"[warning] at <notebook>:6:1--6:75:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:6:50--6:53\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:30--2:33\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:41--2:44\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:52--2:55\r\n",
" to 3\r\n",
"[warning] at <notebook>:2:1--3:18:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>>)\r\n",
" at <notebook>:2:63--2:66\r\n",
" to 3\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:16:52--16:54\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 2nd type parameter\r\n",
" of expression (>>)\r\n",
" at <notebook>:17:40--17:42\r\n",
" to 1\r\n",
"[warning] at <notebook>:11:18--17:46:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:13:21--13:22\r\n",
" to 0\r\n",
"[warning] at <notebook>:2:1--3:57:\r\n",
" Defaulting 3rd type parameter\r\n",
" of expression (!)\r\n",
" at <notebook>:2:19--2:20\r\n",
" to 0\r\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"test1 where (test1,_,_) = ExpandKey 0x3243f6a8885a308d313198a2e0370734"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"[[50, 136, 49, 224], [67, 90, 49, 55], [246, 48, 152, 7],\r\n",
" [168, 141, 162, 52]]\r\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"aesEncrypt (0x3243f6a8885a308d313198a2e0370734, 0x2b7e151628aed2a6abf7158809cf4f3c) == 0x3925841d02dc09fbdc118597196a0b32"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"text": [
"True\r\n"
]
}
],
"prompt_number": 20
}
],
"metadata": {}
}
]
}
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