File: MD5Aux.hs

package info (click to toggle)
haskell-crypto 4.2.4-1
  • links: PTS, VCS
  • area: main
  • in suites: wheezy
  • size: 344 kB
  • sloc: haskell: 2,949; makefile: 2
file content (355 lines) | stat: -rw-r--r-- 12,775 bytes parent folder | download | duplicates (4)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
module Data.Digest.MD5Aux 
   (md5,  md5s,  md5i,
    MD5(..), ABCD(..), 
    Zord64, Str(..), BoolList(..), WordList(..)) where

import Data.Char
import Data.Bits
import Data.Word

{-
Nasty kludge to create a type Zord64 which is really a Word64 but works
how we want in hugs ands nhc98 too...
Also need a rotate left function that actually works.

#ifdef __GLASGOW_HASKELL__
#define rotL rotateL
#include "Zord64_EASY.hs"
#else

> import Zord64_HARD
 
> rotL :: Word32 -> Rotation -> Word32
> rotL a s = shiftL a s .|. shiftL a (s-32)

#endif
-}

rotL x = rotateL x
type Zord64 = Word64

-- ===================== TYPES AND CLASS DEFINTIONS ========================


type XYZ = (Word32, Word32, Word32)
type Rotation = Int
newtype ABCD = ABCD (Word32, Word32, Word32, Word32) deriving (Eq, Show)
newtype Str = Str String
newtype BoolList = BoolList [Bool]
newtype WordList = WordList ([Word32], Zord64)

-- Anything we want to work out the MD5 of must be an instance of class MD5

class MD5 a where
 get_next :: a -> ([Word32], Int, a) -- get the next blocks worth
 --                     \      \   \------ the rest of the input
 --                      \      \--------- the number of bits returned
 --                       \--------------- the bits returned in 32bit words
 len_pad :: Zord64 -> a -> a         -- append the padding and length
 finished :: a -> Bool               -- Have we run out of input yet?


-- Mainly exists because it's fairly easy to do MD5s on input where the
-- length is not a multiple of 8

instance MD5 BoolList where
 get_next (BoolList s) = (bools_to_word32s ys, length ys, BoolList zs)
  where (ys, zs) = splitAt 512 s
 len_pad l (BoolList bs)
  = BoolList (bs ++ [True]
                 ++ replicate (fromIntegral $ (447 - l) .&. 511) False
                 ++ [l .&. (shiftL 1 x) > 0 | x <- (mangle [0..63])]
             )
  where mangle [] = []
        mangle xs = reverse ys ++ mangle zs
         where (ys, zs) = splitAt 8 xs
 finished (BoolList s) = s == []


-- The string instance is fairly straightforward

instance MD5 Str where
 get_next (Str s) = (string_to_word32s ys, 8 * length ys, Str zs)
  where (ys, zs) = splitAt 64 s
 len_pad c64 (Str s) = Str (s ++ padding ++ l)
  where padding = '\128':replicate (fromIntegral zeros) '\000'
        zeros = shiftR ((440 - c64) .&. 511) 3
        l = length_to_chars 8 c64
 finished (Str s) = s == ""


-- YA instance that is believed will be useful

instance MD5 WordList where
 get_next (WordList (ws, l)) = (xs, fromIntegral taken, WordList (ys, l - taken))
  where (xs, ys) = splitAt 16 ws
        taken = if l > 511 then 512 else l .&. 511
 len_pad c64 (WordList (ws, l)) = WordList (beginning ++ nextish ++ blanks ++ size, newlen)
  where beginning = if length ws > 0 then start ++ lastone' else []
        start = init ws
        lastone = last ws
        offset = c64 .&. 31
        lastone' = [if offset > 0 then lastone + theone else lastone]
        theone = shiftL (shiftR 128 (fromIntegral $ offset .&. 7))
                        (fromIntegral $ offset .&. (31 - 7))
        nextish = if offset == 0 then [128] else []
        c64' = c64 + (32 - offset)
        num_blanks = (fromIntegral $ shiftR ((448 - c64') .&. 511) 5)
        blanks = replicate num_blanks 0
        lowsize = fromIntegral $ c64 .&. (shiftL 1 32 - 1)
        topsize = fromIntegral $ shiftR c64 32
        size = [lowsize, topsize]
        newlen = l .&. (complement 511)
               + if c64 .&. 511 >= 448 then 1024 else 512
 finished (WordList (_, z)) = z == 0


instance Num ABCD where
 ABCD (a1, b1, c1, d1) + ABCD (a2, b2, c2, d2) = ABCD (a1 + a2, b1 + b2, c1 + c2, d1 + d2)


-- ===================== EXPORTED FUNCTIONS ========================


-- The simplest function, gives you the MD5 of a string as 4-tuple of
-- 32bit words.

md5 :: (MD5 a) => a -> ABCD
md5 m = md5_main False 0 magic_numbers m


-- Returns a hex number ala the md5sum program

md5s :: (MD5 a) => a -> String
md5s = abcd_to_string . md5


-- Returns an integer equivalent to the above hex number

md5i :: (MD5 a) => a -> Integer
md5i = abcd_to_integer . md5


-- ===================== THE CORE ALGORITHM ========================


-- Decides what to do. The first argument indicates if padding has been
-- added. The second is the length mod 2^64 so far. Then we have the
-- starting state, the rest of the string and the final state.

md5_main :: (MD5 a) =>
            Bool   -- Have we added padding yet?
         -> Zord64 -- The length so far mod 2^64
         -> ABCD   -- The initial state
         -> a      -- The non-processed portion of the message
         -> ABCD   -- The resulting state
md5_main padded ilen abcd m
 = if finished m && padded
   then abcd
   else md5_main padded' (ilen + 512) (abcd + abcd') m''
 where (m16, l, m') = get_next m
       len' = ilen + fromIntegral l
       ((m16', _, m''), padded') = if not padded && l < 512
                                   then (get_next $ len_pad len' m, True)
                                   else ((m16, l, m'), padded)
       abcd' = md5_do_block abcd m16'


-- md5_do_block processes a 512 bit block by calling md5_round 4 times to
-- apply each round with the correct constants and permutations of the
-- block

md5_do_block :: ABCD     -- Initial state
             -> [Word32] -- The block to be processed - 16 32bit words
             -> ABCD     -- Resulting state
md5_do_block abcd0 w = abcd4
 where (r1, r2, r3, r4) = rounds
       {-
       map (\x -> w !! x) [1,6,11,0,5,10,15,4,9,14,3,8,13,2,7,12]
                       -- [(5 * x + 1) `mod` 16 | x <- [0..15]]
       map (\x -> w !! x) [5,8,11,14,1,4,7,10,13,0,3,6,9,12,15,2]
                       -- [(3 * x + 5) `mod` 16 | x <- [0..15]]
       map (\x -> w !! x) [0,7,14,5,12,3,10,1,8,15,6,13,4,11,2,9]
                       -- [(7 * x) `mod` 16 | x <- [0..15]]
       -}
       perm5 [c0,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15]
        = [c1,c6,c11,c0,c5,c10,c15,c4,c9,c14,c3,c8,c13,c2,c7,c12]
       perm5 _ = error "broke at perm5"
       perm3 [c0,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15]
        = [c5,c8,c11,c14,c1,c4,c7,c10,c13,c0,c3,c6,c9,c12,c15,c2]
       perm3 _ = error "broke at perm3"
       perm7 [c0,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12,c13,c14,c15]
        = [c0,c7,c14,c5,c12,c3,c10,c1,c8,c15,c6,c13,c4,c11,c2,c9]
       perm7 _ = error "broke at perm7"
       abcd1 = md5_round md5_f abcd0        w  r1
       abcd2 = md5_round md5_g abcd1 (perm5 w) r2
       abcd3 = md5_round md5_h abcd2 (perm3 w) r3
       abcd4 = md5_round md5_i abcd3 (perm7 w) r4


-- md5_round does one of the rounds. It takes an auxiliary function and foldls
-- (md5_inner_function f) to repeatedly apply it to the initial state with the
-- correct constants

md5_round :: (XYZ -> Word32)      -- Auxiliary function (F, G, H or I
                                  -- for those of you with a copy of
                                  -- the prayer book^W^WRFC)
          -> ABCD                 -- Initial state
          -> [Word32]             -- The 16 32bit words of input
          -> [(Rotation, Word32)] -- The list of 16 rotations and
                                  -- additive constants
          -> ABCD                 -- Resulting state
md5_round f abcd s ns = foldl (md5_inner_function f) abcd ns'
 where ns' = zipWith (\x (y, z) -> (y, x + z)) s ns


-- Apply one of the functions md5_[fghi] and put the new ABCD together

md5_inner_function :: (XYZ -> Word32)    -- Auxiliary function
                   -> ABCD               -- Initial state
                   -> (Rotation, Word32) -- The rotation and additive
                                         -- constant (X[i] + T[j])
                   -> ABCD               -- Resulting state
md5_inner_function f (ABCD (a, b, c, d)) (s, ki) = ABCD (d, a', b, c)
 where mid_a = a + f(b,c,d) + ki
       rot_a = rotL mid_a s
       a' = b + rot_a


-- The 4 auxiliary functions

md5_f :: XYZ -> Word32
md5_f (x, y, z) = z `xor` (x .&. (y `xor` z))
{- optimised version of: (x .&. y) .|. ((complement x) .&. z) -}

md5_g :: XYZ -> Word32
md5_g (x, y, z) = md5_f (z, x, y)
{- was: (x .&. z) .|. (y .&. (complement z)) -}

md5_h :: XYZ -> Word32
md5_h (x, y, z) = x `xor` y `xor` z

md5_i :: XYZ -> Word32
md5_i (x, y, z) = y `xor` (x .|. (complement z))


-- The magic numbers from the RFC.

magic_numbers :: ABCD
magic_numbers = ABCD (0x67452301, 0xefcdab89, 0x98badcfe, 0x10325476)


-- The 4 lists of (rotation, additive constant) tuples, one for each round

rounds :: ([(Rotation, Word32)],
           [(Rotation, Word32)],
           [(Rotation, Word32)],
           [(Rotation, Word32)])
rounds = (r1, r2, r3, r4)
 where r1 = [(s11, 0xd76aa478), (s12, 0xe8c7b756), (s13, 0x242070db),
             (s14, 0xc1bdceee), (s11, 0xf57c0faf), (s12, 0x4787c62a),
             (s13, 0xa8304613), (s14, 0xfd469501), (s11, 0x698098d8),
             (s12, 0x8b44f7af), (s13, 0xffff5bb1), (s14, 0x895cd7be),
             (s11, 0x6b901122), (s12, 0xfd987193), (s13, 0xa679438e),
             (s14, 0x49b40821)]
       r2 = [(s21, 0xf61e2562), (s22, 0xc040b340), (s23, 0x265e5a51),
             (s24, 0xe9b6c7aa), (s21, 0xd62f105d), (s22,  0x2441453),
             (s23, 0xd8a1e681), (s24, 0xe7d3fbc8), (s21, 0x21e1cde6),
             (s22, 0xc33707d6), (s23, 0xf4d50d87), (s24, 0x455a14ed),
             (s21, 0xa9e3e905), (s22, 0xfcefa3f8), (s23, 0x676f02d9),
             (s24, 0x8d2a4c8a)]
       r3 = [(s31, 0xfffa3942), (s32, 0x8771f681), (s33, 0x6d9d6122),
             (s34, 0xfde5380c), (s31, 0xa4beea44), (s32, 0x4bdecfa9),
             (s33, 0xf6bb4b60), (s34, 0xbebfbc70), (s31, 0x289b7ec6),
             (s32, 0xeaa127fa), (s33, 0xd4ef3085), (s34,  0x4881d05),
             (s31, 0xd9d4d039), (s32, 0xe6db99e5), (s33, 0x1fa27cf8),
             (s34, 0xc4ac5665)]
       r4 = [(s41, 0xf4292244), (s42, 0x432aff97), (s43, 0xab9423a7),
             (s44, 0xfc93a039), (s41, 0x655b59c3), (s42, 0x8f0ccc92),
             (s43, 0xffeff47d), (s44, 0x85845dd1), (s41, 0x6fa87e4f),
             (s42, 0xfe2ce6e0), (s43, 0xa3014314), (s44, 0x4e0811a1),
             (s41, 0xf7537e82), (s42, 0xbd3af235), (s43, 0x2ad7d2bb),
             (s44, 0xeb86d391)]
       s11 = 7
       s12 = 12
       s13 = 17
       s14 = 22
       s21 = 5
       s22 = 9
       s23 = 14
       s24 = 20
       s31 = 4
       s32 = 11
       s33 = 16
       s34 = 23
       s41 = 6
       s42 = 10
       s43 = 15
       s44 = 21


-- ===================== CONVERSION FUNCTIONS ========================


-- Turn the 4 32 bit words into a string representing the hex number they
-- represent.

abcd_to_string :: ABCD -> String
abcd_to_string (ABCD (a,b,c,d)) = concat $ map display_32bits_as_hex [a,b,c,d]


-- Split the 32 bit word up, swap the chunks over and convert the numbers
-- to their hex equivalents.

display_32bits_as_hex :: Word32 -> String
display_32bits_as_hex w = swap_pairs cs
 where cs = map (\x -> getc $ (shiftR w (4*x)) .&. 15) [0..7]
       getc n = (['0'..'9'] ++ ['a'..'f']) !! (fromIntegral n)
       swap_pairs (x1:x2:xs) = x2:x1:swap_pairs xs
       swap_pairs _ = []

-- Convert to an integer, performing endianness magic as we go

abcd_to_integer :: ABCD -> Integer
abcd_to_integer (ABCD (a,b,c,d)) = rev_num a * 2^(96 :: Int)
                                 + rev_num b * 2^(64 :: Int)
                                 + rev_num c * 2^(32 :: Int)
                                 + rev_num d

rev_num :: Word32 -> Integer
rev_num i = toInteger j `mod` (2^(32 :: Int))
 --         NHC's fault ~~~~~~~~~~~~~~~~~~~~~
 where j = foldl (\so_far next -> shiftL so_far 8 + (shiftR i next .&. 255))
                 0 [0,8,16,24]

-- Used to convert a 64 byte string to 16 32bit words

string_to_word32s :: String -> [Word32]
string_to_word32s "" = []
string_to_word32s ss = this:string_to_word32s ss'
 where (s, ss') = splitAt 4 ss
       this = foldr (\c w -> shiftL w 8 + (fromIntegral.ord) c) 0 s


-- Used to convert a list of 512 bools to 16 32bit words

bools_to_word32s :: [Bool] -> [Word32]
bools_to_word32s [] = []
bools_to_word32s bs = this:bools_to_word32s rest
 where (bs1, bs1') = splitAt 8 bs
       (bs2, bs2') = splitAt 8 bs1'
       (bs3, bs3') = splitAt 8 bs2'
       (bs4, rest) = splitAt 8 bs3'
       this = boolss_to_word32 [bs1, bs2, bs3, bs4]
       bools_to_word8 = foldl (\w b -> shiftL w 1 + if b then 1 else 0) 0
       boolss_to_word32 = foldr (\w8 w -> shiftL w 8 + bools_to_word8 w8) 0


-- Convert the size into a list of characters used by the len_pad function
-- for strings

length_to_chars :: Int -> Zord64 -> String
length_to_chars 0 _ = []
length_to_chars p n = this:length_to_chars (p-1) (shiftR n 8)
         where this = chr $ fromIntegral $ n .&. 255