-
Notifications
You must be signed in to change notification settings - Fork 7
/
Copy pathZUC.cry
310 lines (283 loc) · 11.5 KB
/
ZUC.cry
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
// Copyright (c) 2011-2018 Galois, Inc.
// An implementation of ZUC, Version 1.5
// Version info: If the following variable is set to True, then we implement
// Version 1.5 of ZUC. Otherwise, version 1.4 is implemented. There are
// precisely two points in the implementation where the difference matters,
// search for occurrences of version1_5 to spot them.
// Note that the ZUC test vectors below will not work for version 1.4, as the
// old test vectors are no longer published.
module Primitive::Symmetric::Cipher::Stream::ZUC where
version1_5 : Bit
version1_5 = True
// addition in GF(2^31-1) over a list of terms
add : {a} (fin a) => [a][31] -> [31]
add xs =
sums ! 0
where
sums =
[0] #
[plus (s, x) | s <- sums
| x <- xs]
// the binary addition specified in the note at the end of section 3.2
plus : ([31], [31]) -> [31]
plus (a, b) =
if sab @ 0 then sab' + 1 else sab'
where
sab : [32]
sab = ((zero : [1]) # a) + ((zero : [1]) # b)
sab' : [31]
sab' = drop sab
// The ZUC LFSR is 16 31-bit words
type LFSR = [16][31]
// Section 3.2
LFSRWithInitializationMode : ([31], LFSR) -> LFSR
LFSRWithInitializationMode (u, ss) =
ss @@ [1 .. 15] # [s16]
where
v = add [s <<< c | s <- ss @@ [15, 13, 10, 4, 0, 0]
| c <- [15, 17, 21, 20, 8, 0]]
vu = if version1_5 then add [v, u] else v ^ u
s16 = if vu == 0 then `0x7FFFFFFF else vu
// Section 3.2
LFSRWithWorkMode : LFSR -> LFSR
LFSRWithWorkMode ss =
ss @@ [1 .. 15] # [s16]
where
v = add [s <<< c | s <- ss @@ [15, 13, 10, 4, 0, 0]
| c <- [15, 17, 21, 20, 8, 0]]
s16 = if v == 0 then `0x7FFFFFFF else v
// Section 3.3
BitReorganization : LFSR -> [4][32]
BitReorganization ss =
[ hi s15 # lo s14
, lo s11 # hi s9
, lo s7 # hi s5
, lo s2 # hi s0]
where
lo : [31] -> [16]
hi : [31] -> [16]
lo x = x @@ [15 .. 30]
hi x = x @@ [0 .. 15]
[s0, s2, s5, s7, s9, s11, s14, s15] = ss @@ [0, 2, 5, 7, 9, 11, 14, 15]
// Section 3.4
F : ([3][32], [2][32]) -> ([32], [2][32])
F ([X0, X1, X2], [R1, R2]) =
(W, [R1', R2'])
where
W = (X0 ^ R1) + R2
W1 = R1 + X1
W2 = R2 ^ X2
[W1H, W1L] = split W1
[W2H, W2L] = split W2
R1' = S (L1 (W1L # W2H))
R2' = S (L2 (W2L # W1H))
// Section 3.4.1
S : [32] -> [32]
S X =
Y0 # Y1 # Y2 # Y3
where
[X0, X1, X2, X3] = split X
[Y0, Y1, Y2, Y3] = [S0 X0, S1 X1, S2 X2, S3 X3]
// Example 8
property example8 = S(0x12345678) == 0xF9C05A4E
S0 : [8] -> [8]
S1 : [8] -> [8]
S2 : [8] -> [8]
S3 : [8] -> [8]
S0 x = S0Table @ x
S1 x = S1Table @ x
S2 = S0
S3 = S1
// Table 3.1
S0Table : [256][8]
S0Table =
[0x3E, 0x72, 0x5B, 0x47, 0xCA, 0xE0, 0x00, 0x33, 0x04, 0xD1, 0x54,
0x98, 0x09, 0xB9, 0x6D, 0xCB, 0x7B, 0x1B, 0xF9, 0x32, 0xAF, 0x9D,
0x6A, 0xA5, 0xB8, 0x2D, 0xFC, 0x1D, 0x08, 0x53, 0x03, 0x90, 0x4D,
0x4E, 0x84, 0x99, 0xE4, 0xCE, 0xD9, 0x91, 0xDD, 0xB6, 0x85, 0x48,
0x8B, 0x29, 0x6E, 0xAC, 0xCD, 0xC1, 0xF8, 0x1E, 0x73, 0x43, 0x69,
0xC6, 0xB5, 0xBD, 0xFD, 0x39, 0x63, 0x20, 0xD4, 0x38, 0x76, 0x7D,
0xB2, 0xA7, 0xCF, 0xED, 0x57, 0xC5, 0xF3, 0x2C, 0xBB, 0x14, 0x21,
0x06, 0x55, 0x9B, 0xE3, 0xEF, 0x5E, 0x31, 0x4F, 0x7F, 0x5A, 0xA4,
0x0D, 0x82, 0x51, 0x49, 0x5F, 0xBA, 0x58, 0x1C, 0x4A, 0x16, 0xD5,
0x17, 0xA8, 0x92, 0x24, 0x1F, 0x8C, 0xFF, 0xD8, 0xAE, 0x2E, 0x01,
0xD3, 0xAD, 0x3B, 0x4B, 0xDA, 0x46, 0xEB, 0xC9, 0xDE, 0x9A, 0x8F,
0x87, 0xD7, 0x3A, 0x80, 0x6F, 0x2F, 0xC8, 0xB1, 0xB4, 0x37, 0xF7,
0x0A, 0x22, 0x13, 0x28, 0x7C, 0xCC, 0x3C, 0x89, 0xC7, 0xC3, 0x96,
0x56, 0x07, 0xBF, 0x7E, 0xF0, 0x0B, 0x2B, 0x97, 0x52, 0x35, 0x41,
0x79, 0x61, 0xA6, 0x4C, 0x10, 0xFE, 0xBC, 0x26, 0x95, 0x88, 0x8A,
0xB0, 0xA3, 0xFB, 0xC0, 0x18, 0x94, 0xF2, 0xE1, 0xE5, 0xE9, 0x5D,
0xD0, 0xDC, 0x11, 0x66, 0x64, 0x5C, 0xEC, 0x59, 0x42, 0x75, 0x12,
0xF5, 0x74, 0x9C, 0xAA, 0x23, 0x0E, 0x86, 0xAB, 0xBE, 0x2A, 0x02,
0xE7, 0x67, 0xE6, 0x44, 0xA2, 0x6C, 0xC2, 0x93, 0x9F, 0xF1, 0xF6,
0xFA, 0x36, 0xD2, 0x50, 0x68, 0x9E, 0x62, 0x71, 0x15, 0x3D, 0xD6,
0x40, 0xC4, 0xE2, 0x0F, 0x8E, 0x83, 0x77, 0x6B, 0x25, 0x05, 0x3F,
0x0C, 0x30, 0xEA, 0x70, 0xB7, 0xA1, 0xE8, 0xA9, 0x65, 0x8D, 0x27,
0x1A, 0xDB, 0x81, 0xB3, 0xA0, 0xF4, 0x45, 0x7A, 0x19, 0xDF, 0xEE,
0x78, 0x34, 0x60]
// Table 3.2
S1Table : [256][8]
S1Table =
[0x55, 0xC2, 0x63, 0x71, 0x3B, 0xC8, 0x47, 0x86, 0x9F, 0x3C, 0xDA,
0x5B, 0x29, 0xAA, 0xFD, 0x77, 0x8C, 0xC5, 0x94, 0x0C, 0xA6, 0x1A,
0x13, 0x00, 0xE3, 0xA8, 0x16, 0x72, 0x40, 0xF9, 0xF8, 0x42, 0x44,
0x26, 0x68, 0x96, 0x81, 0xD9, 0x45, 0x3E, 0x10, 0x76, 0xC6, 0xA7,
0x8B, 0x39, 0x43, 0xE1, 0x3A, 0xB5, 0x56, 0x2A, 0xC0, 0x6D, 0xB3,
0x05, 0x22, 0x66, 0xBF, 0xDC, 0x0B, 0xFA, 0x62, 0x48, 0xDD, 0x20,
0x11, 0x06, 0x36, 0xC9, 0xC1, 0xCF, 0xF6, 0x27, 0x52, 0xBB, 0x69,
0xF5, 0xD4, 0x87, 0x7F, 0x84, 0x4C, 0xD2, 0x9C, 0x57, 0xA4, 0xBC,
0x4F, 0x9A, 0xDF, 0xFE, 0xD6, 0x8D, 0x7A, 0xEB, 0x2B, 0x53, 0xD8,
0x5C, 0xA1, 0x14, 0x17, 0xFB, 0x23, 0xD5, 0x7D, 0x30, 0x67, 0x73,
0x08, 0x09, 0xEE, 0xB7, 0x70, 0x3F, 0x61, 0xB2, 0x19, 0x8E, 0x4E,
0xE5, 0x4B, 0x93, 0x8F, 0x5D, 0xDB, 0xA9, 0xAD, 0xF1, 0xAE, 0x2E,
0xCB, 0x0D, 0xFC, 0xF4, 0x2D, 0x46, 0x6E, 0x1D, 0x97, 0xE8, 0xD1,
0xE9, 0x4D, 0x37, 0xA5, 0x75, 0x5E, 0x83, 0x9E, 0xAB, 0x82, 0x9D,
0xB9, 0x1C, 0xE0, 0xCD, 0x49, 0x89, 0x01, 0xB6, 0xBD, 0x58, 0x24,
0xA2, 0x5F, 0x38, 0x78, 0x99, 0x15, 0x90, 0x50, 0xB8, 0x95, 0xE4,
0xD0, 0x91, 0xC7, 0xCE, 0xED, 0x0F, 0xB4, 0x6F, 0xA0, 0xCC, 0xF0,
0x02, 0x4A, 0x79, 0xC3, 0xDE, 0xA3, 0xEF, 0xEA, 0x51, 0xE6, 0x6B,
0x18, 0xEC, 0x1B, 0x2C, 0x80, 0xF7, 0x74, 0xE7, 0xFF, 0x21, 0x5A,
0x6A, 0x54, 0x1E, 0x41, 0x31, 0x92, 0x35, 0xC4, 0x33, 0x07, 0x0A,
0xBA, 0x7E, 0x0E, 0x34, 0x88, 0xB1, 0x98, 0x7C, 0xF3, 0x3D, 0x60,
0x6C, 0x7B, 0xCA, 0xD3, 0x1F, 0x32, 0x65, 0x04, 0x28, 0x64, 0xBE,
0x85, 0x9B, 0x2F, 0x59, 0x8A, 0xD7, 0xB0, 0x25, 0xAC, 0xAF, 0x12,
0x03, 0xE2, 0xF2]
// Section 3.4.2
L1 : [32] -> [32]
L1 X = X ^ X <<< 2 ^ X <<< 10 ^ X <<< 18 ^ X <<< 24
// Section 3.4.2
L2 : [32] -> [32]
L2 X = X ^ X <<< 8 ^ X <<< 14 ^ X <<< 22 ^ X <<< 30
// Section 3.5
LoadKey : ([128], [128]) -> LFSR
LoadKey (key, iv) =
[k # d # i | k <- ks
| i <- is
| d <- ds]
where
ks : [16][8]
ks = split key
is : [16][8]
is = split iv
ds : [16][15]
ds =
[ 0b100010011010111, 0b010011010111100
, 0b110001001101011, 0b001001101011110
, 0b101011110001001, 0b011010111100010
, 0b111000100110101, 0b000100110101111
, 0b100110101111000, 0b010111100010011
, 0b110101111000100, 0b001101011110001
, 0b101111000100110, 0b011110001001101
, 0b111100010011010, 0b100011110101100
]
type ZUC = (LFSR, [32], [32])
// Return an infinite sequence of ZUC states by applying the initialization step
// repeatedly. This is a generalization of section 3.6.1
InitializeZUC : ([128], [128]) -> [inf]ZUC
InitializeZUC (key, iv) =
outs
where
initLFSR = LoadKey (key, iv)
outs = [(initLFSR, 0, 0)] # [step out | out <- outs]
step (lfsr, R1, R2) =
(LFSRWithInitializationMode (drop (w >> 1), lfsr), R1', R2')
where
[X0, X1, X2, X3] = BitReorganization lfsr
(w', [R1', R2']) = F ([X0, X1, X2], [R1, R2])
w = if version1_5 then w' else w' ^ X3
// Section 3.6.2
WorkingStage : ZUC -> ZUC
WorkingStage (lfsr, R1, R2) =
(lfsr', R1', R2')
where
[X0, X1, X2, _] = BitReorganization lfsr
(_, [R1', R2']) = F ([X0, X1, X2], [R1, R2])
lfsr' = LFSRWithWorkMode lfsr
// Section 3.6.2
ProductionStage : ZUC -> ([32], ZUC)
ProductionStage (lfsr, R1, R2) =
(w ^ X3, (lfsr', R1', R2'))
where
[X0, X1, X2, X3] = BitReorganization lfsr
(w, [R1', R2']) = F ([X0, X1, X2], [R1, R2])
lfsr' = LFSRWithWorkMode lfsr
// ZUC API
ZUC : [128] -> [128] -> [inf][32]
ZUC key iv =
tail [w | (w, _) <- zucs]
where
initZuc = WorkingStage (InitializeZUC (key, iv) @ 32)
zucs = [(zero, initZuc)] # [ProductionStage zuc | (_, zuc) <- zucs]
// Test vectors
property ZUC_TestVectors =
t1 /\ t2 /\ t3 /\ t4
where
t1 = take (ZUC zero zero ) == [0x27BEDE74, 0x018082DA]
t2 = take (ZUC (~zero) (~zero)) == [0x0657CFA0, 0x7096398B]
t3 = take (ZUC (join [ 0x3D, 0x4C, 0x4B, 0xE9, 0x6A, 0x82, 0xFD, 0xAE
, 0xB5, 0x8F, 0x64, 0x1D, 0xB1, 0x7B, 0x45, 0x5B
])
(join [ 0x84, 0x31, 0x9A, 0xA8, 0xDE, 0x69, 0x15, 0xCA
, 0x1F, 0x6B, 0xDA, 0x6B, 0xFB, 0xD8, 0xC7, 0x66
])) == [0x14F1C272, 0x3279C419]
t4 = take ks # [ks @ 1999] == [0xED4400E7, 0x0633E5C5, 0x7A574CDB]
where
ks = ZUC (join [ 0x4D, 0x32, 0x0B, 0xFA, 0xD4, 0xC2, 0x85, 0xBF
, 0xD6, 0xB8, 0xBD, 0x00, 0xF3, 0x9D, 0x8B, 0x41
])
(join [ 0x52, 0x95, 0x9D, 0xAB, 0xA0, 0xBF, 0x17, 0x6E
, 0xCE, 0x2D, 0xC3, 0x15, 0x04, 0x9E, 0xB5, 0x74
])
// 3.3-3.6 of the implementor's test data document lists "LFSR-state at the
// beginning", which is immediately after running LoadKey.
property LoadKey_TestVectors =
[ LoadKey(k, iv) == lfsr0
| k <- ks
| iv <- ivs
| lfsr0 <- lfsr0s
] == ~0
where
ks = [ 0
, ~0
, 0x3d4c4be96a82fdaeb58f641db17b455b
, 0x4d320bfad4c285bfd6b8bd00f39d8b41
]
ivs = [ 0
, ~0
, 0x84319aa8de6915ca1f6bda6bfbd8c766
, 0x52959daba0bf176ece2dc315049eb574
]
lfsr0s = [ [ `0x0044d700, `0x0026bc00, `0x00626b00, `0x00135e00
, `0x00578900, `0x0035e200, `0x00713500, `0x0009af00
, `0x004d7800, `0x002f1300, `0x006bc400, `0x001af100
, `0x005e2600, `0x003c4d00, `0x00789a00, `0x0047ac00
]
, [ `0x7fc4d7ff, `0x7fa6bcff, `0x7fe26bff, `0x7f935eff
, `0x7fd789ff, `0x7fb5e2ff, `0x7ff135ff, `0x7f89afff
, `0x7fcd78ff, `0x7faf13ff, `0x7febc4ff, `0x7f9af1ff
, `0x7fde26ff, `0x7fbc4dff, `0x7ff89aff, `0x7fc7acff
]
, [ `0x1ec4d784, `0x2626bc31, `0x25e26b9a, `0x74935ea8
, `0x355789de, `0x4135e269, `0x7ef13515, `0x5709afca
, `0x5acd781f, `0x47af136b, `0x326bc4da, `0x0e9af16b
, `0x58de26fb, `0x3dbc4dd8, `0x22f89ac7, `0x2dc7ac66
]
, [ `0x26c4d752, `0x1926bc95, `0x05e26b9d, `0x7d135eab
, `0x6a5789a0, `0x6135e2bf, `0x42f13517, `0x5f89af6e
, `0x6b4d78ce, `0x5c2f132d, `0x5eebc4c3, `0x001af115
, `0x79de2604, `0x4ebc4d9e, `0x45f89ab5, `0x20c7ac74
]
]
// Collision attack on ZUC. Only version1.5 is resistant to it. Thus, the
// following theorem holds only when version1_5 is set to True.
//
// NB. We only compare the first output of the InitializeZUC sequence, as it
// cuts down on the problem size and is sufficient to ensure the iv's will be
// the same. That is, if this theorem fails, then so would the final iv's used
// by ZUC.
//
// Use a solver other than CVC4; Z3 and Boolector do it quickly.
property ZUC_isResistantToCollisionAttack k iv1 iv2 =
if iv1 != iv2
then InitializeZUC (k, iv1) @ 1 != InitializeZUC (k, iv2) @ 1
else True