cryptol/examples/simon.cry
2014-04-17 15:34:25 -07:00

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/*
* Copyright (c) 2013-2014 Galois, Inc.
* Distributed under the terms of the BSD3 license (see LICENSE file)
*/
/* Cryptol specification of the Simon block cipher
* Author: David Lazar
*/
///////////////////////////////////////////////////////////////////////
// parameters
///////////////////////////////////////////////////////////////////////
module simon where
Simon32_64 = encrypt `{n=16,m=4,T=32,j=0}
Simon48_72 = encrypt `{n=24,m=3,T=36,j=0}
Simon48_96 = encrypt `{n=24,m=4,T=36,j=1}
Simon64_96 = encrypt `{n=32,m=3,T=42,j=2}
Simon64_128 = encrypt `{n=32,m=4,T=44,j=3}
Simon96_96 = encrypt `{n=48,m=2,T=52,j=2}
Simon96_144 = encrypt `{n=48,m=3,T=54,j=3}
Simon128_128 = encrypt `{n=64,m=2,T=68,j=2}
Simon128_192 = encrypt `{n=64,m=3,T=69,j=3}
Simon128_256 = encrypt `{n=64,m=4,T=72,j=4}
Simon32_64' = decrypt `{n=16,m=4,T=32,j=0}
Simon48_72' = decrypt `{n=24,m=3,T=36,j=0}
Simon48_96' = decrypt `{n=24,m=4,T=36,j=1}
Simon64_96' = decrypt `{n=32,m=3,T=42,j=2}
Simon64_128' = decrypt `{n=32,m=4,T=44,j=3}
Simon96_96' = decrypt `{n=48,m=2,T=52,j=2}
Simon96_144' = decrypt `{n=48,m=3,T=54,j=3}
Simon128_128' = decrypt `{n=64,m=2,T=68,j=2}
Simon128_192' = decrypt `{n=64,m=3,T=69,j=3}
Simon128_256' = decrypt `{n=64,m=4,T=72,j=4}
// check only a few of them for now
property correctSimon32_64 k b = Simon32_64' k (Simon32_64 k b) == b
property correctSimon64_96 k b = Simon64_96' k (Simon64_96 k b) == b
property correctSimon96_144 k b = Simon96_144' k (Simon96_144 k b) == b
property correctSimon128_128 k b = Simon128_128' k (Simon128_128 k b) == b
property correctSimon128_256 k b = Simon128_256' k (Simon128_256 k b) == b
property uniqueExpandSimon32_64 k1 k2 = (k1 == k2) || (expandKey `{n=16,m=4,T=32,j=0} k1 != expandKey `{n=16,m=4,T=32,j=0} k2)
property uniqueExpandSimon48_72 k1 k2 = (k1 == k2) || (expandKey `{n=24,m=3,T=36,j=0} k1 != expandKey `{n=24,m=3,T=36,j=0} k2)
property uniqueExpandSimon48_96 k1 k2 = (k1 == k2) || (expandKey `{n=24,m=4,T=36,j=1} k1 != expandKey `{n=24,m=4,T=36,j=1} k2)
property uniqueExpandSimon64_96 k1 k2 = (k1 == k2) || (expandKey `{n=32,m=3,T=42,j=2} k1 != expandKey `{n=32,m=3,T=42,j=2} k2)
property uniqueExpandSimon64_128 k1 k2 = (k1 == k2) || (expandKey `{n=32,m=4,T=44,j=3} k1 != expandKey `{n=32,m=4,T=44,j=3} k2)
property uniqueExpandSimon96_96 k1 k2 = (k1 == k2) || (expandKey `{n=48,m=2,T=52,j=2} k1 != expandKey `{n=48,m=2,T=52,j=2} k2)
property uniqueExpandSimon96_144 k1 k2 = (k1 == k2) || (expandKey `{n=48,m=3,T=54,j=3} k1 != expandKey `{n=48,m=3,T=54,j=3} k2)
property uniqueExpandSimon128_128 k1 k2 = (k1 == k2) || (expandKey `{n=64,m=2,T=68,j=2} k1 != expandKey `{n=64,m=2,T=68,j=2} k2)
property uniqueExpandSimon128_192 k1 k2 = (k1 == k2) || (expandKey `{n=64,m=3,T=69,j=3} k1 != expandKey `{n=64,m=3,T=69,j=3} k2)
property uniqueExpandSimon128_256 k1 k2 = (k1 == k2) || (expandKey `{n=64,m=4,T=72,j=4} k1 != expandKey `{n=64,m=4,T=72,j=4} k2)
// A weak key theorem would look something like:
// :prove exists (\k1 -> exists (\k2 -> forall (\x -> Simon32_64 k1 (Simon32_64 k2 x) != x)))
///////////////////////////////////////////////////////////////////////
// round function
///////////////////////////////////////////////////////////////////////
R k (x, y) = (y ^ f x ^ k, x)
// inverse
R' k (x, y) = (y, x ^ f y ^ k)
f x = ((x <<< 1) && (x <<< 8)) ^ (x <<< 2)
///////////////////////////////////////////////////////////////////////
// encryption / decryption
///////////////////////////////////////////////////////////////////////
encrypt : {n, m, T, j}
( fin n, fin m, fin T, fin j
, n >= 2, 4 >= m, T >= 4, T-1 >= m
) => [m][n] -> ([n], [n]) -> ([n], [n])
encrypt k0 b0 = bs ! 0
where
bs = [b0] # [ R k b | b <- bs | k <- ks ]
ks = expandKey `{n=n,m=m,T=T,j=j} (reverse k0)
decrypt : {n, m, T, j}
( fin n, fin m, fin T, fin j
, n >= 2, 4 >= m, T >= 4, T-1 >= m
) => [m][n] -> ([n], [n]) -> ([n], [n])
decrypt k0 b0 = bs ! 0
where
bs = [b0] # [ R' k b | b <- bs | k <- reverse ks ]
ks = expandKey `{n=n,m=m,T=T,j=j} (reverse k0)
///////////////////////////////////////////////////////////////////////
// key expansion
///////////////////////////////////////////////////////////////////////
expandKey : {n, m, T, j}
( fin n, fin m, fin T, fin j
, n >= 2, 4 >= m, T >= 4, T-1 >= m
) => [m][n] -> [T][n]
expandKey k0 = k
where
k = k0 # [ r where
o = k @ (i - 1) >>> 3
p = if `m == 4 then o ^ k @ (i - 3) else o
q = p ^ p >>> 1
r = ~ k @ (i - `m) ^ q ^ z ^ 3
z = Z @ `j @ ((i - `m) % 62)
| i <- [m .. T - 1]
]
// TODO specify how Z is constructed
Z = [[1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0,
0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1,
0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0],
[1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0,
0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1,
0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0],
[1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1,
0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1,
1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1],
[1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1,
0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0,
0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1],
[1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1,
1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1,
0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1]]
///////////////////////////////////////////////////////////////////////
// tests
///////////////////////////////////////////////////////////////////////
tests = [t01,t02,t03,t04,t05,t06,t07,t08,t09]
property testsPass = tests == ~zero
t00 = Simon32_64 [0x1918, 0x1110, 0x0908, 0x0100] (0x6565, 0x6877) == (0xc69b, 0xe9bb)
t01 = Simon48_72 [0x121110, 0x0a0908, 0x020100] (0x612067, 0x6e696c) == (0xdae5ac, 0x292cac)
t02 = Simon48_96 [0x1a1918, 0x121110, 0x0a0908, 0x020100] (0x726963, 0x20646e) == (0x6e06a5, 0xacf156)
t03 = Simon64_96 [0x13121110, 0x0b0a0908, 0x03020100] (0x6f722067, 0x6e696c63) == (0x5ca2e27f, 0x111a8fc8)
t04 = Simon64_128 [0x1b1a1918, 0x13121110, 0x0b0a0908, 0x03020100] (0x656b696c, 0x20646e75) == (0x44c8fc20, 0xb9dfa07a)
t05 = Simon96_96 [0x0d0c0b0a0908, 0x050403020100] (0x2072616c6c69, 0x702065687420) == (0x602807a462b4, 0x69063d8ff082)
t06 = Simon96_144 [0x151413121110, 0x0d0c0b0a0908, 0x050403020100] (0x746168742074, 0x73756420666f) == (0xecad1c6c451e, 0x3f59c5db1ae9)
t07 = Simon128_128 [0x0f0e0d0c0b0a0908, 0x0706050403020100] (0x6373656420737265, 0x6c6c657661727420) == (0x49681b1e1e54fe3f, 0x65aa832af84e0bbc)
t08 = Simon128_192 [0x1716151413121110, 0x0f0e0d0c0b0a0908, 0x0706050403020100] (0x206572656874206e, 0x6568772065626972) == (0xc4ac61effcdc0d4f, 0x6c9c8d6e2597b85b)
t09 = Simon128_256 [0x1f1e1d1c1b1a1918, 0x1716151413121110, 0x0f0e0d0c0b0a0908, 0x0706050403020100] (0x74206e69206d6f6f, 0x6d69732061207369) == (0x8d2b5579afc8a3a0, 0x3bf72a87efe7b868)