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88 lines
2.9 KiB
Plaintext
88 lines
2.9 KiB
Plaintext
/* Source:
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Alexander Semenov
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Institute for System Dynamics and Control Theory
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Russian Academy of Sciences
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*/
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Trivium_stream : [93] -> [84] -> [111] -> [inf]
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Trivium_stream R1 R2 R3 = stream
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where
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(stream, ra, rb, rc) = shift_regs R1 R2 R3
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type N = 300
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Trivium : ([93], [84], [111]) -> [N]Bit
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Trivium (reg1, reg2, reg3) = keystream
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where
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keystream = take`{N} (Trivium_stream reg1 reg2 reg3)
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shift : {d} (fin d, d >=1) => [d] -> Bit -> [d]
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shift fill bit = fills
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where
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fills = [bit]#(drop`{1} (fill >> 1))
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shift_regs : {d,e,f} (fin d, fin e, fin f, d >=1, e >=1, f>=1) => [d] -> [e] -> [f] -> ([inf],[inf][d],[inf][e],[inf][f])
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shift_regs r1 r2 r3 = (stream, regA, regB, regC)
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where
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s1 = [(f1 @ 65) ^ (f1 @ 92) | f1 <- regA]
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s2 = [(f2 @ 68) ^ (f2 @ 83) | f2 <- regB]
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s3 = [(f3 @ 65) ^ (f3 @ 110) | f3 <- regC]
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stream = s1 ^ s2 ^ s3
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t1 = [(f1 @ 65) ^ ((f1 @ 90) && (f1 @ 91)) ^ (f1 @ 92) ^ (f2 @ 77) |
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f2 <- regB |
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f1 <- regA ]
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t2 = [(f2 @ 68) ^ ((f2 @ 81) && (f2 @ 82)) ^ (f2 @ 83) ^ (f3 @ 86) |
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f2 <- regB |
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f3 <- regC ]
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t3 = [(f3 @ 65) ^ ((f3 @ 108) && (f3 @ 109)) ^ (f3 @ 110) ^ (f1 @ 68)|
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f1 <- regA |
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f3 <- regC ]
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regA = [r1] # [shift f b| f <- regA | b <- t3]
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regB = [r2] # [shift f b| f <- regB | b <- t1]
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regC = [r3] # [shift f b| f <- regC | b <- t2]
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Trivium_alt : ([93], [84], [111]) -> [N]Bit
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Trivium_alt (r1, r2, r3) = take`{N} (s1 ^ s2 ^ s3)
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where
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a_65 = drop`{27} a_92
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a_68 = drop`{24} a_92
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a_90 = drop`{2} a_92
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a_91 = drop`{1} a_92
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a_92 = reverse r1 # t3
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b_68 = drop`{15} b_83
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b_77 = drop`{6} b_83
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b_81 = drop`{2} b_83
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b_82 = drop`{1} b_83
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b_83 = reverse r2 # t1
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c_65 = drop`{45} c_110
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c_86 = drop`{24} c_110
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c_108 = drop`{2} c_110
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c_109 = drop`{1} c_110
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c_110 = reverse r3 # t2
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s1 = a_65 ^ a_92
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s2 = b_68 ^ b_83
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s3 = c_65 ^ c_110
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t1 = s1 ^ (a_90 && a_91) ^ b_77
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t2 = s2 ^ (b_81 && b_82) ^ c_86
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t3 = s3 ^ (c_108 && c_109) ^ a_68
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/*********************************************************/
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iv1 = 0b111111111111111111101111111111111111111011111111111111111110111111111111111111101111111111111
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iv2 = 0b000000000000000000001000000000000000000001000000000000000000001000000000000000000001
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iv3 = 0b111111111111111110111111111111111111101111111111111111111011111111111111111110111111111111100000000000000000000
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test_keystream = 0b011111110111101111110100001110000000000000100010000000000000000100011000101100001110001011011010101010000100101110001111100011000110000101001011001111011101110110111010011011010110001000111101101111101100101001000111010001010011111110011100100011101010011110101001001000011100001111111100000001110001
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property Trivium_correct = (Trivium(iv1, iv2, iv3)) == test_keystream
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property Trivium_search (x, y, z) = (Trivium(x, y, z)) == test_keystream
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property Trivium_alt_correct = (Trivium_alt(iv1, iv2, iv3)) == test_keystream
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property Trivium_alt_equivalent x = take`{200}(Trivium_alt x) == take (Trivium x)
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