# Algorithme COMP128 (A3/A8) du GSM # Traduction en Python du code de # Marc Briceno, Ian Goldberg et David Wagner. # Suivi d'une mise en oeuvre de l'attaque par collisions: # Recherche de collisions et reconstruction de la clef Ki # Tables de compression. table_0 = [ 102,177,186,162, 2,156,112, 75, 55, 25, 8, 12,251,193,246,188, 109,213,151, 53, 42, 79,191,115,233,242,164,223,209,148,108,161, 252, 37,244, 47, 64,211, 6,237,185,160,139,113, 76,138, 59, 70, 67, 26, 13,157, 63,179,221, 30,214, 36,166, 69,152,124,207,116, 247,194, 41, 84, 71, 1, 49, 14, 95, 35,169, 21, 96, 78,215,225, 182,243, 28, 92,201,118, 4, 74,248,128, 17, 11,146,132,245, 48, 149, 90,120, 39, 87,230,106,232,175, 19,126,190,202,141,137,176, 250, 27,101, 40,219,227, 58, 20, 51,178, 98,216,140, 22, 32,121, 61,103,203, 72, 29,110, 85,212,180,204,150,183, 15, 66,172,196, 56,197,158, 0,100, 45,153, 7,144,222,163,167, 60,135,210,231, 174,165, 38,249,224, 34,220,229,217,208,241, 68,206,189,125,255, 239, 54,168, 89,123,122, 73,145,117,234,143, 99,129,200,192, 82, 104,170,136,235, 93, 81,205,173,236, 94,105, 52, 46,228,198, 5, 57,254, 97,155,142,133,199,171,187, 50, 65,181,127,107,147,226, 184,218,131, 33, 77, 86, 31, 44, 88, 62,238, 18, 24, 43,154, 23, 80,159,134,111, 9,114, 3, 91, 16,130, 83, 10,195,240,253,119, 177,102,162,186,156, 2, 75,112, 25, 55, 12, 8,193,251,188,246, 213,109, 53,151, 79, 42,115,191,242,233,223,164,148,209,161,108, 37,252, 47,244,211, 64,237, 6,160,185,113,139,138, 76, 70, 59, 26, 67,157, 13,179, 63, 30,221, 36,214, 69,166,124,152,116,207, 194,247, 84, 41, 1, 71, 14, 49, 35, 95, 21,169, 78, 96,225,215, 243,182, 92, 28,118,201, 74, 4,128,248, 11, 17,132,146, 48,245, 90,149, 39,120,230, 87,232,106, 19,175,190,126,141,202,176,137, 27,250, 40,101,227,219, 20, 58,178, 51,216, 98, 22,140,121, 32, 103, 61, 72,203,110, 29,212, 85,204,180,183,150, 66, 15,196,172, 197, 56, 0,158, 45,100, 7,153,222,144,167,163,135, 60,231,210, 165,174,249, 38, 34,224,229,220,208,217, 68,241,189,206,255,125, 54,239, 89,168,122,123,145, 73,234,117, 99,143,200,129, 82,192, 170,104,235,136, 81, 93,173,205, 94,236, 52,105,228, 46, 5,198, 254, 57,155, 97,133,142,171,199, 50,187,181, 65,107,127,226,147, 218,184, 33,131, 86, 77, 44, 31, 62, 88, 18,238, 43, 24, 23,154, 159, 80,111,134,114, 9, 91, 3,130, 16, 10, 83,240,195,119,253] table_1 = [ 19, 11, 80,114, 43, 1, 69, 94, 39, 18,127,117, 97, 3, 85, 43, 27,124, 70, 83, 47, 71, 63, 10, 47, 89, 79, 4, 14, 59, 11, 5, 35,107,103, 68, 21, 86, 36, 91, 85,126, 32, 50,109, 94,120, 6, 53, 79, 28, 45, 99, 95, 41, 34, 88, 68, 93, 55,110,125,105, 20, 90, 80, 76, 96, 23, 60, 89, 64,121, 56, 14, 74,101, 8, 19, 78, 76, 66,104, 46,111, 50, 32, 3, 39, 0, 58, 25, 92, 22, 18, 51, 57, 65,119,116, 22,109, 7, 86, 59, 93, 62,110, 78, 99, 77, 67, 12,113, 87, 98,102, 5, 88, 33, 38, 56, 23, 8, 75, 45, 13, 75, 95, 63, 28, 49,123,120, 20,112, 44, 30, 15, 98,106, 2,103, 29, 82,107, 42,124, 24, 30, 41, 16,108,100,117, 40, 73, 40, 7,114, 82,115, 36,112, 12,102,100, 84, 92, 48, 72, 97, 9, 54, 55, 74, 113,123, 17, 26, 53, 58, 4, 9, 69,122, 21,118, 42, 60, 27, 73, 118,125, 34, 15, 65,115, 84, 64, 62, 81, 70, 1, 24,111,121, 83, 104, 81, 49,127, 48,105, 31, 10, 6, 91, 87, 37, 16, 54,116,126, 31, 38, 13, 0, 72,106, 77, 61, 26, 67, 46, 29, 96, 37, 61, 52, 101, 17, 44,108, 71, 52, 66, 57, 33, 51, 25, 90, 2,119,122, 35] table_2 = [ 52, 50, 44, 6, 21, 49, 41, 59, 39, 51, 25, 32, 51, 47, 52, 43, 37, 4, 40, 34, 61, 12, 28, 4, 58, 23, 8, 15, 12, 22, 9, 18, 55, 10, 33, 35, 50, 1, 43, 3, 57, 13, 62, 14, 7, 42, 44, 59, 62, 57, 27, 6, 8, 31, 26, 54, 41, 22, 45, 20, 39, 3, 16, 56, 48, 2, 21, 28, 36, 42, 60, 33, 34, 18, 0, 11, 24, 10, 17, 61, 29, 14, 45, 26, 55, 46, 11, 17, 54, 46, 9, 24, 30, 60, 32, 0, 20, 38, 2, 30, 58, 35, 1, 16, 56, 40, 23, 48, 13, 19, 19, 27, 31, 53, 47, 38, 63, 15, 49, 5, 37, 53, 25, 36, 63, 29, 5, 7] table_3 = [ 1, 5, 29, 6, 25, 1, 18, 23, 17, 19, 0, 9, 24, 25, 6, 31, 28, 20, 24, 30, 4, 27, 3, 13, 15, 16, 14, 18, 4, 3, 8, 9, 20, 0, 12, 26, 21, 8, 28, 2, 29, 2, 15, 7, 11, 22, 14, 10, 17, 21, 12, 30, 26, 27, 16, 31, 11, 7, 13, 23, 10, 5, 22, 19] table_4 = [ 15, 12, 10, 4, 1, 14, 11, 7, 5, 0, 14, 7, 1, 2, 13, 8, 10, 3, 4, 9, 6, 0, 3, 2, 5, 6, 8, 9, 11, 13, 15, 12] table = [ table_0, table_1, table_2, table_3, table_4 ] def hex2(n): # hexadecimal sur 2 caracteres pour n < 256 return "%02X"% n def A3A8(rand, key): # listes de 16 entiers <256 x = {} # 32 octets bit={} # 128 octets simoutput={} for i in range(16,32): x[i] = rand[i-16] for i in range(1,9): for j in range(0,16): x[j] = key[j] for j in range(0,5): for k in range(0, 1<>(3-k)) & 1) % 256 if i < 8: for j in range(0,16): x[j+16] = 0 for k in range(0,8): next_bit = ((8*j + k)*17) % 128 x[j+16] |= bit[next_bit] << (7-k) % 256 for i in range(0,4): simoutput[i] = ((x[2*i]<<4) | x[2*i+1]) % 256 for i in range(0,6): simoutput[4+i] = ((x[2*i+18]<<6) | (x[2*i+18+1]<<2) | (x[2*i+18+2]>>2)) % 256 simoutput[4+6] = ((x[2*6+18]<<6) | (x[2*6+18+1]<<2)) % 256 simoutput[4+7] = 0 return(simoutput) def a38str(rand,key): # Convertit en une chaine hex de 16 caracteres d = A3A8(rand,key) return(''.join([hex2(d[i]) for i in range(0,12)])) # Attaque par recherche de collisions def find_collision(x,Ki):# octets x et x+8 a = [0]*16; found = False dd = {} for i in range(0,256): a[x] = i for j in range(0,256): a[x+8]=j # Conversion en chaines s = a38str(a,Ki) # pour premiers tests seulement if dd.has_key(s): # La version finale utilisera found = True # des clefs entieres et n'imprimera pas print "Collision found:" print dd[s] b = ''.join(map(hex2,a)) print b print "Hash: ", s return (dd[s],b) break else: dd[s] = ''.join(map(hex2,a)) if found: break def find_partial_key(x,c1,c2): # octets x et x+8, c1, c2 collision # par exemple # c1= '00000000002000000000000000ee0000' # c2= '00000000006800000000000000f80000' chal1 = map(lambda s: int(s,16),[c1[2*i:2*i+2] for i in range(0,16)]) chal2 = map(lambda s: int(s,16),[c2[2*i:2*i+2] for i in range(0,16)]) Ki= [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] for i in range(0,256): for j in range(0,256): Ki[x]=i; Ki[x+8]=j if A3A8(chal1,Ki) == A3A8(chal2,Ki): print "Partial key:",Ki return(''.join(map(hex2,Ki))) if __name__ == "__main__": # Reconstruction de la clef Ki # On teste avec une clef aleatoire # construite ainsi: # from random import randint # b = [randint(0,255) for i in range(0,16)] # b est la clef secrete Ki b = [4, 139, 193, 234, 147, 176, 248, 39, 51, 214, 124, 25, 38, 124, 145, 214] for i in range(0,16): print a38str([i]+[0]*15, b) print print "Example: Ki = " +"%02X"*16 % tuple(b) print K = [] for i in range(8): c = find_collision(i,b) k = find_partial_key(i, *c) K.append(k) print ''.join([K[i][2*i:2*i+2] for i in range(8)]+[K[i][2*i+16:2*i+18] for i in range(8)])