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cribdrag.sage
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cribdrag.sage
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'''
A general purpose Hill Cipher cracker using crib dragging of a known
plaintext. Supports 3x3 key matrices.
'''
import sys
KPT = "letusmeetxx"
# Proof of Concept
ciphertext = "HBCDFNOPIKLB"
trans_letter_to_num = {
'A' : 0,
'B' : 1,
'C' : 2,
'D' : 3,
'E' : 4,
'F' : 5,
'G' : 6,
'H' : 7,
'I' : 8,
'J' : 9,
'K' : 10,
'L' : 11,
'M' : 12,
'N' : 13,
'O' : 14,
'P' : 15,
'Q' : 16,
'R' : 17,
'S' : 18,
'T' : 19,
'U' : 20,
'V' : 21,
'W' : 22,
'X' : 23,
'Y' : 24,
'Z' : 25,
}
trans_num_to_letter = {v: k for k, v in trans_letter_to_num.items()}
modulo = len(trans_num_to_letter)
print("Modulo: " + str(modulo))
print("Cipher Alphabet: ")
print(trans_num_to_letter)
def letter_to_num(c):
return trans_letter_to_num[c]
def num_to_letter(n):
return trans_num_to_letter[n]
def generate_keys(system1_solution, system2_solution, system3_solution):
keys = []
for (a, b, c) in system1_solution:
for (d, e, f) in system2_solution:
for (g, h, i) in system3_solution:
keys.append([[a, b, c], [d, e, f], [g, h, i]])
return keys
def text_mat_to_str(m):
text = ""
for c in range(len(m[0])):
for r in range(len(m)):
text += num_to_letter(int(m[r][c]))
return text
def decrypt(trans_letter_to_num, ciphertext, KPT):
if len(KPT) < 11:
raise Exception("Known plaintext is too short. If you don't have enough "
"characters to meet the required length, please input a guess.")
ciphertext = list(ciphertext)
ciphertext = [letter_to_num(x) for x in ciphertext]
ciphertext_blocks = []
for x in range(0, len(ciphertext) - 2, 3):
ciphertext_blocks.append([ciphertext[x], ciphertext[x+1], ciphertext[x+2]])
print("Ciphertext: ", ciphertext_blocks)
ciphertext_blocks_mat = Matrix(IntegerModRing(modulo), ciphertext_blocks).transpose()
# |a b c|
# Solve for the key |d e f| such that (key * known plaintext = known ciphertext)
# |g h i|
# After the key is found, attempt to invert it. The original encryption key
# must have been invertible. If the key is invertible, then invert it, and
# right-multiply it by the ciphertext to get the decrypted plaintext.
# (key inverse * known ciphertext)
# = (key inverse * key * known plaintext)
# = (identity * known plaintext)
# = known plaintext
for offset in range(len(ciphertext)-len(KPT)+1):
mapping = []
if offset % 3 == 0:
mapping.append((letter_to_num(KPT[0]), ciphertext[offset]))
mapping.append((letter_to_num(KPT[1]), ciphertext[offset+1]))
mapping.append((letter_to_num(KPT[2]), ciphertext[offset+2]))
mapping.append((letter_to_num(KPT[3]), ciphertext[offset+3]))
mapping.append((letter_to_num(KPT[4]), ciphertext[offset+4]))
mapping.append((letter_to_num(KPT[5]), ciphertext[offset+5]))
mapping.append((letter_to_num(KPT[6]), ciphertext[offset+6]))
mapping.append((letter_to_num(KPT[7]), ciphertext[offset+7]))
mapping.append((letter_to_num(KPT[8]), ciphertext[offset+8]))
elif offset % 3 == 2:
mapping.append((letter_to_num(KPT[1]), ciphertext[offset+1]))
mapping.append((letter_to_num(KPT[2]), ciphertext[offset+2]))
mapping.append((letter_to_num(KPT[3]), ciphertext[offset+3]))
mapping.append((letter_to_num(KPT[4]), ciphertext[offset+4]))
mapping.append((letter_to_num(KPT[5]), ciphertext[offset+5]))
mapping.append((letter_to_num(KPT[6]), ciphertext[offset+6]))
mapping.append((letter_to_num(KPT[7]), ciphertext[offset+7]))
mapping.append((letter_to_num(KPT[8]), ciphertext[offset+8]))
mapping.append((letter_to_num(KPT[9]), ciphertext[offset+9]))
else:
mapping.append((letter_to_num(KPT[2]), ciphertext[offset+2]))
mapping.append((letter_to_num(KPT[3]), ciphertext[offset+3]))
mapping.append((letter_to_num(KPT[4]), ciphertext[offset+4]))
mapping.append((letter_to_num(KPT[5]), ciphertext[offset+5]))
mapping.append((letter_to_num(KPT[6]), ciphertext[offset+6]))
mapping.append((letter_to_num(KPT[7]), ciphertext[offset+7]))
mapping.append((letter_to_num(KPT[8]), ciphertext[offset+8]))
mapping.append((letter_to_num(KPT[9]), ciphertext[offset+9]))
mapping.append((letter_to_num(KPT[10]), ciphertext[offset+10]))
var('a', 'b', 'c')
system1_solution = solve_mod([
mapping[0][0]*a + mapping[1][0]*b + mapping[2][0]*c == mapping[0][1],
mapping[3][0]*a + mapping[4][0]*b + mapping[5][0]*c == mapping[3][1],
mapping[6][0]*a + mapping[7][0]*b + mapping[8][0]*c == mapping[6][1],
], modulo)
if len(system1_solution) == 0:
continue
var('d', 'e', 'f')
system2_solution = solve_mod([
mapping[0][0]*d + mapping[1][0]*e + mapping[2][0]*f == mapping[1][1],
mapping[3][0]*d + mapping[4][0]*e + mapping[5][0]*f == mapping[4][1],
mapping[6][0]*d + mapping[7][0]*e + mapping[8][0]*f == mapping[7][1],
], modulo)
if len(system2_solution) == 0:
continue
var('g', 'h', 'i')
system3_solution = solve_mod([
mapping[0][0]*g + mapping[1][0]*h + mapping[2][0]*i == mapping[2][1],
mapping[3][0]*g + mapping[4][0]*h + mapping[5][0]*i == mapping[5][1],
mapping[6][0]*g + mapping[7][0]*h + mapping[8][0]*i == mapping[8][1],
], modulo)
if len(system3_solution) == 0:
continue
print("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")
#print "Possible solutions: "
#print "(a, b, c): " + str(system1_solution)
#print "(d, e, f): " + str(system2_solution)
#print "(g, h, i): " + str(system3_solution)
print("Offset: " + str(offset))
for key in generate_keys(system1_solution, system2_solution, system3_solution):
key_mat = Matrix(IntegerModRing(modulo), key)
if key_mat.is_invertible():
inv_key = key_mat.inverse()
#print "Key: "
#print key_mat.numpy()
#print "Key inverse: "
#print inv_key.numpy()
print(text_mat_to_str((inv_key * ciphertext_blocks_mat).numpy()))
else:
#print "Key not invertible!"
pass
if __name__ == '__main__':
decrypt(trans_letter_to_num, ciphertext, KPT)