def crack_ciphertext(public_key, ciphertext):
matrix = liblll.create_matrix_from_knapsack(public_key, ciphertext)
reduced_basis = liblll.lll_reduction(matrix)
guess = liblll.best_vect_knapsack(reduced_basis)
if 1 in guess:
return util.convert_bits_to_string(''.join([str(x) for x in guess]))
def reduce_basis(p1,p2): mat_basis = liblll.create_matrix([[p1[0],p2[0]],[p1[1],p2[1]]]) mat_reduced = liblll.lll_reduction(mat_basis) a0 = mat_reduced[0][0].numerator # lll library creates fractions with denominator 1, so grab numerator a1 = mat_reduced[0][1].numerator b0 = mat_reduced[1][0].numerator b1 = mat_reduced[1][1].numerator return [[a0,b0],[a1,b1]]
def reduce_basis(p1, p2):
mat_basis = liblll.create_matrix([[p1[0], p2[0]], [p1[1], p2[1]]])
mat_reduced = liblll.lll_reduction(mat_basis)
a0 = mat_reduced[0][
0].numerator # lll library creates fractions with denominator 1, so grab numerator
a1 = mat_reduced[0][1].numerator
b0 = mat_reduced[1][0].numerator
b1 = mat_reduced[1][1].numerator
return [[a0, b0], [a1, b1]]
def solve_knapsack_liblll(a, m):
"""
a is the list of elements
m is the expected subset sum
"""
for curr_m in (m, sum(a) - m):
matrix = create_matrix_from_knapsack(a, curr_m)
reduced = lll_reduction(matrix)
try:
return (find_solution_vector(reduced, a, curr_m), int(m == curr_m))
except SolutionNotFound:
pass
raise SolutionNotFound()
def attack_by_lll(msg_cipher, public_key_vector):
text_clear = ""
for i in range(0, len(msg_cipher)):
element_message_cipher = msg_cipher[i]
base_vector_list = attacking.create_base_vector_list(public_key_vector,element_message_cipher)
matrix_to_lll_reduction = liblll.create_matrix(base_vector_list)
reduced_matrix = liblll.lll_reduction(matrix_to_lll_reduction)
deciphered_bit_sequence = attacking.get_first_column_as_bit_sequence(reduced_matrix)
bit_to_text = utility.convert_bit_to_text(deciphered_bit_sequence, len(public_key_vector))
text_clear += bit_to_text
print("clear-text/cracked-text : => " +str(text_clear))
write_in_file("text_clear.txt",text_clear)
return True
def decipher_as_attacker(ciphered_vector, public_key_vector):
t = time.process_time()
print("\nAs an " + constants.bold_attribute + "ATTACKER" + constants.attribute_default +
", you own the ciphered vector, public key vector. \n" +
constants.foreground_colorant_green +
"So, you can decipher the cipher text with using lattice reduction." + constants.attribute_default + "\n")
print("Deciphering part is about to start...\n")
deciphered_text = ""
print("LLL basis lattice reduction algorithm is about to start...\n")
for i in range(0, len(ciphered_vector)):
ciphered_message = ciphered_vector[i]
base_vector_list = attacking.create_base_vector_list(public_key_vector, ciphered_message)
if utility.log_enabled:
print("base_vector_list: " + str(base_vector_list) + "\n")
matrix_to_lll_reduction = liblll.create_matrix(base_vector_list)
if utility.log_enabled:
print("matrix_to_lll_reduction:\n")
liblll.print_mat(matrix_to_lll_reduction)
print("\n")
reduced_matrix = liblll.lll_reduction(matrix_to_lll_reduction)
if utility.log_enabled:
print("reduced_matrix:\n")
liblll.print_mat(reduced_matrix)
print("\n")
deciphered_bit_sequence = attacking.get_first_column_as_bit_sequence(reduced_matrix)
if utility.log_enabled:
print("deciphered_bit_sequence:\n")
liblll.print_mat(deciphered_bit_sequence)
print("\n")
bit_to_text = utility.convert_bit_to_text(deciphered_bit_sequence, len(public_key_vector))
deciphered_text += bit_to_text
print("Lattice reduction algorithm is over.\n")
print("Finished to decipher the text in " + str(time.process_time()-t) + " ms as an attacker.\n\n" +
"Original text: " +
str(deciphered_text))
return True
for i, vi in enumerate(v):
row = [k * vi] + ([0] * i) + [1] + ([0] * (len(v) - i - 1))
row = map(lambda x: Fraction(x), row)
M.append(row)
### LLL time : bitches ###
def print_matrix(m, name):
print name
for r in m:
print r
from liblll import lll_reduction
print_matrix(M, 'M:')
Mr = lll_reduction(M)
print_matrix(Mr, 'Mr:')
Ms = [x[1:] for x in Mr]
print_matrix(Ms, 'Ms:')
k1 = 74385634756347465439475374765172563 # 716238129874897247894615317635178653875363187536781350385107359713876
from liblll import lll_reduction
vecs = [
(1, -1, 3),
(1, 0, 5),
(1, 2, 6)
]
vecs = [
(2, 2),
(-1, 4),
]
out = lll_reduction(vecs)
import matplotlib.pyplot as plt
def scale(n, m):
x = vecs[0][0] * n + vecs[1][0] * m
y = vecs[0][1] * n + vecs[1][1] * m
return (x, y)
v1 = scale(6, 7)
v2 = scale(13, 6)
vecs = [v1, v2]
xs = []
ys = []
for n in range(0, 25):
from liblll import lll_reduction
vecs = [(1, -1, 3), (1, 0, 5), (1, 2, 6)]
vecs = [
(2, 2),
(-1, 4),
]
out = lll_reduction(vecs)
import matplotlib.pyplot as plt
def scale(n, m):
x = vecs[0][0] * n + vecs[1][0] * m
y = vecs[0][1] * n + vecs[1][1] * m
return (x, y)
v1 = scale(6, 7)
v2 = scale(13, 6)
vecs = [v1, v2]
xs = []
ys = []
for n in range(0, 25):
for m in range(0, 25):
x = vecs[0][0] * n + vecs[1][0] * m
y = vecs[0][1] * n + vecs[1][1] * m
xs.append(x)