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# -*- coding: UTF-8 -*-
"""Bounded CTF key recovery for Vigenere, Hill and Enigma I."""
import itertools
import json
import heapq
import math
from collections import Counter
from string import ascii_uppercase
from ..__common__ import add, ensure_str
from .enigma import enigma_factory
from .substitution import _score
ENGLISH = (8.167, 1.492, 2.782, 4.253, 12.702, 2.228, 2.015, 6.094, 6.966, .153, .772, 4.025,
2.406, 6.749, 7.507, 1.929, .095, 5.987, 6.327, 9.056, 2.758, .978, 2.360, .150, 1.974, .074)
def _vigenere_decrypt(text, key):
output, cursor = [], 0
for char in text:
if char.upper() not in ascii_uppercase:
output.append(char)
continue
base = 65 if char.isupper() else 97
output.append(chr((ord(char) - base - key[cursor % len(key)]) % 26 + base))
cursor += 1
return "".join(output)
def recover_vigenere_key(plaintext, ciphertext):
pairs = [(plain.upper(), cipher.upper()) for plain, cipher in zip(ensure_str(plaintext), ensure_str(ciphertext))
if plain.upper() in ascii_uppercase and cipher.upper() in ascii_uppercase]
stream = [(ord(cipher) - ord(plain)) % 26 for plain, cipher in pairs]
for size in range(1, len(stream) + 1):
if all(value == stream[index % size] for index, value in enumerate(stream)):
return "".join(chr(value + 65) for value in stream[:size])
return ""
def crack_vigenere(ciphertext, max_key_length=20, limit=10):
source = ensure_str(ciphertext)
letters = [ord(char) - 65 for char in source.upper() if char in ascii_uppercase]
if len(letters) < 4:
raise ValueError("Vigenere cracking requires at least four letters")
candidates = []
for size in range(1, min(int(max_key_length), max(1, len(letters) // 2)) + 1):
key = []
for offset in range(size):
column = letters[offset::size]
observed = Counter(column)
key.append(min(range(26), key=lambda shift: sum(
(observed[(letter + shift) % 26] - len(column) * ENGLISH[letter] / 100) ** 2 /
max(.01, len(column) * ENGLISH[letter] / 100) for letter in range(26))))
plaintext = _vigenere_decrypt(source, key)
candidates.append({"text": plaintext, "key": "".join(chr(value + 65) for value in key),
"key_length": size, "score": round(_score(plaintext), 3)})
return sorted(candidates, key=lambda value: value["score"], reverse=True)[:max(1, int(limit))]
def _determinant(matrix):
if len(matrix) == 1:
return matrix[0][0]
return sum((-1) ** column * matrix[0][column] * _determinant(
[row[:column] + row[column + 1:] for row in matrix[1:]]) for column in range(len(matrix)))
def _inverse(matrix):
determinant = _determinant(matrix) % 26
inverse = pow(determinant, -1, 26)
return [[((-1) ** (row + column) * _determinant(
[line[:row] + line[row + 1:] for index, line in enumerate(matrix) if index != column]) * inverse) % 26
for column in range(len(matrix))] for row in range(len(matrix))]
def _multiply(left, right):
return [[sum(left[row][index] * right[index][column] for index in range(len(right))) % 26
for column in range(len(right[0]))] for row in range(len(left))]
def recover_hill_key(plaintext, ciphertext, dimension=2):
size = int(dimension)
plain = [ord(char) - 65 for char in ensure_str(plaintext).upper() if char in ascii_uppercase]
cipher = [ord(char) - 65 for char in ensure_str(ciphertext).upper() if char in ascii_uppercase]
blocks = min(len(plain), len(cipher)) // size
if size < 2 or blocks < size:
raise ValueError("Hill recovery needs at least dimension squared aligned letters")
plain_blocks = [plain[index * size:(index + 1) * size] for index in range(blocks)]
cipher_blocks = [cipher[index * size:(index + 1) * size] for index in range(blocks)]
for selected in itertools.combinations(range(blocks), size):
p = [[plain_blocks[column][row] for column in selected] for row in range(size)]
c = [[cipher_blocks[column][row] for column in selected] for row in range(size)]
try:
key = _multiply(c, _inverse(p))
except ValueError:
continue
if all([sum(key[row][column] * block[column] for column in range(size)) % 26 for row in range(size)] ==
cipher_blocks[index] for index, block in enumerate(plain_blocks)):
return key
raise ValueError("no Hill key matches the aligned plaintext/ciphertext")
def crack_hill(ciphertext, dimension=2, limit=10):
"""Exhaustively crack a 2x2 Hill key; larger matrices use recover_hill_key."""
if int(dimension) != 2:
raise ValueError("ciphertext-only Hill cracking is bounded to 2x2 matrices")
source = "".join(char for char in ensure_str(ciphertext).upper() if char in ascii_uppercase)
if len(source) < 8 or len(source) % 2:
raise ValueError("2x2 Hill cracking requires an even ciphertext of at least eight letters")
values = [ord(char) - 65 for char in source]
candidates = []
serial = 0
for a, b_, c, d in itertools.product(range(26), repeat=4):
determinant = (a * d - b_ * c) % 26
if math.gcd(determinant, 26) != 1:
continue
inverse = pow(determinant, -1, 26)
matrix = ((d * inverse % 26, -b_ * inverse % 26), (-c * inverse % 26, a * inverse % 26))
plaintext = "".join(chr((matrix[row][0] * values[index] + matrix[row][1] * values[index + 1]) % 26 + 65)
for index in range(0, len(values), 2) for row in range(2))
item = (_score(plaintext), serial, {"text": plaintext, "key": [[a, b_], [c, d]]})
serial += 1
if len(candidates) < limit:
heapq.heappush(candidates, item)
continue
if item[0] > candidates[0][0]:
heapq.heapreplace(candidates, item)
return [dict(value, score=round(score, 3)) for score, _, value in sorted(candidates, reverse=True)]
def crack_enigma(ciphertext, crib="", rotor_orders=("I.II.III",), reflectors=("B", "C"), rings="AAA", limit=10):
source, target = ensure_str(ciphertext), ensure_str(crib).upper()
if target and (len(target) < 3 or any(char not in ascii_uppercase for char in target)):
raise ValueError("Enigma recovery requires an alphabetic crib of at least three letters")
candidates, serial = [], 0
for rotors, reflector, positions in itertools.product(rotor_orders, reflectors,
map("".join, itertools.product(ascii_uppercase, repeat=3))):
plaintext = enigma_factory(rotors, reflector, positions, rings)(source)[0]
if target and target not in "".join(char for char in plaintext if char in ascii_uppercase):
continue
value = {"text": plaintext, "rotors": rotors, "reflector": reflector,
"positions": positions, "rings": rings}
if target:
candidates.append(value)
if len(candidates) >= limit:
break
continue
item = (_score(plaintext), serial, value)
serial += 1
if len(candidates) < limit:
heapq.heappush(candidates, item)
continue
if item[0] > candidates[0][0]:
heapq.heapreplace(candidates, item)
if target:
return candidates
return [dict(value, score=round(score, 3)) for score, _, value in sorted(candidates, reverse=True)]
def vigenere_crack_decode(text, errors="strict"):
source = ensure_str(text)
result = json.dumps(crack_vigenere(source), ensure_ascii=False, indent=2)
return result, len(source)
def hill_recover_decode(dimension=""):
def decode(text, errors="strict"):
source = ensure_str(text)
plaintext, ciphertext = source.splitlines()[:2]
result = json.dumps(recover_hill_key(plaintext, ciphertext, int(dimension or 2)))
return result, len(source)
return decode
def hill_crack_decode(text, errors="strict"):
source = ensure_str(text)
result = json.dumps(crack_hill(source), ensure_ascii=False, indent=2)
return result, len(source)
def enigma_crack_decode(crib=""):
def decode(text, errors="strict"):
source = ensure_str(text)
result = json.dumps(crack_enigma(source, crib), ensure_ascii=False, indent=2)
return result, len(source)
return decode
add("crack_vigenere", None, vigenere_crack_decode, r"^crack[-_]vigenere$")
add("hill_recover", None, hill_recover_decode, r"^hill[-_](?:recover|known)(?:[-_]([2-6]))?$")
add("hill_crack", None, hill_crack_decode, r"^hill[-_](?:crack|auto)$")
add("enigma_crack", None, enigma_crack_decode,
r"^enigma[-_](?:crack|recover)(?:[-_]([a-zA-Z]{3,32}))?$")