Cryptopals.py

from base64 import b16decode, b16encode, b64encode
import operator
from math import sqrt
from collections import namedtuple

def parse_hex(s):
    return b16decode(s, casefold=True)

def problem_1():
    hx = "49276d206b696c6c696e6720796f757220627261696e206c696b65206120706f69736f6e6f7573206d757368726f6f6d"
    b = parse_hex(hx)
    print(str(b64encode(b), encoding="UTF-8"))

def fixed_xor(barray1, barray2):
    return bytes([a ^ b for a, b in zip(barray1, barray2)])

def problem_2():
    a = fixed_xor(parse_hex("1c0111001f010100061a024b53535009181c"),
                  parse_hex("686974207468652062756c6c277320657965"))
    print(str(a, encoding="UTF-8"))

def single_xor(barray, b):
    return bytes([a ^ b for a in barray])

ENGLISH_TEXT = """
    I see Barsad, and Cly, Defarge, The Vengeance [a lieutenant of Madame Defarge], the Juryman, the Judge, long ranks of the new oppressors who have risen on the destruction of the old, perishing by this retributive instrument, before it shall cease out of its present use. I see a beautiful city and a brilliant people rising from this abyss, and, in their struggles to be truly free, in their triumphs and defeats, through long years to come, I see the evil of this time and of the previous time of which this is the natural birth, gradually making expiation for itself and wearing out.

    I see the lives for which I lay down my life, peaceful, useful, prosperous and happy, in that England which I shall see no more. I see Her with a child upon her bosom, who bears my name. I see her father, aged and bent, but otherwise restored, and faithful to all men in his healing office, and at peace. I see the good old man [Mr. Lorry], so long their friend, in ten years" time enriching them with all he has, and passing tranquilly to his reward.

    I see that I hold a sanctuary in their hearts, and in the hearts of their descendants, generations hence. I see her, an old woman, weeping for me on the anniversary of this day. I see her and her husband, their course done, lying side by side in their last earthly bed, and I know that each was not more honoured and held sacred in the other"s soul, than I was in the souls of both.

    I see that child who lay upon her bosom and who bore my name, a man winning his way up in that path of life which once was mine. I see him winning it so well, that my name is made illustrious there by the light of his. I see the blots I threw upon it, faded away. I see him, fore-most of just judges and honoured men, bringing a boy of my name, with a forehead that I know and golden hair, to this place—then fair to look upon, with not a trace of this day"s disfigurement—and I hear him tell the child my story, with a tender and a faltering voice.

    It is a far, far better thing that I do, than I have ever done; it is a far, far better rest that I go to than I have ever known.
"""

ALPHABET_SIZE = 256

def byte_counts(barray):
    """
    Returns a vector of length 256. Index 'i' contains the number of occurrences
    of bytes equal to 'i' in barray.
    """
    d = [0] * ALPHABET_SIZE
    for b in barray:
        d[b] += 1
    return d

def calc_magnitude(v):
    magnitude_squared = 0
    for i in v:
        magnitude_squared += i * i
    return sqrt(magnitude_squared)

def normalized_vector(v):
    magnitude = calc_magnitude(v)
    assert magnitude != 0
    return [i / magnitude for i in v]

def generate_normalized_vector(barray):
    """
    Given byte array barray, return a normalized vector of the byte counts.
    """
    return normalized_vector(byte_counts(barray))

def subtract_vector(v1, v2):
    """
    Returns a new vector by subtracting v2 from v1, without modifying v1 or v2.
    """
    assert len(v1) == len(v2)
    return [v1[i] - v2[i] for i in range(len(v1))]

def dist_between(v1, v2):
    return calc_magnitude(subtract_vector(v1, v2))

RankedGuess = namedtuple("RankedGuess", "rank guess")

def similarity_rank_guesses(reference_vector, guesses):
    """
    Return a list of guesses sorted by their similarity to the normalized
    reference vector. Each guess is a byte array.
    """
    ranked_guesses = []
    for guess in guesses:
        guess_vector = generate_normalized_vector(guess)
        try:
            dst = dist_between(reference_vector, guess_vector)
            ranked_guesses.append(RankedGuess(dst, guess))
        except AssertionError:
            ranked_guesses.append(RankedGuess(math.inf, guess))
    return ranked_guesses

def problem_3():
    english_bytes = bytes(ENGLISH_TEXT, encoding="UTF-8")
    norm_english_vector = generate_normalized_vector(english_bytes)

    ciphertext_s = "1b37373331363f78151b7f2b783431333d78397828372d363c78373e783a393b3736"
    ciphertext_bytes = parse_hex(ciphertext_s)

    guesses = [single_xor(ciphertext_bytes, i) for i in range(256)]
    ranked_guesses = similarity_rank_guesses(norm_english_vector, guesses)
    best_ranked_guess = min(ranked_guesses, key=lambda x: x.rank)
    print(str(best_ranked_guess.guess, encoding="UTF-8"))

PROBLEM_4_STRINGS = """0e3647e8592d35514a081243582536ed3de6734059001e3f535ce6271032
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def problem_4():
    english_bytes = bytes(ENGLISH_TEXT, encoding="UTF-8")
    norm_english_vector = generate_normalized_vector(english_bytes)

    barrays = [parse_hex(s) for s in PROBLEM_4_STRINGS.split()]
    guesses = []
    for barray in barrays:
        for i in range(ALPHABET_SIZE):
            guesses.append(single_xor(barray, i))
    ranked_guesses = similarity_rank_guesses(norm_english_vector, guesses)
    best_ranked_guess = min(ranked_guesses, key=lambda x: x.rank)
    print(str(best_ranked_guess.guess, encoding="UTF-8").strip())

def repeat_xor(b1, b2):
    return bytes([b1[i] ^ b2[i % len(b2)] for i in range(len(b1))])

def prhex(b):
    return str(b16encode(b), encoding="UTF-8").lower()

def problem_5():
    s = "Burning 'em, if you ain't quick and nimble\nI go crazy when I hear a cymbal"
    x = "ICE"
    print(prhex(repeat_xor(bytes(s, encoding="UTF-8"), bytes(x, "UTF-8"))))

if __name__ == "__main__":
    problem_1()
    problem_2()
    problem_3()
    problem_4()
    problem_5()