Лабораторная 3 / rancsevaya

import random
from sympy import mod_inverse

def gen_superincr_seq(n, start=2):
    seq = [random.randint(start, start + 5)]
    for _ in range(n - 1):
        seq.append(sum(seq) + random.randint(1, 10))
    return seq

def gen_keys(n=8):
    priv_key = gen_superincr_seq(n)
    m = sum(priv_key) + random.randint(10, 20)
    w = random.randint(2, m - 1)
    while True:
        try:
            w_inv = mod_inverse(w, m)
            break
        except:
            w = random.randint(2, m - 1)

    pub_key = [(w * x) % m for x in priv_key]
    return priv_key, pub_key, w, m, w_inv

def to_bits(num, length):
    return list(map(int, bin(num)[2:].zfill(length)))

def from_bits(bits):
    return int("".join(map(str, bits)), 2)

def encrypt(num, pub_key):
    bits = to_bits(num, len(pub_key))
    print(f"  ->байт {num} в битах: {bits}")
    c = sum(b * pk for b, pk in zip(bits, pub_key))
    return c

def decrypt(cipher, priv_key, w_inv, m):
    s = (cipher * w_inv) % m
    print(f"  ->расшифровка суммы {cipher}: s = {s}")
    bits = []
    for val in reversed(priv_key):
        if val <= s:
            bits.append(1)
            s -= val
        else:
            bits.append(0)
    bits.reverse()
    print(f"     восстановленные биты: {bits}")
    return from_bits(bits)

def split_to_bytes(num_str):
    num = int(num_str)
    bytes_list = []
    while num > 0:
        bytes_list.insert(0, num % 256)
        num //= 256
    return bytes_list

def combine_bytes(bytes_list):
    num = 0
    for b in bytes_list:
        num = num * 256 + b
    return str(num)

def backpack_demo():
    num_str = input("Число: ")

    priv_key, pub_key, w, m, w_inv = gen_keys(8)

    print(f"\nЗакрытый ключ: {priv_key}")
    print(f"Открытый ключ:  {pub_key}")
    print(f"w = {w}, m = {m}, w^(-1) mod m = {w_inv}\n")

    byte_blocks = split_to_bytes(num_str)
    print(f"Число в байтах: {byte_blocks}")

    enc_blocks = []
    for b in byte_blocks:
        enc_blocks.append(encrypt(b, pub_key))
    print(f"\nЗашифрованные блоки: {enc_blocks}")

    dec_blocks = []
    for c in enc_blocks:
        dec_blocks.append(decrypt(c, priv_key, w_inv, m))
    print(f"\nРасшифрованные байты:{dec_blocks}")

    dec_str = combine_bytes(dec_blocks)

    print(f"\nРасшифрованное число: {dec_str}")

if __name__ == "__main__":
	backpack_demo()