Algorytmy kryptograficzne | Laboratorium 5

  1. Uzupełnnij implementację kryptosystemu DES.

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    from typing import List
    
    IP = (
        58, 50, 42, 34, 26, 18, 10, 2,
        60, 52, 44, 36, 28, 20, 12, 4,
        62, 54, 46, 38, 30, 22, 14, 6,
        64, 56, 48, 40, 32, 24, 16, 8,
        57, 49, 41, 33, 25, 17, 9,  1,
        59, 51, 43, 35, 27, 19, 11, 3,
        61, 53, 45, 37, 29, 21, 13, 5,
        63, 55, 47, 39, 31, 23, 15, 7
    )
    
    IP_INV = (
        40, 8, 48, 16, 56, 24, 64, 32,
        39, 7, 47, 15, 55, 23, 63, 31,
        38, 6, 46, 14, 54, 22, 62, 30,
        37, 5, 45, 13, 53, 21, 61, 29,
        36, 4, 44, 12, 52, 20, 60, 28,
        35, 3, 43, 11, 51, 19, 59, 27,
        34, 2, 42, 10, 50, 18, 58, 26,
        33, 1, 41, 9,  49, 17, 57, 25
    )
    
    E = (
        32, 1,  2,  3,  4,  5,
        4,  5,  6,  7,  8,  9,
        8,  9,  10, 11, 12, 13,
        12, 13, 14, 15, 16, 17,
        16, 17, 18, 19, 20, 21,
        20, 21, 22, 23, 24, 25,
        24, 25, 26, 27, 28, 29,
        28, 29, 30, 31, 32, 1
    )
    
    P = (
        16, 7,  20, 21,
        29, 12, 28, 17,
        1,  15, 23, 26,
        5,  18, 31, 10,
        2,  8,  24, 14,
        32, 27, 3,  9,
        19, 13, 30, 6,
        22, 11, 4,  25
    )
    
    S_BOXES = (
        # S1
        (
            (14, 4, 13, 1, 2, 15, 11, 8, 3, 10, 6, 12, 5, 9, 0, 7),
            (0, 15, 7, 4, 14, 2, 13, 1, 10, 6, 12, 11, 9, 5, 3, 8),
            (4, 1, 14, 8, 13, 6, 2, 11, 15, 12, 9, 7, 3, 10, 5, 0),
            (15, 12, 8, 2, 4, 9, 1, 7, 5, 11, 3, 14, 10, 0, 6, 13),
        ),
        # S2
        (
            (15, 1, 8, 14, 6, 11, 3, 4, 9, 7, 2, 13, 12, 0, 5, 10),
            (3, 13, 4, 7, 15, 2, 8, 14, 12, 0, 1, 10, 6, 9, 11, 5),
            (0, 14, 7, 11, 10, 4, 13, 1, 5, 8, 12, 6, 9, 3, 2, 15),
            (13, 8, 10, 1, 3, 15, 4, 2, 11, 6, 7, 12, 0, 5, 14, 9),
        ),
        # S3
        (
            (10, 0, 9, 14, 6, 3, 15, 5, 1, 13, 12, 7, 11, 4, 2, 8),
            (13, 7, 0, 9, 3, 4, 6, 10, 2, 8, 5, 14, 12, 11, 15, 1),
            (13, 6, 4, 9, 8, 15, 3, 0, 11, 1, 2, 12, 5, 10, 14, 7),
            (1, 10, 13, 0, 6, 9, 8, 7, 4, 15, 14, 3, 11, 5, 2, 12),
        ),
        # S4
        (
            (7, 13, 14, 3, 0, 6, 9, 10, 1, 2, 8, 5, 11, 12, 4, 15),
            (13, 8, 11, 5, 6, 15, 0, 3, 4, 7, 2, 12, 1, 10, 14, 9),
            (10, 6, 9, 0, 12, 11, 7, 13, 15, 1, 3, 14, 5, 2, 8, 4),
            (3, 15, 0, 6, 10, 1, 13, 8, 9, 4, 5, 11, 12, 7, 2, 14),
        ),
        # S5
        (
            (2, 12, 4, 1, 7, 10, 11, 6, 8, 5, 3, 15, 13, 0, 14, 9),
            (14, 11, 2, 12, 4, 7, 13, 1, 5, 0, 15, 10, 3, 9, 8, 6),
            (4, 2, 1, 11, 10, 13, 7, 8, 15, 9, 12, 5, 6, 3, 0, 14),
            (11, 8, 12, 7, 1, 14, 2, 13, 6, 15, 0, 9, 10, 4, 5, 3),
        ),
        # S6
        (
            (12, 1, 10, 15, 9, 2, 6, 8, 0, 13, 3, 4, 14, 7, 5, 11),
            (10, 15, 4, 2, 7, 12, 9, 5, 6, 1, 13, 14, 0, 11, 3, 8),
            (9, 14, 15, 5, 2, 8, 12, 3, 7, 0, 4, 10, 1, 13, 11, 6),
            (4, 3, 2, 12, 9, 5, 15, 10, 11, 14, 1, 7, 6, 0, 8, 13),
        ),
        # S7
        (
            (4, 11, 2, 14, 15, 0, 8, 13, 3, 12, 9, 7, 5, 10, 6, 1),
            (13, 0, 11, 7, 4, 9, 1, 10, 14, 3, 5, 12, 2, 15, 8, 6),
            (1, 4, 11, 13, 12, 3, 7, 14, 10, 15, 6, 8, 0, 5, 9, 2),
            (6, 11, 13, 8, 1, 4, 10, 7, 9, 5, 0, 15, 14, 2, 3, 12),
        ),
        # S8
        (
            (13, 2, 8, 4, 6, 15, 11, 1, 10, 9, 3, 14, 5, 0, 12, 7),
            (1, 15, 13, 8, 10, 3, 7, 4, 12, 5, 6, 11, 0, 14, 9, 2),
            (7, 11, 4, 1, 9, 12, 14, 2, 0, 6, 10, 13, 15, 3, 5, 8),
            (2, 1, 14, 7, 4, 10, 8, 13, 15, 12, 9, 0, 3, 5, 6, 11),
        ),
    )
    
    PC1 = (
        57, 49, 41, 33, 25, 17, 9,
        1,  58, 50, 42, 34, 26, 18,
        10, 2,  59, 51, 43, 35, 27,
        19, 11, 3,  60, 52, 44, 36,
        63, 55, 47, 39, 31, 23, 15,
        7,  62, 54, 46, 38, 30, 22,
        14, 6,  61, 53, 45, 37, 29,
        21, 13, 5,  28, 20, 12, 4
    )
    
    SHIFT_SCHEDULE = (1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1)
    
    PC2 = (
        14, 17, 11, 24, 1,  5,
        3,  28, 15, 6,  21, 10,
        23, 19, 12, 4,  26, 8,
        16, 7,  27, 20, 13, 2,
        41, 52, 31, 37, 47, 55,
        30, 40, 51, 45, 33, 48,
        44, 49, 39, 56, 34, 53,
        46, 42, 50, 36, 29, 32
    )
    
    
    def int_to_bytes(x: int, length: int) -> bytes:
        return x.to_bytes(length, "big")
    
    
    def bytes_to_int(b: bytes) -> int:
        return int.from_bytes(b, "big")
    
    
    def generate_subkeys(key64: int) -> List[int]:
        pass
    
    
    def feistel(R: int, subkey48: int) -> int:
        pass
    
    
    def des_encrypt_block(block64: int, key64: int) -> int:
        pass
    
    
    def des_decrypt_block(block64: int, key64: int) -> int:
        pass
    
    
    
    if __name__ == "__main__":
        key = 0x133457799BBCDFF1
        pt  = 0x0123456789ABCDEF
        ct_expected = 0x85E813540F0AB405
    
        ct = des_encrypt_block(pt, key)
        print(f"CT = {ct:016X} (oczekiwane {ct_expected:016X})")
        assert ct == ct_expected
    
        pt_back = des_decrypt_block(ct, key)
        assert pt_back == pt
    
        try:
            from Crypto.Cipher import DES
            import secrets
    
            for i in range(50):
                key_r = secrets.randbits(64)
                pt_r  = secrets.randbits(64)
    
                key_rb = int_to_bytes(key_r, 8)
                pt_rb  = int_to_bytes(pt_r, 8)
    
                ct_r = des_encrypt_block(pt_r, key_r)
                ct_r_lib = bytes_to_int(DES.new(key_rb, DES.MODE_ECB).encrypt(pt_rb))
    
                assert ct_r == ct_r_lib
    
                pt_r_back = des_decrypt_block(ct_r_lib, key_r)
                pt_r_back_lib  = bytes_to_int(
                    DES.new(key_rb, DES.MODE_ECB).decrypt(int_to_bytes(ct_r, 8))
                )
    
                assert pt_r_back == pt_r == pt_r_back_lib
    
            print("Losowe testy OK.")
    
        except ImportError:
            print("Potrzebna biblioteka pycryptodome -> pip install pycryptodome.")
    
  2. Przeprowadź atak meet-in-the-middle na 2DES. Dla uproszczenia, obetniemy przestrzeń kluczy do $\{0,1,2,…,2^{24}-1\}$, a każdy klucz rozszerzymy do klucza 64-bitowego przez funkcje:

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    def _set_odd_parity(key: bytes) -> bytes:
        b = bytearray(key)
        for i in range(8):
            v = b[i] & 0xFE
            parity = ((v.bit_count() & 1) ^ 1)
            b[i] = v | parity
        return bytes(b)
    
     def seed24_to_des64(seed: int) -> bytes:
         state = (seed | 1) ^ 0x9E3779B97F4A7C15
         out = bytearray(8)
         for i in range(8):
             x = state
             x ^= (x >> 12) & 0xFFFFFFFFFFFFFFFF
             x ^= (x << 25) & 0xFFFFFFFFFFFFFFFF
             x ^= (x >> 27) & 0xFFFFFFFFFFFFFFFF
             state = (x * 0x2545F4914F6CDD1D) & 0xFFFFFFFFFFFFFFFF
             seven = (state >> 57) & 0x7F
             out[i] = seven << 1
         return _set_odd_parity(bytes(out))
    

    Wyznacz klucze, których użyto do szyfrowania 2DES dla

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    Tekst jawny: 0x4D49544D61747461
    Szyfrogram:  0xD4A27CCB8666688D