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Math Help - Block cipher(cryptography)

  1. #1
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    Block cipher(cryptography)

    The block cipher \left(\mathcal{P},\mathcal{C},\mathcal{K},\mathcal  {E},\mathcal{D}\right) is defined as follows. The alphabet is {0,1}, block length is 3 and the key space \mathcal{K} is \mathbb{Z}_8. Given a key n\in\mathbb{Z}_8 and a plaintext p, let p' be p written as a decimal number. We define E_n(p) to be p'+nmod8 written as a 3-digit binary number (possibly with initial zeros), and we define D_n(p) in exactly the same way. The functions E_n and D_n are the encryption and decryption functions respectively of the cryptosystem.

    (a) Find E_5(110),E_2(001),E_0(101).
    (b) Given an excryption key n, find a corresponding decryption key

    Any help would be greatly appreciated, thanks=)
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  2. #2
    A Plied Mathematician
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    For part (a), it looks as though you simply add n to the plaintext, and then mod out 8. Example:

    E_{3}(010_{2})=2+3\;\text{mod}\;8=5\;\text{mod}\;8  =101_{2}.

    Here I've used the subscript 2 to indicate that I'm writing the number base 2.

    Does that make sense?

    For part (b), you have to find a way to invert the operation in part (a). So, taking my example, we had better find that

    D_{n}(101_{2})=010_{2}, using some integer n. How do you undo addition? How do you undo addition modulo an integer?
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  3. #3
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    Hi Ackbeet, thanks a lot for your post, I understand now =)
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  4. #4
    A Plied Mathematician
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    You're welcome. Have a good one!
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