Homework: Breaking Bad Ciphers

1. Consider the following encryption device. Cipher block size is 32 bits. There are 8 rounds and key size is 32 * 8 = 256 bits. In each round 32 bits are used. Call them k_0, k_1, ..., k_7. There is a permutation P that applies to the 32 bit block and permutes the bits. Here is the cipher:

              input
                |
              [ P ]
                |
               (+)<---- k_0
                |
              [ P ]
                |
               (+)<---- k_1
                |
                .
                .
                .
                |
               (+)<---- k_7
                |
              [ P ]
                |
             output
   

   • Break this cipher using chosen-plaintext attack (recover the key).
   • Break this cipher using known-plaintext attact (recover the key).
   • How may key bits are there really?
2. Consider the following encryption. Block size is 32 bits. The encryption is a permutation of the bits in the 32 bit block, therefore the key is an integer in the range 0 through 32!-1.
   • Break this cipher using a chosen-plaintext attack (recover the key).
   • Break this cipher using a known-plaintext attack (you don't get to chose the plaintext, but assume they are random 32 bit numbers. Recover the key).
   • How may key bits are there?
3. Combining ciphers and break the composite. That is, there are 256 bits of XOR key and log_2 32! bits of permutation key. Hint: Differential cryptanalysis can remove the key in order to probe the permutation.