Homework: Breaking Bad Ciphers

Burton Rosenberg
Out: 6 February 2003
Due: 13 February 2003

  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
    
  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.
  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.