CIS 6930: Cryptographic Protocols

Last modified 2004.09.16

Homeworks

• HW1: due Tues 9/7/04
  1. 1.{2}
  2. Consider the two basic types of simple ciphers: (polyalphabetic) substitution (S) and transposition (T). Compare the product cipher that results from composing S with S, S then T, T then S, and T with T, assuming the ciphers are of different lengths. (Note that length for S means the period of key repetition, while for T it is the block length). In particular, how, if at all, does it affect the strength of the resulting cipher? Assume the lengths are L1 for the first and L2 for the second, with encryption applying the first, then the second cipher when composing them.
  3. Devise a transposition cipher that does not simply break the plaintext into blocks and shuffle the positions within each block. The cipher should still be periodic, in the sense that for some period L, if the plaintext p_i at position i becomes the ciphertext c_i+j for position i+j, then for all k>0, c_kL+i+j = p_kL+i.
• HW2: due 9/21/04
  1. 3.3
  2. 3.10
  3. 3.12
  4. 3.16
  5. 4.1
  6. 4.3
  7. 4.11
  8. 4.17
  9. Consider a keyed block encryption function E and message M broken into blocks M_1, M_2,.... At each block consider a possible binary function before encryption with inputs I_1 and I_2 and output O_1, then encryption of O_1 with output O_2, then another binary function with inputs I_3=O_2 and I_4, with output O_3 = ciphertext. If possible output taps from which the inputs for the next block are considered, they may include I_1, I_2, or O_1 before encryption, and O_2 or O_3 after encryption. By arranging different combinations of outputs of block_i-1 to inputs of block_i, we may obtain the variety of modes of DES, plus some others. Inputs may also be constants, so these possibilities should also be considered.

     Describe the modes of DES in these terms, and analyze the other possible modes that result from these input/output pairings. Which of these may be useful and which are not? Why or why not? Justify your answers.