Exercises

You must type your answers in a word processing system, and create a PDF.

You can work on your own, or you can work in pairs. If you work in a pair, only one of you should submit the answers (of course, both will get the credit). Please note on your answers that you worked as a pair, and please mention both IDnumbers.

1. Assume a simple two round Feistel block cipher with an 8 bit key and 16 bit block size. We have two rounds, with i = 0 and i = 1, and two round keys.

Theround keys are defined as K_i = K + 75 → i (mod256). The Feistel function is f(Ki, Ri) = 127? (Ki + Ri) (mod256), where Ri id the decimal representation of the right 8 bit sof the in put block.

Encrypt the message block M = (V, S) with key K = Y. Use the ASCII encoding of capital letters where A is encoded as 65. It is sufficient to give your result as apair of decimalnumbers.

2. For each of the following block ciphers E1and E2, explain whether the cipher is a secure pseudorandom permutation. (In both cases, the key size and the block size are 128bits.)
(a) E₁(k, m) = km.
(b) E₂(k, m) = (m - k mod 2128) k.

3. Compute the following:
(a) 1234567890 ?5678901234 mod 7890123456.
(b) (x²+ 1)(x³+ x + 1) mod x⁴+ x+1.

4. Let E be a secure block cipher (say, AES). Consider each of the following modes of operation. For each one, say whether it is secure or not, and briefly explain youranswer.

(a) Theen cryption by kof m₁||m₂||...||mnisc0||c₁||c₂||...||c_n,wherec₀ is a randomly chosen "initialisation vector" of appropriate size, and
c_i= E(k, m_i) c_i-1(i>0).

(b) Theen cryption by kofm₁||m₂||...||mnisN||c₁||c₂||...||c_n,whereN is a randomly chosen nonce of appropriate size, and c_i= E(k,N mi).

5. Find the first 20 bytes of the output of the RC4 algorithm when run with the key K = [1,2,3].