CS 266 Assignment 1. Due March 1, 2011. No late assignment will be accepted unless medical or family reasons, suitably documented. The assignment is due during the class time on the due day. 1. Page 92. Problem 1 2. Page 92. Problem 5 3. Page 92. Problem 6 4. Page 114. Problem 2 5. Page 114. Problem 4 6. Suppose a sequence of plaintext blocks, x_1, x_2, .. x_n, is encrypted using DES, producing ciphertext blocks, y_1, y_2, .. , y_n. Suppose that one ciphertext block, say y_I, is transmitted incorrectly (i.e. some 1's are changed to 0's and vice versa). Show that the number of plaintext blocks that will be decrypted incorrectly is equal to one if ECB or OFB modes were used for encryption; and equal to two if CBC or CFB modes were used. Problems for graduate students: 7. Prove that DES dncryption can be done by applying the DES encryption algorithm to the ciphertext with the key schedule reversed. 8. Let DES(x,K) represents the encryption of plaintext x with key K using the DES cryptosystem. Suppose y=DES(x,K) and y'=DES(c(x),c(K)), where c(.) denotes the bitwise complement of its argument. Prove that y'=c(y). 9. One way to strengthen DES is by double encryption: Given 2 keys, K_1 and K_2, define y=e_{K_2}(e_{K_1}(x)). If it happened that the encryption function e_{k_2} was the same as the decryption function d_{K_{1}}, then K_1 and K_2 are said to be dual keys. a) Prove that if C_0 is either all 0's or all 1's and D_0 is either all 0's or all 1's then K is self-dual. b) Prove that the following keys (given in hexadecimal notation) are self-dual: 0101010101010101.