CS 266 Assignment 1.
Due Feb 23, 2012.



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 [chapter 3]
2.	Page 92. Problem 5
3.      Page 92. Problem 6
4.	Page 114. Problem 2 [chapter 4]
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.