Cryptography / spring 2012

Exercise 2, week 4

1. A well-known attack against authentication is ”birthday attack”, where one tries to find such x and y (x ≠ y) that h(x) = h(y), where h is the hash function. This is called ”birthday attack”, because in a small group of people one usually finds a pair of people who have the same birthday. How many people are needed for that the probability of finding a pair of people with the birthday is at least 0.5?

2. Show that the decoding algorithm of DES is the reverse of the coding algorithm of DES.

3. a) Compute A3 ● 59 in GF (2⁸).

b) Apply Rijndael column mix-operation to the word A3 57 C2 35.

4. Show that the number 1111 is not a prime (Hint: Fermat’s little theorem).

5. Compute f(30) by definition and by theorems presented in lectures.