Applied Cryptography

1. Which parameters and design choices determine the actual algorithm of a Feistel cipher?

(25 points)

2. What is the difference between differential and linear cryptanalysis? (10 points)

3. List three classes of polynomial arithmetic. (15 points)

4. Does the set of residue classes modulo 3 form a group? (10 points)

a. with respect to addition?

b. with respect to multiplication?

5. Find integers x such that: (15 points)

a. 5x 4 (mod 3)

b. 7x 6 (mod 5)

c. 9x 8 (mod 7)

Please provide step by step details how to achieve the answers

6. In this text we assume that the modulus is a positive integer. But the definition of the expression

a mod n also makes perfect sense if n is negative. Determine the following: (20 points)

a. 5 mod 3

b. 5 mod -3

c. -5 mod 3

d. -5 mod -3

7. A modulus of 0 does not fit the definition, but is defined by convention as follows:

a mod 0 = a. With this definition in mind, what does the following expression mean:

a b (mod 0)

(10 points)

8. Using the extended Euclidean algorithm, and find the multiplicative inverse of

2

a. 1234 mod 4321

b. 24140 mod 40902

c. 550 mod 1769

Please provide step by step details how to achieve the answers (15 points)

9. Develop a set of tables similar to Table 5.1 (the 7the edition book, page 132) or Table 4.5 (6th

edition textbook, page 105) for GF(5). (20 points)

10. Develop a set of tables similar to Table 5.3 (the 7th edition book, page 144) or Table 4.7 (the 6th

edition book, page 117) for GF(4) with m(x) = x2 + x +1 (20 points)

160 points total.