# Cryptography

For a string of bits S, let S* denote the complementary string obtained by changing all the 1s to 0s and all the 0s to 1s. Show that if the DES key K encrypts P to C, then K* encrypts P* to C*. (Hint: This has nothing to do with the structure of the S-boxes. To do the problem, just work through the encryption algorithm.) 9 marks

2. Suppose the key for round 0 in AES consists of 128 bits, each of which is 1. Determine the key components W(4), W(5), W(6), W(7), for the end of the first round. 10 marks

3. Given an RSA modulus of 55 and encryption exponent 3:

(a) find the decryption modulus d; 2 marks

(b) show, efficiently, that for a message m encrypted to c using this scheme, we have cd â‰¡ m (mod 55). 3 marks

4. Let p = 123456791, q = 987654323 and e = 127. Let the message m = 14152019010605. Using Maple, compute me (mod q); then use the Chinese remainder theorem to combine these to get me â‰¡ c (mod pq). Verify by computing me and c (mod pq) directly. 6 marks

5. Use a Maple procedure for the Baby Step, Giant Step algorithm to solve 8576 â‰¡ 3x (mod 53047). 10 marks

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**Category**: Sample Questions