Reference no: EM133236600
1. What is the difference between diffusion and confusion?
2. Which parameters and design choices determine the actual algorithm of a Feistel cipher?
3. What are three broad categories of applications of public-key cryptosystems?
4. Let p = 7919, q = 6203, and e = 65537 in RSA Algorithm.
(a) Find private-key d = e -1 ( mod φ(pq)) using the extended Euclidean Algorithm. Show the intermediate steps.
(b) Use the public key e to encrypt the message "Gold". To convert the message to an integer, assume that lowercase letters a, b, . . . , z are mapped to integers 0, 1, . . . , 25 respectively and uppercase letters A, B, . . . , Z are mapped to integers 26, 27,. . . ,51 respectively. Show the intermediate steps.
(c) Use the private key d calculated in part (a) to decrypt the ciphertext obtained in part (b). Compare the result with the original plain-text. Are they equal?
(d) Repeat parts parts (b) and (c) for plaintext "Yard". Explain why decrypting the encrypted plaintext "Yard" does not result in the original plaintext.
(e) Describe the set of plaintexts that can be encrypted/decrypted with this RSA algorithm successfully without the issue illustrated in part (d).
5. Alice and Bob would like to share a symmetric key before establishing a secure connection. To exchange this key, they use Diffie-Hellman algorithm with q = 7789 and α = 7001 where q is prime and α is its primitive root.
(a) Assuming that Alice picks private key XA = 6004, calculate her public key YA.
(b) Assuming that Bob picks private key XB = 4037, calculate his public key YB.
(c) Calculate the symmetric key that Alice and Bob share after exchanging their public keys.
(d) Find the ciphertext generated by ElGamal Algorithm applied on message "ha". Use the letter to number mappings specified in question 4.b.