Cryptography — DU B.Sc. (Hons.) Mathematics Previous Year Question Papers

Attempt two parts from each question. • 1. (a) Write short notes on any two of the following : (i) Vigenère Cipher - (i) Euler's Totient Function (b) Determine the ged of 24140 and 16762 using Euclid's Algorithm: Also, convert the obtained ged into binary form. (c) Verify whether a(x)=x?+x+1and(x)=x+ x5 + x3 + x3 + 1 are inverses of each other in Z(28) with irreducible polynomial m(x) = x° + 2. (a) Explain the Vernam Cipher with an example. How is it different from the One-Time Pad ? (b) Solve the following for x, x = 7 (mod 21) (c) Convert the plaintext "MOVEFAST" into ciphertext using the Hill Cipher with key (a) Perform the forward MixColumn transformation for the first column of the plaintext .(b) Briefly explain the encryption and decryption process of the AddRoundKey step in AES along with the rationale behind it. 7.5 (c) Perform encryption and decryption using the RSA algorithm for p = 5, 9 = 11, public key b. = 3 and the' plaintext value X = 9. 7.5 4. (a) Explain the step-by-step process of the Diffie-Hellman key exchange for q = 11 and"a primitive root a = 2 by taking Xy = 5 and XB = 7. 7.5 highlighting its advantages and limitations. (c) Briefly describe the single round of DES algorithm with the help of an (i) Key generation process (public and private keys) (i) Encryption procedure, including computation of Cy and Cz. : (iii) Decryption process used to recover the plaintext. (b) For E11 (1, 7), show that the point G = (3, 2) belongs to the curve. (c) Give the linear algebra interpretation of Shamir's threshold scheme. Find the determinant of the matrix : What is a rotated XOR-based hash function? Explain how it provides an improvement over the basic XOR-based hash function. Compute the hash value for the following message blocks using the Rotated XOR operation: (b) Consider the ElGamal Digital Signature Scheme over the finite field GF(19) with primitive root a = 10. Alice selects her private key XA = 16. (i) Compute Alice's publie key › (i) For a message with hash value m = 14, Alice chooses I = 5: Generate the signature pair (Sy, Sz). ÷ =