Let the two primes p = 41 and q = 17 be given as set-up parameters for RSA. Which of the parameters e1 = 32, e2 = 49 is a valid RSA exponent? Justify your choice. Compute the corresponding private key Kpr = (p,q,d). Use the extended Euclidean algorithm for the inversion and point out every calculation step.

Recall that the simplified AES algorithm encrypts v as = T(Š(M(T(Š(v + ko))) + k1)) + k2, as described in the notes. The operations are: Add key, S-box, Shift row (T), Mix column (M), Add key, S-box, Shift row (T again), Add key. Write down an expression for the decryption of c in terms of the inverse of S (you don't need to calculate the inverse of S but, if necessary, compute the inverses of M and T).

A.Given p=25, q=9, and e=7, generate the public key (n,e) and the private key (n,d) using the RSA Key generation algorithm. (Use Excel for computations) b. Given Bob's public key of (85, 7) and private key of (85, 55), show how Alice can encrypt m=3 to send to Bob. Show the ciphertext. c. Given Bob's public key of (85, 7) and private key of (85, 55), show how Bob can decrypt the ciphertext y=2 received from Alice. Show the plaintext. d. Using the fast exponentiation method, determine 530 mod 47. Show your work.

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