A. Find the prime factorization of 7007. Also describe and show how you find it in step by step.

B. Please give the definition of Euler's Totient function correctly and clearly as well as concisely.

C. Determine the value ø (41) and ø (231). (Note: ø (n) is Euler's Totient function)

D. What is the difference between an index and a discrete logarithm?

E. Describe in general terms an efficient procedure (step by step) for picking a prime number.

F. What are the principal elements of a public-key cryptosystem?

G. What are the roles of the public and private key?

H. Perform encryption/decryption for the following given conditions by using RSA algorithm in Section 9.2 of the textbook.

p = 3; q =11; e = 7; M = 5;