1. Using the Extended Euclidean Algorithm, find x and y such that 23 x + 40 y = 1. 3.

2. Suppose solving the above equation was part of the process of finding the private key (d), given the public key e being 23 and Totient(n) being 40. What is the value of the private key? Show how d is derived.

3. During the process of generating an RSA key pair, two prime numbers were chosen, with p = 1,373 and q = 4,219. Determine the value of n and the value of Totient(n).

4 (continued from above) List the smallest 10 numbers that are greater than 1000 and are candidates for being selected as the public key.

5 Can the number 1995 be selected as the public key? Justify your answer.

6 (continued from above) Suppose the number 2467 was chosen as the public key. Show how the private key, d, would be calculated.

7 (continued from above) Show how the number 10 would be encrypted by the public key. What is the produced ciphertext?

8 (continued from above) Show how the ciphertext 23 would be decrypted by the private key.