1. What are the roles of the public and private key? 2. What is a one-way function? 3. Perform encryption and decryption using the RSA algorithm for the following: a. p = 3; 9 = 11, e = 7;M = 5 b. p = 5; 9 = 11, e = 3; M = 9 c. p = 7; q = 11, e = 17;M = 8 d. p = 11; g = 13, e = 11;M = 7 e. p = 17: q = 31, e = 7;M = 2 4. In a public-key system using RSA, you intercept the ciphertext C = 10 sent to a user whose public key is e = 5, n= 35. What is the plaintext M? 5. In an RSA system, the public key of a given user is e = 31, n. = 3599. What is the private key of this user? Hint: First use trial-and-error to determine p and q; then use the extended Euclidean algorithm to find the multiplicative inverse of 31 modulo o(n). 6. Use the fast exponentiation algorithm to determine 55% mod 1234. Show the steps involved in the computation. 7. Here is another realization of the fast exponentiation algorithm. Demonstrate that it is equivalent to the exponentiation algorithm