Problem 1. Suppose you are Bob and want to construct a way for others to secretly send you messages. Using the RSA Key Choice identify the public information (n, e) RSA Key Generator 1. Choose 2 prime numbers p and q 2. Compute n=pq 3. Choose that is relatively prime to (p- 1)(q 1). . Compute d the inverse of e nodulo (p 1) (q-1) , Publish e and n 6. Keep d secret a. Using the primes p-251, q = 131, and the exponent c 7 run the RSA Key Generator to construct a public pair (n, e) and the private key d b. Suppose Alice wants to send the message 201 to you using the public information (n, e) identified above i. What message would she send you? (i.e., determine y modulo n.) In SageMath and WolframAlpha the command to compute this is mod(,n). ii. Show that this message is encoded correctly, that is, compute y modulo n to ensure it returns 201 c. Using two primes of your choice p, q, and an exponent e of your choice run the RSA Key Generator to construct a public pair (n, e) and the private key d. d. (Bonus) Write a program that performs the RSA Key Gen. In SageMath, you can use the Extended Euclidean Algorithm xged(a, 6) that returns the list gcd(a, b), s,4] such that as+bt ged(a, . For other languages, there may be a buil in inverse function that can find the inverse of modulo b (often called "Modular Inverse)