Question: Need Help on this problem 1. Let Mi = 10749. (a) Use Lenstra's Elliptic Curve Factorization Algorithm to factor M1. (b) Suppose Alice and Bob

Need Help on this problem

1. Let Mi = 10749. (a) Use Lenstra's Elliptic Curve Factorization Algorithm to factor M1. (b) Suppose Alice and Bob are exchanging messages using RSA. Alice's public key is (N, e) = (10749, 55). Bob uses this to encrypt his message; he sends Alice the ciphertext c = 10618. Use your work in part a to decrypt Bob's message. Then decode the message using the ASCII table. (c) Now let N2 = 10763 = 47 * 229. Discuss the security of using M and N2 in RSA. Which value is more secure against an attack by Lenstra's algorithm? Which value is more secure against an attack by Fermat factorization? Which is more secure against an attack by Pollard's p-1 method? Be as specific as possible (discuss the number of steps for each algorithm)

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