Assignment 3 (Due on April 13, 2012) Undergrad students will need to specify which 6 out of 8 problems that she/he is submitting. Problem 1: Find multiplicative inverses (if it exists): ---------------------------------------- a) 177 mod 1077: b) 311 mod 2431: Problem 2: Compute 53^165 mod 401 using the square and multiply algorithm ------------------------------------------------------------------------- You are required to show all steps. Problem 3: pg 182 no. 3 ----------------------- Problem 4: pg 183 no. 8 ----------------------- Problem 5: Show that 129 is not a prime without factoring: (Apply testing algorithm) --------------------------------------------------------- (without any division) Problem 6: In RSA scheme, suppose Trudy knows the public key of Alan. Suppose further that Alan is stupid enough to publicly annouce the the difference of the 2 primes p-q == S. How can Trudy break this scheme? Problem 7: Suppose Michael has an RSA cryptosystem with modulus n and encryption exponent b1, and Stanley has an RSA cryptosystem with the same modulus n with encryption exponent b2. Suppose also that GCD(b1,b2)=1. Now, consider the situation that arises if Diana encrypts the same plaintext x to send to both Michael and Stanley. Suppose Alan sees both ciphertext that Diana sends to Michael and Stanley. How can Alan obtain the message x? Problem 8: In class, we discuss the problem of using e=3. Suppose the public key of Bob, Bart and Bert are (e,n)= (3,161), (3,209), (3,221). Alan sends the same message to Bob, Bart, and Bert, encrypted with their respective public key. Alan sends Bob, Bart, and Bert, 6 mod 161, 113 mod 209 and 177 mod 221 respectively. Using Chinese reminder theorem as illustrated in class (without factoring, or guessing), find the message that Alan sends to them.