Problem 4. Bob decides to use RSA with the public key N = 5754027577. In order to guard against transmission errors, Bob tells Alice to encrypt her message twice, once using the encryption exponent ei = 65537 and once using the encryption exponent e2 = 9929. (Notice that ged(e1, 2) = 1 - so this is bad based on the above remark a. Suppose Alice wishes to send the message m= 1337. What two ciphertexts, ci and C2, does she send to Bob? b. Find u and v such that | 65537-1u+9929-t=1 and compute ccmod N to see it returns m = 1337. c. Eve intercepts the two encrypted messages C1 = 4913548069 and C2 = 2032701608. Assuming that Eve also knows N and the two encryption exponents, e, and ez, use the method described above to help Eve recover Alice's plaintext without finding a factorization of N. Remark 2 (Short Message Attacks - Vi). One of the uses of RSA is to transmit keys for use in symmetric cryptosystems. In this case, N could be a few hundred digits, while the message could have only a few digits. For example, suppose the message m has 16 or fewer digits. In this situation, with a relatively short message, the plaintext can be retrieved without factoring N or finding d. For really short messages, say m