(2 pts) The goal of this exercise is to compute a private RSA key and decrypt a message, given a public key. We will use the modulus n = 2537, which is a produce to two primes.

[This is typical of the RSA system which chooses two large primes at random generally, and multiplies them to

ﬁnd It. The public will know R but the two prime factors are kept private.] Now we choose our public key 6 = 235. This will work since gcd(235_, QM 2537)) : 1. [In general as

long as we choose an c with gcd(e, $8537» I l, the system will work.] For very large primes, computing the private key, 11, is not feasible, but with our tiny example, you should be

able to compute d, which is the mod $(2537) inverse of 235. (I: Now, assume that a message has been encrypted using the public key and that encrypted message is the

number 12. Using your private key, determine the number that comprises that unencrypted message. message =