Cryptography Exercises, Session 3
1. Consider the affine cryptosystem. How many keys can be used for ciphering in the
English alphabet with 26 letters? Can you generalize it to alphabet with n letters?
2. Using the algorithm for computing powers in modular arithmetic (which was
mentioned in the lecture), compute 5^33 mod 7.
3. Compute the inverse of 10 mod 23.
4. In an information system of employers, salary is encrypted using RSA. Does it provide
confidentiality? What happens if we use ElGamal encryption?
5. Consider a secret auction with several buyers. A buyer encrypts his offer (price, which
he is willing to pay): if he is willing to pay t crowns, he encrypts the number gt and
sends it encrypted by RSA. The buyer with highest offer takes the object of auction.
In this auction you saw the encrypted offer of your rival: a person you don’t want to
win the auction. Can you construct an offer with a slightly higher price? How does it
change if it will be used Elgamal encryption?
6. See also the exercises in the Course reader, Chapters 3 to 5.