Cryptography

1. Compute 25^{33} mod 7.

2. Find GCD(186, 254) using Euclid algorithm.

3. Find m, n such that 186m + 254n = d, where d is the answer to the previous question.

4. Find 35^{−1} mod 71.

5. Test pseudoprimality of 641 for base 8.

6. Give public key and secret key for RSA for the following data: p = 47, q = 71, e = 19.

7. (Huiswerk) Using the previous result encrypt the message ”sell”. (Every English letter is associated a number in the natural alphabetic order.)