1. Find GCD(8,12)?

2. Find two possible integer values of x in the congruence 2x+1 8 mod 5?

3. What do you mean by encryption and decryption?

Tutorial Exercises

1. Use the Euclidean algorithm to evaluate gcd (2093, 836).

2. Solve the following congruent equations.

(a) 2x+1 4 mod 5

(b) 1-3x 9 mod 4

3. A more general class of encryption function is provided by an affine cipher.

: , () ( + ) , = {0, 1,2, ... , 1}, where the secret key a and b are integers and gcd(a,n)=1.

The corresponding decryption function is -1 : , -1 () ( ) , where c is an integer chosen so that 1 . Find the decryption key for the affine cipher with n=26, a=11 and b=8. Encrypt the message with cord 5, 10 and 16.

4. Write an algorithm for evaluating xn where n is a positive integer? What is the dominant operation in this algorithm?