7.5.3.3. Pseudocode for Square and Multiply

Try these first

1. 1.

   What is 10 mod 3?

   Hint

   Remember, you divide and find the remainder.

2. 2.

   Is -15 congruent to 3 mod 6?

   Hint

   Calculate -15 mod 6.

3. 3.

   What is the result of 15 mod 4?

   • 1
   • 2
   • 3

   Hint

   Perform the division and see what is left.

4. 4.

   True or False: The Square and Multiply algorithm is inefficient for calculating modular exponentiation.

   • True
   • False

   Hint

   Consider its application in cryptography.

5. 5.

   Compute 7^1001 mod 13 using the Square and Multiply algorithm.

   Hint

   First, track each multiplication and the modulo operation to keep numbers manageable.

6. 6.

   Show that both 22 and -10 are congruent mod 12.

   Hint

   Perform the modulus calculation for both numbers separately.