7.5.3. Modular Exponentiation

Try these first

1. 1.

   What is 7 mod 3?

   Hint

   Think about how many times 3 fits into 7.

2. 2.

   Is 10 ≡ 4 mod 6 true or false?

   Hint

   Calculate both `10 mod 6` and `4 mod 6`.

3. 3.

   What is the result of 9 mod 4?

   • 1
   • 2
   • 3

   Hint

   Consider how many times 4 fits into 9.

4. 4.

   Is the operation a / b well-defined in modular arithmetic?

   • True
   • False

   Hint

   Recall our discussion on modular operations!

5. 5.

   Given a = 3, b = 20, and N = 5, compute 3^20 mod 5 using the square and multiply method.

   Hint

   Break down your steps and check accumulated powers.

6. 6.

   Design an algorithm to compute mod 2^n efficiently given an n-bit integer.

   Hint

   Focus on which bits are `1` in your binary number.