7.5.3.1. Naive Approach for Modular Exponentiation

Try these first

1. 1.

   What does modular exponentiation represent?

   Hint

   Think about the operation with base, power, and modulus.

2. 2.

   Describe the naive approach briefly.

   Hint

   What is the outcome after all multiplicative steps?

3. 3.

   What is the result of 2^3 % 3?

   • 0
   • 1
   • 2

   Hint

   Calculate the power first, then take the modulus.

4. 4.

   The naive approach for modular exponentiation is efficient.

   • True
   • False

   Hint

   Consider the multiplication steps involved.

5. 5.

   Compute 5^200 % 7 using both the naive method and the square and multiply method. Analyze the time taken for both methods.

   Hint

   What is the binary representation of `200`?

6. 6.

   How many multiplications would you perform in the naive method for a^b % N where a = 12, b = 50, N = 13? Compare that with the tally from the square and multiply method.

   Hint

   Convert `50` to binary to see the trend!