7.5.2. Complexity Measurement

Try these first

1. 1.

   What is 7 mod 3?

   Hint

   Divide 7 by 3 and find the remainder.

2. 2.

   Is -4 mod 5 equal to 1?

   Hint

   Calculate the remainder when adjusting, it should still be in the range.

3. 3.

   What is 5 mod 2?

   • 1
   • 2
   • 3

   Hint

   Think about the remainder when performing division.

4. 4.

   Congruence means two numbers have the same what when divided by a modulus?

   Hint

   Recall the definition of congruence.

5. 5.

   Demonstrate the inefficiency of the naive modular exponentiation approach compared to the square and multiply method, with specific examples.

   Hint

   Calculate the intermediate powers and how they accumulate.

6. 6.

   Analyze a scenario where determining congruences can simplify a large addition and provide the calculation.

   Hint

   Use smaller numbers by reducing before performing addition.