7.6. Summary and References

Try these first

1. 1.

   What is 9 modulo 4?

   Hint

   Think of how many times 4 fits into 9.

2. 2.

   Is 8 congruent to 2 modulo 3?

   Hint

   Calculate the remainder of both numbers when divided by 3.

3. 3.

   What is the result of 14 modulo 5?

   • 2
   • 3
   • 4

   Hint

   Think about how many times 5 fits into 14.

4. 4.

   True or False: Division is always well-defined in modular arithmetic.

   • True
   • False

   Hint

   Consider cases where the divisor is congruent to zero.

5. 5.

   Using the square and multiply method, calculate 2^13 modulo 19 and explain each step.

   Hint

   Make sure to convert the exponent to binary and track your calculations carefully.

6. 6.

   Why is it important for cryptographic algorithms to use modular exponentiation? Discuss with examples.

   Hint

   Think about key generation and secure message transmission in cryptography.