8.6. AKS Primality Testing Algorithm

Try these first

1. 1.

   What is a prime number?

   Hint

   Think about what divisors mean.

2. 2.

   Is 9 a prime number?

   Hint

   Count the divisors of 9.

3. 3.

   What defines a prime number?

   • Divisible by only itself
   • Divisible by itself and 1
   • All of the above

   Hint

   Think about the factors of a prime number.

4. 4.

   Is the AKS algorithm exponential?

   • True
   • False

   Hint

   Remember the definitions of polynomial and exponential time.

5. 5.

   Explain why primality testing is crucial in cryptography and how AKS contributes.

   Hint

   Consider the role of prime numbers in security.

6. 6.

   Provide a mathematical proof or example where a number tested by the naive method might give misleading results for a composite number.

   Hint

   Think about the efficiency of checking divisors.