Lecture: Strong Pseudoprimes and a Probabalistic Primality Test

Background Material

• Modular Arithmetic and Fast Exponentiation
• RSA and CRT

Reading

• Chapter 6 of the text.

Topics

1. Review Fermat's Theorem
2. Strong Pseudoprimes
3. Quadratic residues, Wilson's theorem and Euler's test.
4. Probabalistic primality testing

Maple Worksheet

1. strongpprime.mw - Maple worksheet illustrating pseudoprimes, Euler's test and a probabilistic primality test.

Practice Assignment

1. Experiment to verify that for a prime number that the strong pseudoprime test is always satisfied.
2. Using Maple, empirically verify Wilson's lemma and Euler's test. What happens when the input is not prime?
3. Investigate for several composite numbers that some of the numbers that are relatively prime to the number do NOT satisfy the strong psuedoprime test. How many such numbers fail the test and how many pass the test?
4. Exc. 6.11, 6.12, 6.14, 6.15, 6.21 from the text.