Lecture 8: Quadratic Reciprocity and the Solovay-Strassen Primality Test

Background Material

• Lecture 6 on RSA
• Lecture 7 on Pseudoprimes, quadratic residues, and probabalistic primality testing

Topics

1. Review quadratic residues and Euler's test.
2. Legendre symbol and quadratic reciprocity
3. Jacobi symbol and quadratic reciprocity
4. An algorithm for computing the Jacobi symbol
5. Solovay-Strassen primality test

Maple Worksheet

1. lec8.mw - Maple worksheet illustrating the legendre and jacobi symbols, quadratic reciprocity and an algorithm for computing the jacobi symbol, and the Solovay-Strassen primality test.