Los Angeles Math Circle

11/15 -- Group B: Quadratic Reciprocity and Extensions to Cryptography (Paul Bunn)

We will begin with a review of basic number theory/abstract algebra, discussing the "integers modulo N." We will move on to discussions of how to determine if a number is a "quadratic residue" modulo N, introducing the Legendre and Jacobi symbols. We'll conclude by using these tools to build an encryption scheme, which we'll play around with at the end.