Past Events

Goldwasser-Micali Cryptosystem & Quadratic Reciprocity Law

Jinho Kim and Mayexciliana Cardenas Montoya

April 6th, 2018

Using the Quadratic Reciprocity Law, one can efficiently check whether a given number is a square in a field with prime characteristic. We will present the Goldwasser-Micali system, a probabilistic encryption which uses the ambiguity of the Jacobi symbol to encrypt a single bit.

Integer Factorization & Quadratic Sieve

Jonathan Zhao and Weija Zhou

March 23rd, 2018

Using the difference of squares, one can factor numbers in three simple steps: relation building (via the quadratic sieve), elimination, and GCD computation. We will describe these steps in detail and illustrate them with numerous examples.

Primality Testing

Jefrey Judes and Brandon Doherty

March 16th, 2018

This talk is dedicated to the Miller-Rabin primality test. After describing the test and how it works, we study its efficiency and compare it to other primality tests such as AKS.

Introduction to the RSA Cryptosystem

Chris Kapulkin

March 9th, 2018

I will explain the mathematical background behind RSA, including finding k-th roots mod p and mod N. After that, I will present the RSA scheme and explain why it is secure.