Group: DM

Discrete Mathematics

Department of Computer Science
Florida State University

The discrete math group deals mostly with number theory and modern algebra problems. The group's current focus is developing software that generates primitive polynomials over GF(2) of a Mersenne Prime degree. After this software has been fully optimized, we will use it to help us implement the Mersenne Twister psuedorandom number generator.

Time: Wednesdays 8:00 AM
Place: 486 Dirac Science Library
Dr. Chi-Ok Hwang
  Chi-Ok's home page Shyam Lakshmin
Jason Parker
PRNG Group
Testing Group
QRNG Group
Discrete Group
QMC Group
Finance Group
Prof. Michael Mascagni
Ethan Kromhout
Project 6
Software Determining ith Primitive Polynomial

Primitive polynomials are essential and basic in pseudo-random and quasi-random number generation. In this project of software developement determining i-th primitive polynomial, given a primitive polynomial of degree d, we find all the other primitive polynomials of degree d.
Project 8
Finding Primitive Roots

One problem necessary to our group's research is finding primitive roots of a prime p. We are mostly concerned with p being a Mersenne Prime, where p=2^k-1. A number a is a primitive root of an integer n if a is relatively prime to n and a is of order phi(n) modulo n. In the case where n is prime, phi(n) = n-1. For a to have order n-1, n-1 must be the smallest exponent j for which 2^j = 1 mod n. This happens if a^((n-1)/d)!=1 for every prime divisor d of n-1. The main obstacle in this process is finding all prime factor of n-1. If one only checks prime divisors below a certain bound, he has only some probablity of a being a primitive root of n-1. If one has found a primitive root a, a^i is also a primitive root for all i such that gcd(i,n-1)=1.