Jon's research is in the area of algorithmic number theory, which is the design, analysis, and implementation of computer algorithms to solve problems from number theory. Some of the most important problems in this area are factoring large integers and testing integers for primality. Perhaps the most important application for number theoretic algorithms is in public-key cryptography. Jon has done joint work with Butler students, and his research makes use of Butler's new supercomputer, the Big Dawg.
Articles
A Randomized Sublinear Time Parallel GCD Algorithm for the EREW PRAM, Information Processing Letters (2010)
Computing Prime Harmonic Sums (with Eric Bach and Dominic Klyve), Mathematics of Computation (2009)
We discuss a method for computing Σ 𝑝≤𝑥 1/𝑝, using time about 𝑥2/3 and space...
Modular exponentiation via the explicit Chinese remainder theorem (with Daniel J. Bernstein), Mathematics of Computaion (2007)
In this paper we consider the problem of computing xe mod m for large integers...
EPICS: A Service Learning Program at Butler University (with Panos K. Linos), Proceedings of the Frontiers of Education Conference (2005)
In this paper we present our experiences teaching EPICS (Engineering Projects In Community Service) at...
Genetic Algorithms for the Extended GCD Problem, Journal of Symbolic Computation (1997)
We present several genetic algorithms for solving the extended greatest common divisor problem. After de...
Contributions to Books
Fast Bounds on the Distribution of Smooth Numbers (with Scott T. Parsell), Proceedings of the 7th International Symposium on Algorithmic Number Theory (2006)
In this paper we present improvements to Bernstein’s algorithm, which finds rigorous upper and lower...
The Pseudosquares Prime Sieve, Proceedings of the 7th International Symposium on Algorithmic Number Theory (2006)
We present the pseudosquares prime sieve, which finds all primes up to n.