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Texas A&M Number Theory Seminar

Department of Mathematics
Blocker 624
Wednesdays, 1:45–2:45 PM

Maurice Rojas

Texas A&M University

Wednesday, February 13, 2019

Blocker 624, 1:45PM

Title: Faster point counting over prime power rings and pseudo-random generators

Abstract: We discuss a recent advance enabling a simple, randomized polynomial-time algorithm to count the roots of any polynomial in one variable over the prime power ring Z/(p^k). (The best previous general algorithms were exponential.) We also show how this implies a fast algorithm for computing certain Igusa zeta functions. These zeta functions, along with several other families of zeta functions, have been proposed as a method for generating one-way functions and pseudo-random generators by Anshel, Goldfeld, and Zuniga-Galindo. We'll review the latter connections as well.

This is joint work with Yuyu Zhu, and build upon earlier joint work with Qi Cheng, Shuhong Gao, Leann Kopp, Natalie Randall, and Daqing Wan.