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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.