The Discrete Lambert Map
Number Theory
2015-09-02 v1
Abstract
The goal of this paper is to analyze the discrete Lambert map x to xg^x modulo a power of a prime p which is important for security and verification of the ElGamal digital signature scheme. We use p-adic methods (p-adic interpolation and Hensel's Lemma) to count the number of solutions x of xg^x congruent to c modulo powers of an odd prime p and c, g are fixed integers. At the same time, we discover special patterns in the solutions.
Cite
@article{arxiv.1509.00412,
title = {The Discrete Lambert Map},
author = {Anne Waldo and Caiyun Zhu},
journal= {arXiv preprint arXiv:1509.00412},
year = {2015}
}
Comments
12 pages, submitted to the Rose-Hulman Institute of Technology Mathematics Journal