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arXiv · 1509.00412

The Discrete Lambert Map

Anne Waldo·Caiyun Zhu
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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.

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Anne Waldo, Caiyun Zhu. 2015-09-01. The Discrete Lambert Map. https://arxiv.org/abs/1509.00412

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