The Discrete Lambert Map
Abstract
The goal of this paper is to analyze the discrete Lambert map x to xgx 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 xgx 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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.