The Discrete Lambert Map
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Publication:4691614
zbMATH Open1398.11012arXiv1509.00412MaRDI QIDQ4691614
Publication date: 24 October 2018
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.
Full work available at URL: https://arxiv.org/abs/1509.00412
Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Congruences; primitive roots; residue systems (11A07)
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