Discrete Logarithms - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Book Sections Year : 2016

Discrete Logarithms

Logarithmes discrets

Abstract

The Discrete Logarithm Problem (DLP) is one of the most used mathematical problems in asymmetric cryptography design, the other one being the integer factorization. It is intrinsically related to the Diffie-Hellman problem (DHP). DLP can be stated in various groups. It must be hard in well-chosen groups, so that secure-enough cryptosystems can be built. In this chapter, we present the DLP, the various cryptographic problems based on it, the commonly used groups, and the major algorithms available at the moment to compute discrete logarithms in such groups. We also list the groups that must be avoided for security reasons. Our computational model will be that of classical computers. It is to be noted that in the quantum model, DLP can be solved in polynomial time for cyclic groups.

Keywords

Fichier principal
Vignette du fichier
16_GuillevicMorain_Chapter9_DiscreteLogarithms_v2.pdf (599.96 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01420485 , version 1 (20-12-2016)
hal-01420485 , version 2 (13-12-2017)

Identifiers

  • HAL Id : hal-01420485 , version 2

Cite

Aurore Guillevic, François Morain. Discrete Logarithms. Nadia El Mrabet; Marc Joye. Guide to pairing-based cryptography, CRC Press - Taylor and Francis Group, pp.42, 2016, 9781498729505. ⟨hal-01420485v2⟩
1018 View
4264 Download

Share

Gmail Facebook Twitter LinkedIn More