Estimates for Discrete Logarithm Computations in Finite Fields of Small Characteristic

Rob Granger

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

Abstract

We give estimates for the running-time of the function field sieve (FFS) to compute discrete logarithms in $\F_{p^n}^{\times}$ for small~$p$. Specifically, we obtain sharp probability estimates that allow us to select optimal parameters in cases of cryptographic interest, without appealing to the heuristics commonly relied upon in an asymptotic analysis. We also give evidence that for any fixed field size some may be weaker than others of a different characteristic or field representation, and compare the relative difficulty of computing discrete logarithms via the FFS in such cases.
Translated title of the contributionEstimates for Discrete Logarithm Computations in Finite Fields of Small Characteristic
Original languageEnglish
Title of host publicationCryptography and Coding
Subtitle of host publication9th IMA International Conference, Cirencester, UK, December 16-18, 2003. Proceedings
PublisherSpringer Berlin Heidelberg
Pages190 - 206
Number of pages16
ISBN (Electronic)9783540409748
ISBN (Print)9783540206637
DOIs
Publication statusPublished - Dec 2003

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume2898
ISSN (Print)0302-9743

Bibliographical note

Publisher: Springer

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