# Estimates for Discrete Logarithm Computations in Finite Fields of Small Characteristic

Rob Granger

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

7 Citations (Scopus)

## 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 contribution Estimates for Discrete Logarithm Computations in Finite Fields of Small Characteristic English Cryptography and Coding 9th IMA International Conference, Cirencester, UK, December 16-18, 2003. Proceedings Springer Berlin Heidelberg 190 - 206 16 9783540409748 9783540206637 https://doi.org/10.1007/978-3-540-40974-8_16 Published - Dec 2003

### Publication series

Name Lecture Notes in Computer Science Springer 2898 0302-9743

### Bibliographical note

Publisher: Springer

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