A note on discrete logarithms in finite fields
type: Item
instance of: scholarly article
title: A note on discrete logarithms in finite fields
zbMATH Open document ID: 0749.11055
DOI: 10.1007/BF01189026
author: G. C. Meletiou
author: Gary L. Mullen
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 1992-12-14T00:00:00Z
review text: Let \(F_ q\) denote the finite field of order \(q\), \(q=p^ n\geq 3\), \(p\) prime and \(F^*_ q\) the cyclic multiplicative group of nonzero elements. If \(\alpha\in F^*_ q\) is primiitve, the discrete logarithm of \(\beta\in F^*_ q\) to base \(\alpha\) is the unique integer \(x\) such that \(\beta=\alpha^ x\). It was previously shown that for \(q=p\) a prime \[ \log_ \alpha\beta=\sum^{p-2}_{i=1}(1-\alpha^ i)^{-1}\beta^ i. \] This note generalizes this formula to cases where the base is not necessarily a primitive element and to prime power fields.
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 94A60
zbMATH DE Number: 79160
zbMATH Keywords: cryptography
zbMATH Keywords: finite field
zbMATH Keywords: discrete logarithm
reviewed by: Ian Blake
MaRDI profile type: Publication
cites work: Q3216750
cites work: Q3765876
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description: scientific article; zbMATH DE number 79160