Discrete logarithms in finite fields and their cryptographic significance

Research output: Chapter in Book/Report/Conference proceedingConference contribution

194 Scopus citations

Abstract

Given a primitive element g of a finite field GF(q), the discrete logarithm of a nonzero element u ∈ GF(q) is that integer k, 1 ≤ k ≤ q−1, for which u = g k. The well-known problem of computing discrete logarithms in finite fields has acquired additional importance in recent years due to its applicability in cryptography. Several cryptographic systems would become insecure if an efficient discrete logarithm algorithm were discovered. This paper surveys and analyzes known algorithms in this area, with special attention devoted to algorithms for the fields GF(2n). It appears that in order to be safe from attacks using these algorithms, the value of n for which GF(2n) is used in a cryptosystem has to be very large and carefully chosen. Due in large part to recent discoveries, discrete logarithms in fields GF(2n) are much easier to compute than in fields GF(p) with p prime. Hence the fields GF(2n) ought to be avoided in all cryptographic applications. On the other hand, the fields GF(p) with p prime appear to offer relatively high levels of security.

Original languageEnglish (US)
Title of host publicationAdvances in Cryptology
Subtitle of host publicationProceedings of EUROCRYPT 1984 - A Workshop on the Theory and Application of Cryptographic Techniques
EditorsIngemar Ingemarsson, Norbert Cot, Thomas Beth
PublisherSpringer Verlag
Pages224-314
Number of pages91
ISBN (Print)9783540160762
DOIs
StatePublished - 1985
EventWorkshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1984 - Paris, France
Duration: Apr 9 1984Apr 11 1984

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume209 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

OtherWorkshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1984
CountryFrance
CityParis
Period4/9/844/11/84

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