Analysis of the Herlestam and Johannesson discrete logarithm scheme in \(GF(2^ N)\) for large N
type: Item
instance of: scholarly article
title: Analysis of the Herlestam and Johannesson discrete logarithm scheme in \(GF(2^ N)\) for large N
zbMATH Open document ID: 0567.12012
DOI: 10.1007/BF01934386
author: Shimshon Berkovits
author: Joel E. Sachs
published in: BIT
publication date: 1985-01-01T00:00:00Z
review text: The authors study the complexity of the algorithm of \textit{T. Herlestam} and \textit{R. Johannesson} [1981 IEEE International Symposium on Information Theory, Santa Monica, California, Feb. 1981; cf. BIT 21, 326- 334 (1981; Zbl 0493.12023)] for computing logarithms over \(GF(2^ n)\). Their analysis suggests that the target set (of logarithms that have to be stored) must contain all elements up to about weight n/3-8. This means that even for \(n=63\) the amount of computation needed is prohibitively large.
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 68Q25
zbMATH DE Number: 3904709
zbMATH Keywords: Herlestam-Johannesson algorithm
zbMATH Keywords: logarithms over finite fields
zbMATH Keywords: public key distribution system
zbMATH Keywords: complexity
MaRDI profile type: Publication
cites work: Algebraic coding theory
cites work: On computing logarithms over GF(2**p)
cites work: Q3726006
cites work: An improved algorithm for computing logarithms over&lt;tex&gt;GF(p)&lt;/tex&gt;and its cryptographic significance (Corresp.)
full work available at URL: https://doi.org/10.1007/bf01934386
OpenAlex ID: W2052013517
description: scientific article; zbMATH DE number 3904709