McEliece public key cryptosystems using algebraic-geometric codes
type: Item
instance of: scholarly article
title: McEliece public key cryptosystems using algebraic-geometric codes
zbMATH Open document ID: 0859.94008
DOI: 10.1023/A:1027351723034
author: Heeralal Janwa
author: Oscar Moreno
published in: Designs, Codes and Cryptography
publication date: 1997-04-15T00:00:00Z
review text: In the McEliece public key cryptosystem, a user \(A\) chooses a \(k\times n\) binary generator matrix \(G_A\) of a \(t\)-error correcting binary linear code and publishes the matrix \(G'_A= SG_AP\), where \(P\) is a randomly generated \(k\times k\) non-singular binary matrix and \(P\) is an \(n\times n\) permutation matrix. For a user to send message \(M\), represented as a binary vector of length \(k\), to user \(A\), it is encrypted as \(M'=MG'_A+Z\) where \(Z\) is a random error vector of length \(n\) and weight \(t\), representing \(t\) errors. McEliece suggested using \(G_A\) to be that of a \((1024,524,101)\) Goppa code. The security of such a system has been considered and the conclusion drawn that the work factor/size trade-off is not suitable for practical implementations. This note generalizes the scheme in three ways: by using nonbinary algebraic-geometric codes, using subfield subcodes of these and by using concatenated \(q^m\)-ary AG codes with good \(q\)-ary codes. It is shown that such schemes are capable of achieving a more desirable work factor/size trade-off.
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 94B27
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 68P25
zbMATH DE Number: 934067
zbMATH Keywords: algebraic-geometry codes
zbMATH Keywords: cryptography
zbMATH Keywords: public key cryptosystem
reviewed by: Ian Blake
describes a project that uses: McEliece
MaRDI profile type: Publication
full work available at URL: a:1027351723034
OpenAlex ID: W1851924232
description: scientific article; zbMATH DE number 934067