The cryptanalysis of a public-key implementation of finite group mappings
type: Item
instance of: scholarly article
title: The cryptanalysis of a public-key implementation of finite group mappings
zbMATH Open document ID: 0833.94010
DOI: 10.1007/BF00202270
author: Simon R. Blackburn
author: Jacques Stern
author: Sean Murphy
published in: Journal of Cryptology
publication date: 1995-09-26T00:00:00Z
review text: The authors show that the public-key cryptosystem based on finite group mappings (FGM) proposed by \textit{Minghua Qu} and \textit{S. A. Vanstone} [New public-key cryptosystems based on factorizations of finite groups, Advances in Cryptology -- AUSCRYPT `92, Lect. Notes Comput. Sci. 718 (1993)]\ is not secure. This is done by presenting a generalized decryption algorithm similar to the original one, then using it to show that there are many equivalent private keys, and finally by showing that to calculate an equivalent private key one needs only knowledge of the public key. The authors conclude that not only the cryptosystem studied is not secure even as private-key cryptosystem, but that their analysis makes one to seriously reconsider the security of any cryptosystem which relies on certain generalizations of FGM, the so called transversal logarithmic signatures.
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 20C99
zbMATH DE Number: 784595
zbMATH Keywords: cryptanalysis
zbMATH Keywords: public-key cryptosystem
zbMATH Keywords: finite group mappings
zbMATH Keywords: transversal logarithmic signatures
reviewed by: Jozef Vyskoč
MaRDI profile type: Publication
cites work: Algebraic properties of cryptosystem PGM
full work available at URL: https://doi.org/10.1007/bf00202270
OpenAlex ID: W2004463970
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description: scientific article; zbMATH DE number 784595