On the Security of Two Public Key Cryptosystems Using Non-Abelian Groups

Authors:
M. I. González Vasco;D. Hofheinz;C. Martínez;R. Steinwandt
Affiliations:
Departamento de Matemáticas, Universidad de Oviedo, c/Calvo Sotelo, s/n, 33007 Oviedo, Spain mvasco@orion.ciencias.uniovi.es;Institut für Algorithmen und Kognitive Systeme, Arbeitsgruppe Systemsicherheit, Th. Beth, Universität Karlsruhe, 76128 Karlsruhe, Germany hofheinz@ira.uka.de;Departamento de Matemáticas, Universidad de Oviedo, c/Calvo Sotelo, s/n, 33007 Oviedo, Spain chelo@pinon.ccu.uniovi.es;Institut für Algorithmen und Kognitive Systeme, Arbeitsgruppe Systemsicherheit, Th. Beth, Universität Karlsruhe, 76128 Karlsruhe, Germany steinwan@ira.uka.de
Venue:
Designs, Codes and Cryptography
Year:
2004

Citing 3
Cited 0

A public key cryptosystem based on the word problem

Proceedings of CRYPTO 84 on Advances in cryptology
The complexity of Grigorchuk groups with application to cryptography

Theoretical Computer Science
Properties of Cryptosystem PGM

CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology

Quantified Score

Hi-index	0.00

Visualization

Abstract

The security of two public key encryption schemes relying on the hardness of different computational problems in non-abelian groups is investigated. First, an attack on a conceptual public key scheme based on Grigorchuk groups is presented. We show that from the public data one can easily derive an “equivalent” secret key that allows the decryption of arbitrary messages encrypted under the public key. Hereafter, a security problem in another conceptual public key scheme based on non-abelian groups is pointed out. We show that in the present form the BMW scheme is vulnerable to an attack, which can recover large parts of the private subgroup chain from the public key.