On the wagner–magyarik cryptosystem

Authors:
Françoise Levy-dit-Vehel;Ludovic Perret
Affiliations:
ENSTA, Paris;ENSTA, Paris
Venue:
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Year:
2005

Citing 5
Cited 1

A public key cryptosystem based on the word problem

Proceedings of CRYPTO 84 on Advances in cryptology
Rewriting systems and word problems in a free partially commutative monoid

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INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India

Security analysis of word problem-based cryptosystems

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Abstract

We investigate a monoid variant of the scheme based on the word problem on groups proposed by Wagner and Magyarik at Crypto'84, that has the advantage of being immune to reaction attacks so far. We study the security of this variant. Our main result is a complexity-theoretic one: we show that the problem underlying this cryptosystem, say WM, is NP-hard. We also present an algorithm for solving WM. Its complexity permits to shed light on the size of the parameters to choose to reach a given level of security.