Paper 2002/139

Reaction Attacks on Public Key Cryptosystems Based on the Word Problem

Maria Isabel Gonzalez Vasco and Rainer Steinwandt

Abstract

Wagner and Magyarik outlined a general construction for public key cryptosystems based on the hardness of the word problem for finitely presented groups. At the same time, they gave a specific example of such a system. We prove that their approach is vulnerable to so-called reaction attacks, namely, it is possible to retrieve the private key just by watching the performance of a legitimate recipient.