Search problems in groups and branching processes

Abstract

In this paper, we study complexity of randomly generated instances of Dehn search problems in finitely presented groups. We use Crump–Mode–Jagers (CMJ) processes to show that most of the random instances are easy. Our analysis shows that for any choice of a finitely presented platform group in Wagner–Magyarik public key encryption protocol the majority of random keys can be broken by a polynomial time algorithm.