Search problems in groups and branching processes
  In this paper we study complexity of randomly generated instances of Dehn search problems in finitely presented groups. We use Crump-Mode-Jagers 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-Wagner public key encryption protocol the majority of random keys can be broken by a polynomial time algorithm. 
Pavel Morar and Alexander Ushakov
math.GR