On public-key cryptosystems based on combinatorial group theory

We analyze and critique the public-key cryptosystem, based on combinatorial group theory, that was proposed by Wagner and Magyarik in 1984. This idea is actually not based on the word problem but on another, generally easier, premise problem. Moreover, the idea of the Wagner-Magyarik system is vague, and it is difficult to find a secure realization of this idea. We describe a public-key cryptosystem inspired in part by the Wagner-Magyarik idea, but we also use group actions on words. ∗JCB is supported in part by NSF grant CCR-0310793. †Work supported in part by a Federal Earmark grant for Research in Secure Telecommunication Networks (2004-05)