## Cryptology ePrint Archive: Report 2005/070

On public-key cryptosystems based on combinatorial group theory

Jean-Camille Birget and Spyros S. Magliveras and Michal Sramka

Abstract: 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.

Category / Keywords: public-key cryptography / public-key cryptosystem, combinatorial group theory, Richard Thompson groups, (NP $\cap$ coNP)-complete premise problems