Quasi-inverse based cryptography

Abstract

We are interested in monoids and its applications. If every element x in a monoid has a quasi-inverse y in the sense of von Neumann, that satisfies x·y·x = x and y·x·y = y, the monoid is regular. Our purpose is to use regular monoids to build two abstract algebraic public key cryptosystems: key exchange protocol and public key encryption with keyword search scheme. In addition to illustrating how the two cryptosystems work, we provide instances of these abstract algebraic models and analyse them in terms of cryptanalysis security. © 2013 Springer-Verlag Berlin Heidelberg.