Public-Key cryptosystems based on class semigroups of imaginary quadratic non-maximal orders

Abstract

In this paper we propose a key-exchange system and a public-key encryption scheme based on the class semigroups of imaginary quadratic non-maximal orders, the former is analogous to the Diffie-Hellman's key-exchange system and the latter is similar to the ElGamal's encryption scheme, whose security is based on the difficulty of the discrete logarithm problem of that class semigroup. © 2003 Springer-Verlag Berlin Heidelberg.