On the public key cryptosystems over class semigroups of imaginary quadratic non-maximal orders
Commun. Korean Math. Soc. 2006 Vol. 21, No. 3, 577-586 Printed September 1, 2006
Yongtae Kim, Chang Han Kim Gwangju National University of Education, Semyung University
Abstract : In this paper we will propose the methods for finding the non-invertible ideals corresponding to non-primitive quadratic forms and clarify the structures of class semigroups of imaginary quadratic orders which were given by Zanardo and Zannier , and we will give a general algorithm for calculating power of ideals/classes via the Dirichlet composition of quadratic forms which is applicable to cryptography in the class semigroup of imaginary quadratic non-maximal order and revisit the cryptosystem of Kim and Moon  using a Zanardo and Zannier 's quantity as their secret key, in order to analyze Jacobson 's revised cryptosystem based on the class semigroup which is an alternative of Kim and Moon 's.
Keywords : class semigroup, power of ideals, key exchange system