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 [8], 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 [5] using a Zanardo and Zannier [8]'s quantity as their secret key, in order to analyze Jacobson [7]'s revised cryptosystem based on the class semigroup which is an alternative of Kim and Moon [5]'s.
Keywords : class semigroup, power of ideals, key exchange system
MSC numbers : 11Y40, 94A60
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