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http://dx.doi.org/10.4134/CKMS.2006.21.3.577

ON THE PUBLIC KEY CRYPTOSYSTEMS OVER CLASS SEMIGROUPS OF IMAGINARY QUADRATIC NON-MAXIMAL ORDERS  

Kim, Young-Tae (Department of Mathemathics Education Gwangju National University of Education)
Kim, Chang-Han (Department of Information Security Semyung University)
Publication Information
Communications of the Korean Mathematical Society / v.21, no.3, 2006 , pp. 577-586 More about this Journal
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;
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