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ON THE PUBLIC KEY CRYPTOSYSTEMS OVER CLASS SEMIGROUPS OF IMAGINARY QUADRATIC NON-MAXIMAL ORDERS
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 Title & Authors
ON THE PUBLIC KEY CRYPTOSYSTEMS OVER CLASS SEMIGROUPS OF IMAGINARY QUADRATIC NON-MAXIMAL ORDERS
Kim, Young-Tae; Kim, Chang-Han;
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 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.鳭醜谂Á䰉ê뒀곬麐Ā夏1㔰⸱㠳⸱㌷⸲ㄵЂȂȌ蠀ʏ蘢ꠒꠑ ͧ[2004년 뽧툌ࡕꠑȆ᧽Ʈऀƞ[2004년도 한국비블리아학회 추계학술발표회]
 Keywords
class semigroup;power of ideals;key exchange system;
 Language
English
 Cited by
1.
복소 이차체위에서의 공개키 암호계에 관한 소고,김용태;

한국전자통신학회논문지, 2009. vol.4. 4, pp.270-273
2.
복소 이차 류 반군위에서의 암호계의 안전성에 관한 소고,김용태;

한국전자통신학회논문지, 2011. vol.6. 1, pp.90-96
 References
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2.
D. Cox, Primes of the form $x^2\;+\;ny^2$, Wiley, New York, 1989

3.
W. Diffie and M. Hellman, New directions in cryptography, IEEE Trans. on Inform. Theory 22 (1976), 472-492

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C. F. Gauss, Disquisitiones Arithmeticae , translated by Clarke A. A., SpringerVerlag, New York, 1986

5.
H. Kim and S. Moon, Public-Key Cryptosystems based on Class Semigroups of Imaginary Quadratic Non-maximal Orders, ASISP 2003, LNCS 2727 (2003), 488-497 crossref(new window)

6.
Y. Kim, On the structures of class semiqroups of quadratic non-maximal orders, Honam Mathematical Journal 26 (2004), no. 3, 247-256

7.
Michael J. Jacobson, Jr., The security of cryptosystems based on class semigroups of imaginary quadratic non-maximal orders ASISP 2004, LNCS 3108 (2004), 149-156

8.
P. Zanardo and U. Zannier, The class semigroup of orders in number fields, Math. Proc. Camb.Phil. Soc. 115 (1994), 379-391