Browse > Article
http://dx.doi.org/10.13089/JKIISC.2005.15.4.101

Public Key Cryptosystem Based on Jordan Form  

Lee, Hee-Jung (Kangnam University)
Publication Information
Journal of the Korea Institute of Information Security & Cryptology / v.15, no.4, 2005 , pp. 101-105 More about this Journal
Abstract
Recently a new public key cryptosystem based on a diagonal matrix has been proposed by Zheng. This system uses eigenvalues as a long-term key and random numbers as session key generators. However, there are a couple of flaws in that system. In this paper, we propose a new algorithm in which those flaws are all fixed. Our scheme is based on modular equations over a composite and uses a matrix of Jordan form. We also analyze the security of it.
Keywords
matrix similarity; modular equation; multiple roots;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Serge Lang, Algebra, 2nd. Addison Wesley, 1984
2 Victor Shoup, 'Factoring Polynomials over Finite Fields: Asymptotic Complexity vs. Reality', Proc. IMACS Symposium, Lille, France, 1993
3 허영준, 박혜경, 이건식, 이원호, 유기영, RSA 암호시스템을 위한 모듈러 지수 연 산 프로세서 설계, 정보보호학회 논문지 10권 4호, 2000
4 D.Coppersmith, 'Small solutions to polynomial Equations, and Low Exponent RSA Vulnerabilities', J. of Cryptology 10(4), 1997
5 D.Boneh, G.Durfee, 'Cryptanalysis of RSA with private key d less than $N^{0.292}$', IEEE Trans. on Information Theory vol.46(4), 2000
6 Jiande Zheng, 'A New Public Key Cryptosystem for Constrained Hardware', ISC 2002, LNCS 2433, pp.334-341, 2002, Springer-Verlag
7 E.R. Berlekemp, 'Factoring polynomials over large finite fields', Math. Comp. 24, 713-735 (1970)   DOI   ScienceOn
8 G. Durfee, P. Nguyen, 'Cryptanalysis for the RSA schemes with short secret exponent from Asiacrypt'99', In proceedings of Asiacrypt 2000, LNCS, Springer-Verlag, 2000
9 Zhang, Liu, Kim, 'Attack on A New Public Key Cryptos from ISC'02(LNCS 2433)' Cryptology ePrint Archive, Report 2002/178