臺灣博碩士論文加值系統

在這篇論文裡,我們介紹有關每個密碼系統上的操作方式,並進一步分析,討論每個密碼系統可能的優缺點。

In this thesis,we introduce about the operations of each cryptosystem,then give further analysis,discuss possible advantage and disadvantage of each cryptosystem.

1. Introduction 1
2. Preliminaries of public key cryptosystem 4
3. Schemes of public key cryptosystem 6
3.1. Matrices over a ring 6
3.2. Elliptic curves over the ring Zn 11
3.3. Conic curves over the ring Zn 14
3.4. Polynomials over noncommutative rings 16
3.5. Polynomials over nonabelian groups 21
3.6. Polynomial rings 26
3.7. Idempotent elements 29
3.8. Circulant matrix 34
3.9. Finite nonabelian groups 39
References 42

[1] W. Diffie and M. Hellman. (1976), New directions in cryptography, IEEE Transactions on Information Theory,
Vol. 22 , pp. 644-654.
[2] E. Dawson, A. Clark, and C. Boyd (Eds.): ACISP 2000 LNCS 1841, A Proposal of a New Public Key Cryptosystem Using Matrices over a Ring, pp. 41-48.
[3] Shanghai Jiao Tong University, Shanghai 200240, P. R. China New Public Key Cryptosystems Using Polynomials over Non-commutative Rings , Department of Computer Science and Engineering.
[4] J. Hastad, On using RSA with low exponent in a public key network, Proc. of Crypto'B5, pp.403-408 (1985).
[5] Pieprzyk J.P., Rutkowski D.A., Design of Public-Key Cryptosystems Using Idempotent Elements, Froc. of ELTRCCON, Brighton, UK, 26-28 September, 1904, pp.297-308.
[6] K. Koyama, U. M. Maurer, T. Okamoto, and S. A. Vanstone, “New public-key schemes based on elliptic curves over the ring Zn,in Advances in Cryptology-CRYPTO’91 (Lecture Notes in Computer Science, vol. 576). Berlin, Germany: Springer-Verlag, 1991, pp. 252-266.
[7]F. Pichler(Ed.): Advances in Cryptology - EUROCRYPT '85, LNCS 219, pp.73-78, 1986, on public-key cryptosystems built using polynomial rings.
[8] Proceedings of the 5th WSEAS Int. Conference on Information Security and Privacy, Venice, Italy, November 20-22, 2006,A Public-Key Cryptosystem Scheme on Conic Curves over the Ring Zn.
[9] O. Goldreich, S. Goldwasser and S. Halevi, Public-key Cryptosystems from Lattice Reduction Problems, In Proc. of Crypto'97, volume 1294 of LNCS,pp.112-131, Springer-Verlag, 1997.
[10] DeMing D.E., Cryptography and Data Security, Addison-Wesley Publishing Company, Reading, Messachusetts, 1982.
[11] R.L. Rivest, A. Shamir, and L. Adleman, A method for obtaining digital signatures
and public-key cryptosystems, Communications of the ACAl, Vol. 21, No. 2, pp. 120-126 (1978).
[12] WANG Biao et al. Sci China Ser F-Inf Sci, The improved QV signature scheme based on conic curves over Z_{n} ,Apr. 2009 | vol. 52 | no. 4 | 602-608.
[13] N.Koblitz, Elliptic curve cryptosystems, Mathematics of computation, 48, pp. 203-209, 1987.
[14] V. Miller, Uses of elliptic curves on cryptography, Advances in cryptology: proceedings of
crypto '85, LNCS 218, pp.417-426, New york : Springer-Verlag, 1986.
[15] Rabin, Michael. Digitalized Signatures and Public-Key Functions as Intractable as Factor-
ization. MIT Laboratory for Computer Science, January 1979.
[16] Merkle, Ralph; Hellman, Martin (1978). Hiding information and signatures in trapdoor
knapsacks. Information Theory, IEEE Transactions on 24 (5): 525-530.
[17] S.-H. Paeng, K.-C. Ha, J.-H. Kim, S. Chee and C. Park, New public key cryptosystcm using
nite Non Abelian Groups. In J. Kilian (Ed.): CRYPTO 2001, LNCS 2139, pp. 470-485,
Springer-Verlag, 2001..
[18] T. El-Gamal, A public key cryptosystem and a signature sclieme based on the discrete
logarithm, IEEE Transactions on Information Theory, Vol. 31, NO. '1, pp. 469-472 (1985).
[19] Kenneth H. Rosen, Elementary Number Theory and Its Applications, Fifth Edition.
[20] Mukesh Kumar Singh, Texas Instruments Inc. Public Key Cryptography with Matrices,
Proceedings of the 2004 IEEE, Workshop on Information Assurance, United States Military
Academy, West Point, NY 10-11 June.
[21] P. Nguyen, Cryptanalysis for the Goldreich-Goldwasser-Halevi Cryptosystem form
Crypto'97, In Proc. of Crypto'99, volume 1666 of LNCS,pp. 288-304, Springer-Verlag, 1999.