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Research on Cryptosystems Based on Conic Curve Over Z_n

Author: GeShuJuan
Tutor: LiangXiangQian
School: Shandong University of Science and Technology
Course: Basic mathematics
Keywords: Public-key cryptosystem The ring Z_n conic sections Digital Signature Discrete logarithm Proxy multi-signature
CLC: TN918.1
Type: Master's thesis
Year: 2009
Downloads: 24
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Since Diffie and Hellman proposed public-key cryptosystem , a variety of cryptosystem are emerging , such as the large integer factoring the difficult problem of security based on RSA public-key cryptosystem , solving difficult problems in discrete logarithm security based EIGamal public key cryptography system to the elliptic curve discrete number of solving difficult problems as a security based on elliptic curve public key cryptosystem , these cryptosystems have been better with a wide range of applications , the appropriate standards have been established . In recent years, the conic cryptosystem began to receive attention , because the the conic public key cryptosystem is an extension of the elliptic curve cryptosystem , it not only has the advantage of elliptic curve cryptosystem , and elliptic curve , conic group the computation is easier than on the elliptic curve group , such as conic group plaintext embedding , the order of calculation and the point of operation are easier , especially on which the encoding and decoding can easily be run , and since the introduction of the standard binary algorithm , significantly reducing the amount of computation . Meanwhile , you can also create a the the modulo n conic group , the structure is equivalent to the decomposition of large integers password . The algebraic curve cryptographic algorithm is most interested , in addition to elliptic curve cryptography , the the conic public key cryptosystem C.Shcnorr think . This paper mainly based the conic ring Z_n cryptosystem study and do the following work : 1 introduces the basics of cryptography , especially the details of the mathematical properties of the conic . In -depth study on the basis of the conic ring Z_n used in public-key cryptosystem , given a proxy multi- signature schemes and programs to do numerical simulation , the program of comprehensive utilization of the difficulty of factoring large integers and limited the domain discrete number of solving the difficulty , and enhance the security of the algorithm ; study key agreement based on one based the conic ring Z_n key agreement protocol , the protocol utilizes ring Z_n conic public key cryptography to establish a session key , to improve communication security ; 4 , further improvement of these proxy multi-signature scheme , gives a secure digital signature scheme the conic ring Z_n forward .

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