论文标题:椭圆曲线密码体制的研究和实现
Research and Implementation of Elliptic Curve Cryptosystem
论文作者 高柯俊
论文导师 叶震,论文学位 硕士,论文专业 计算机应用技术
论文单位 合肥工业大学,点击次数 143,论文页数 63页File Size2337k
2002-05-22论文网 http://www.lw23.com/lunwen_162795727/ 有限域;椭圆曲线密码体制;软件实现
finite field;elliptic curve cryptosystem;software implementation
随着Internet的高速发展，信息安全问题越来越受到人们的关注。公钥密码技术是解决信息安全问题的重要手段。和RSA，DSA等公钥密码体制相比，椭圆曲线密码体制(ECC)有着很多优点：单位bit的安全强度高；计算量小；存储空间小；带宽要求低。ECC的这些特点使它在资源受限的环境下(如PDA、手机、智能卡)将会取代RSA，并可能成为通用的公钥加密算法。 本文首先讨论了有限域上基本算术运算的算法，对有限域上的椭圆曲线理论进行了研究，分析了椭圆曲线上的核心算法——数乘算法。然后提出了一种新的基于ECDSA数字签名的身份认证方案。该方案中，用户在证实自己身份的同时不必泄漏自己的秘密信息。对这一认证方案稍加修改，就可以提供用户之间的双向认证功能。最后，给出了以有限域GF(2~(163))为基域的曲线K-163上的ECDH的一个具体实现，该系统具有密钥交换功能，对该系统稍加扩展，就可以提供加密功能和认证功能。
With the high development of Internet, information security has gained more and more attention. An important approach to solving information security is public-key cryptology. Comparing to other public-key cryptosystems such as RSA and DSA, ECC has many advantages including high security per bit, faster computations and reduces in processing power, storage space and bandwidth. These advantages make ECC ideal for constrained environments such as PDAs,cellular phones and smart cards.In this thesis, we first discuss the algorithms of arithmetic operations over binary fields using a polynomial basis representation. Then we analyse the theory of elliptic curves over finite fields and discuss several algorithms for computing a scalar multiplication which is the central operations of ECC .The principle results in this thesis include:(l)We present a new authentication scheme based on ECDSA. In the scheme, two-way authentication may be done between two users without exposing their secret information.(2) we give a software implementation of ECDH on the elliptic curve AM 63 over the binary field GF(2163).
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