论文标题:椭圆曲线密码体制在DSP上的实现
The Implementation of Elliptic Curve Cryptography on DSP Chips
论文作者 孙培千
论文导师 李大兴,论文学位 硕士,论文专业 应用数学
论文单位 山东大学,点击次数 133,论文页数 57页File Size1796k
2005-04-05论文网 http://www.lw23.com/lunwen_77611687/ 椭圆曲线密码体制(ECC); DSP; SEA算法;NAF算法;Frobenius展式;ECDSA
Elliptic Curve Cryptography (ECC); DSP; SEA; NAF; Frobenius; ECDSA
上个世纪80年代,Miller和Koblitz提出了椭圆曲线密码体制(ECC),作为一种新的公钥密码体制,ECC有着强度高、速度快、所需资源少等优势,所以引起全世界许多数学家和密码学家的关注。经过20多年的研究,有关ECC的理论和实现已经取得了很大进展,并被广泛的应用于实践中。许多国家和组织已经制定了ECC的标准,如:IEEE P1363 P1363a、ANSI X9.62 X9.63、ISO/IEC14888等,但是在国内还没有ECC的标准。在实现方面,德国、日本、法国、美国、加拿大等国的很多密码学研究小组及一些公司实现了椭圆曲线密码体制,如加拿大Certicom公司是国际上最著名的ECC密码技术公司,已授权300多家企业使用ECC密码技术。我国也有一些密码学者做了这方面的工作,但产品化还远远不够。 目前,国内有些厂家采用软件实现各种加密算法,如在DSP芯片上用汇编语言实现密码算法,并以此做主芯片制作加密卡。这虽然在安全性和速度上无法与特殊设计的专用密码算法芯片相比,但由于其升级容易、成本低、可以提供相当高的安全性和性能,仍然可以说是一种很好的解决方案。 本文给出了建立和实现椭圆曲线密码体制的全过程,同时结合ECC和TI公司TMS320C54x系列芯片的特点,提出了适合此芯片的椭圆曲线密码体制,并讨论了它的建立和实现。本文重点研究特征为大素数的有限域上的椭圆曲线密码体制,在很多地方都不考虑F_2~m上的情形。作者的主要工作如下: 1、介绍了ECC所需的数学基础。 2、给出了一种随机椭圆曲线密码体制生成的方法和几种现有的实现方法。 3、给出了一类适合TMS320C54x系列芯片的安全椭圆曲线,并给出了生成和实现(Frobenius展式)的方法。 4、给出了使用不同的射影坐标时点加、点倍的计算公式、推导方法、效率比较等。
In the eighties of last century, Miller and Koblitz originate Elliptic Curve Cryptography (ECC). Being a new public key cryptography, ECC has many superiorities such as high intensity, high speed and low resource, etc. So it attracted attention of mathematicians and cryptographers all over the world. In the last 20 years, theory and implementation about ECC have made great progress. A lot of countries and organizations have made standards of ECC, including IEEE P1363 P1363a, ANSI X9.62 X9.63、 ISO/IEC14888 etc. But in china, the standard doesn"t exist. In practice, some research groups and companies have actualized ECC. For example, Certicom of Canada is the most famous corporation in cryptogram technology in the world. It has authorized more than 300 companies to use the ECC cryptogram technology. In China, cryptographers have done some works but the productivity of ECC is far behind the other countries.At the present time, some companies use software to implement some kinds of cryptogram, such as using assemble language to implement cryptogram on DSP chips, and using the DSP as main chip to make encryption card. Although it couldn"t compare with specially designed chips in security and speed, but for its easiness in upgrading, low cost and good capability, we can still consider it as a excellent solving method.Combining the characters of ECC and TMS320C54x chips of TI corporation, this paper proposed the ECC adapted to this kind of chips, and discussed its establishment and implement. In this paper, we mainly discussed ECC on finite field with its characteristic being big prime number. The main works of the author is as follows:1. Introducing the mathematical basis of ECC.2. Proposing a method of establishing one kind of random ECC and some kinds of existing implemented methods.3. Proposing a kind of safe ECC suitable for TMS320C54x chips.4. Proposing the calculating formula and efficiency comparison of point addition and point doubling when using different projective coordinates.5. Improving NAF algorithm and window NAF algorithm.6. Proposing the point multiplying method of only using x coordinate on finite field with its characteristic being big prime number.7. Implementing the Elliptic Curve Digital Signature Algorithm, and comparing the performance with RSA of the same intensity and the same environment.This paper is divided into 6 chapters. In the first chapter we introduced the background of the research of ECC and TMS320C54x chips. In the second chapter we introduce the math basis of ECC. In the third chapter we introduce the basic concept of Elliptic Curve and ECDSA. In the fourth chapter we described the method of creating parameters of random ECC and gived a kind of Elliptic Curve adapt to TMS320C54x chips. In the fifth chapter we studied the fast implement of ECC on DSP chips. We mainly discussed the fast algorithm of point addition, point doubling and point multiplying. We also improved NAF algorithm, window NAF algorithm and introduced Frobenius algorithm. In the last chapter we described the implement of ECDSA, and compared the performance with RSA algorithm of the same intensity and the same environment. The author added notations on all algorithms mentioned in this paper.
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