基于椭圆曲线加密系统的FPGA实现
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摘要
信息安全技术是一门综合的学科，它涉及信息论、计算机科学和密码学等多方面知识，它的主要任务是研究计算机系统和通信网络内信息的保护方法以实现系统内信息的安全、保密、真实和完整。其中，信息安全的核心是密码技术。随着计算机网络不断渗透到各个领域，密码学的应用也随之扩大。数字签名、身份鉴别等都是由密码学派生出来的新技术和应用。
椭圆曲线密码体制(Elliptic Curve Cryptosystem—ECC)是目前已知的所有公钥密码体制中能够提供最高比特强度(strength-per-bit)的一种公钥加密体制，而智能卡已广泛用于金融、电信等领域，利用椭圆曲线密码体制不仅将大大提高智能卡的应用水平而且还将大大拓宽智能卡的应用领域。目前，基于各种密码算法的集成电路芯片已经出现。研究公钥密码系统中椭圆曲线芯片有较大的研究价值和实用价值。
本文在深入研究现代密码学理论特别是椭圆曲线加密理论和技术的基础上，提出了一种椭圆曲线加密算法，并且完成了该算法的硬件设计。
论文的主要内容为：
1．研究了现代密码学相关的基本理论，介绍了密码系统的数学模型、数据加密原理和与椭圆曲线加密密切相关的有限域理论；
2．研究了公钥加密系统中的椭圆曲线加密理论，详细阐述了有限域上椭圆曲线的结构及其基本运算；
3．设计完成了一种基于有限域的椭圆曲线加密算法，主要包括适合于168bit椭圆曲线加密的有限域乘法、加法、除法器的实现；
4．阐述了密码芯片的设计思想和设计流程，完成了密码芯片的电路设计并进行验证；
5．最后以加密芯片在串行通信中的应用方法为例阐述了设计的密码芯片在计算机保密通信中的应用。
Elliptic Curve Cryptosystems on Reconfigurable Hardware
Information security technology is a compositive subject, which includes information theory, computer science, cryptography and other aspects fields. It aims to research the protection method of information, which are transferring in the computer system and communication network. Also it is responsible to the security, secrecy, verity and integrity of the information. Among them, crypto technology is the core of the information security technology.With the computer network continuously penetrating to various fields, the application of cryptography is expending. For example, digital signature, identity distinguish are both the new technology and application derived from the cryptography.
ECC is the one of the known public crypto methods that provide the best strength-per-bit. With the deeper application of IC card in the field of Finance and Telecom, the ECC crypto system will not only upgrade the application level of IC card, but also open up more application fields. Nowadays, more and more IC cores based on all kinds of crypto algorithm appear. The research of the ECC crypto has much of value in research as well as application.
An encryption algorithm, on the basis of deep studying on modern cryptology theories especially the theory of elliptic curve, is presented and an integrated circuit design based on it is described in this dissertation.
This thesis is composed of following parts: the fundamental theory of the modern cryptology is briefly researched, in which the mathematic model of cryptology, data encrypt principle and Galois field theory related with elliptic curve crypto is discussed. Also we study the ECC crypto theory in the field of public crypto system, in which the ECC encrypt principle, safety, reliability, as well as the structure of ECC based on Galois field is focused on. Then we show an algorithm design of the elliptic curve crypto based on Galois field. As a main part, the design theory and concrete solution of it are presented step by step, IC chip design method for implementation of the algorithm is described in detail. Finally, we discuss the application of the ECC crypto in the field of computer secret communication.
椭圆曲线密码体制(Elliptic Curve Cryptosystem—ECC)是目前已知的所有公钥密码体制中能够提供最高比特强度(strength-per-bit)的一种公钥加密体制，而智能卡已广泛用于金融、电信等领域，利用椭圆曲线密码体制不仅将大大提高智能卡的应用水平而且还将大大拓宽智能卡的应用领域。目前，基于各种密码算法的集成电路芯片已经出现。研究公钥密码系统中椭圆曲线芯片有较大的研究价值和实用价值。
本文在深入研究现代密码学理论特别是椭圆曲线加密理论和技术的基础上，提出了一种椭圆曲线加密算法，并且完成了该算法的硬件设计。
论文的主要内容为：
1．研究了现代密码学相关的基本理论，介绍了密码系统的数学模型、数据加密原理和与椭圆曲线加密密切相关的有限域理论；
2．研究了公钥加密系统中的椭圆曲线加密理论，详细阐述了有限域上椭圆曲线的结构及其基本运算；
3．设计完成了一种基于有限域的椭圆曲线加密算法，主要包括适合于168bit椭圆曲线加密的有限域乘法、加法、除法器的实现；
4．阐述了密码芯片的设计思想和设计流程，完成了密码芯片的电路设计并进行验证；
5．最后以加密芯片在串行通信中的应用方法为例阐述了设计的密码芯片在计算机保密通信中的应用。
Elliptic Curve Cryptosystems on Reconfigurable Hardware
Information security technology is a compositive subject, which includes information theory, computer science, cryptography and other aspects fields. It aims to research the protection method of information, which are transferring in the computer system and communication network. Also it is responsible to the security, secrecy, verity and integrity of the information. Among them, crypto technology is the core of the information security technology.With the computer network continuously penetrating to various fields, the application of cryptography is expending. For example, digital signature, identity distinguish are both the new technology and application derived from the cryptography.
ECC is the one of the known public crypto methods that provide the best strength-per-bit. With the deeper application of IC card in the field of Finance and Telecom, the ECC crypto system will not only upgrade the application level of IC card, but also open up more application fields. Nowadays, more and more IC cores based on all kinds of crypto algorithm appear. The research of the ECC crypto has much of value in research as well as application.
An encryption algorithm, on the basis of deep studying on modern cryptology theories especially the theory of elliptic curve, is presented and an integrated circuit design based on it is described in this dissertation.
This thesis is composed of following parts: the fundamental theory of the modern cryptology is briefly researched, in which the mathematic model of cryptology, data encrypt principle and Galois field theory related with elliptic curve crypto is discussed. Also we study the ECC crypto theory in the field of public crypto system, in which the ECC encrypt principle, safety, reliability, as well as the structure of ECC based on Galois field is focused on. Then we show an algorithm design of the elliptic curve crypto based on Galois field. As a main part, the design theory and concrete solution of it are presented step by step, IC chip design method for implementation of the algorithm is described in detail. Finally, we discuss the application of the ECC crypto in the field of computer secret communication.
引文
1．李海泉 李健“计算机网络安全与加密技术”，科学出版社 p37 2001
2．李海泉 李健“计算机网络安全与加密技术”，科学出版社 p312-315 2001
3．李海泉 李健“计算机网络安全与加密技术”，科学出版社 p197-198 2001
4．万哲先“代数和编码(修订本)”科学出版社 p2-4 1976．3
5. Christ of Paar "A New Architecture for a Parallel Finite Field Multiplier with Low Complexity Based on Composite Fields" IEEE Transactions on Computers Vol 45 No7 pp856-861 July 1996
6．卢开澄“计算机密码学”清华大学出版社 p101 1998
7．杨明等“密码编码学与网络安全：原理与实践(第二版)”电子工业出版社 p154-p156 2001
8. Martin Christopher Rosner "Elliptic Curve Cryptosystems on Reconfigurable Hardware" Worcester Polytechnic Institute Master Thesis p20-p25 May 1998
9. Jorge Guajardo "Efficient Algorithms for Elliptic Curve Cryptosystems" Master Thesis May p73-p74 May 1997
10. K.H.Leung, K.W. Ma, W.K.Wong and P.H.W. Leong "FPGA Implementation of a Microcoded Elliptic Curve Cryptographic Processor" IEEE Symposium on Field-Programmable Custom Computing Machines, 2000
11. E.D. Mastrovito. VLSI Architectures for Computations in Galois Fields. PhD thesis, Linkoping University, Dept. Electr. Eng., Linkoping, Sweden, 1991
12. J.L.Massey and J.K. Omura. Computeational method and apparatus for finite field arithmetic. U.S.Patent Application, 1981
13. M.A. Hasan and V.K. Bhargava. Bit-serial systolic divider and multiplier for finite fields GF(2m). IEEE Transactions on Computers, 41(8):972-980, Aug 1992.
14. E.Berlekamp. Bit-serial Reed-Solomon encoders. IEEE Transactions on Information Theory, IT-28(6):869-874, November 1982
15．赵曙光、郭晚由、杨颂华“可编程逻辑器件原理、开发与应用”西安电子科技大学出版社 p16-p26 2000
16．吴玲达、李国辉等“计算机通信”国防科技大学出版社 p157-168 1994．12
17．陈艳敏“调制解调器实用手册”人民邮电出版社 p14-21 1995．7
18．Jan Axelson著“串行端口大全”中国电力出版社 p155-117 p285-289 2001
19．候伯亨、顾新“VHDL硬件描述语言与数字逻辑电路设计”西安电子科技大学出版社 p1-10 1999
20．王小军、乔长阁、边计年、薛宏熙“VHDL简明教程”清华大学出版社 1997
21. Itoh, T. and S. Tsujii: A Fast Algorithm for Computing Multiplicative Inverses in GF(2m) using Normal Bases. Information and Computation 78. 171-177, 1988
22. Recommended Elliptic Curves for federal government use July 1999
2．李海泉 李健“计算机网络安全与加密技术”，科学出版社 p312-315 2001
3．李海泉 李健“计算机网络安全与加密技术”，科学出版社 p197-198 2001
4．万哲先“代数和编码(修订本)”科学出版社 p2-4 1976．3
5. Christ of Paar "A New Architecture for a Parallel Finite Field Multiplier with Low Complexity Based on Composite Fields" IEEE Transactions on Computers Vol 45 No7 pp856-861 July 1996
6．卢开澄“计算机密码学”清华大学出版社 p101 1998
7．杨明等“密码编码学与网络安全：原理与实践(第二版)”电子工业出版社 p154-p156 2001
8. Martin Christopher Rosner "Elliptic Curve Cryptosystems on Reconfigurable Hardware" Worcester Polytechnic Institute Master Thesis p20-p25 May 1998
9. Jorge Guajardo "Efficient Algorithms for Elliptic Curve Cryptosystems" Master Thesis May p73-p74 May 1997
10. K.H.Leung, K.W. Ma, W.K.Wong and P.H.W. Leong "FPGA Implementation of a Microcoded Elliptic Curve Cryptographic Processor" IEEE Symposium on Field-Programmable Custom Computing Machines, 2000
11. E.D. Mastrovito. VLSI Architectures for Computations in Galois Fields. PhD thesis, Linkoping University, Dept. Electr. Eng., Linkoping, Sweden, 1991
12. J.L.Massey and J.K. Omura. Computeational method and apparatus for finite field arithmetic. U.S.Patent Application, 1981
13. M.A. Hasan and V.K. Bhargava. Bit-serial systolic divider and multiplier for finite fields GF(2m). IEEE Transactions on Computers, 41(8):972-980, Aug 1992.
14. E.Berlekamp. Bit-serial Reed-Solomon encoders. IEEE Transactions on Information Theory, IT-28(6):869-874, November 1982
15．赵曙光、郭晚由、杨颂华“可编程逻辑器件原理、开发与应用”西安电子科技大学出版社 p16-p26 2000
16．吴玲达、李国辉等“计算机通信”国防科技大学出版社 p157-168 1994．12
17．陈艳敏“调制解调器实用手册”人民邮电出版社 p14-21 1995．7
18．Jan Axelson著“串行端口大全”中国电力出版社 p155-117 p285-289 2001
19．候伯亨、顾新“VHDL硬件描述语言与数字逻辑电路设计”西安电子科技大学出版社 p1-10 1999
20．王小军、乔长阁、边计年、薛宏熙“VHDL简明教程”清华大学出版社 1997
21. Itoh, T. and S. Tsujii: A Fast Algorithm for Computing Multiplicative Inverses in GF(2m) using Normal Bases. Information and Computation 78. 171-177, 1988
22. Recommended Elliptic Curves for federal government use July 1999
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