平行式橢圓曲線加密處理器設計

Design of Parallel Elliptic Curve Cryptosystem Processor

林達(Da Lin)

指導教授 ： 汪順祥

大同大學/電機資訊學院/通訊工程研究所/碩士(2007年)

摘要

由於近年來網際網路與無線通訊發展迅速，資訊安全日益重要，例如WiMAX，3G通訊。橢圓曲線加密應用於公開金鑰密碼系統上，由於有限體上橢圓曲線所成的群的特性，使得橢圓曲線上的離散對數問題較困難，因此相較現有的公開金鑰密碼系統，能以較小的金鑰長度達成所需的安全性，本論文首先提出平行的NAF與SD2的轉換，據以設計出五種橢圓曲線加密乘法器，最後發展出一個平行式高速的橢圓曲線加密處理器，在平行化處理之後，使得所提出的處理器速度大幅提升。最後我們經由FPGA與軟體 C++ 的模擬結果驗證出所提出橢圓曲線加密處理器的高效率。

關鍵字

橢圓曲線加密 ； 網路安全

並列摘要

Recently, Internet and wireless communication has been highly developed, and the security of information for example in WiMAX and 3G communication are more becomes more important. Elliptic curve (EC) cryptosystem (ECC) is one of the effectively public key cryptography systems. It is based on the difficulty to solve the discrete logarithm problem over the points on an elliptic curve. When ECC compared with other existing public key cryptosystems, the key size is smaller than other cryptosystems in equal security level.
In the thesis, we propose five different design of fast EC multiplier based on the parallel NAF and SD2 conversion, and then use these design to develop a fast parallel ECC processor. The contribution of paralleling operation used in the proposed designs improves the computing speed of ECC processor significantly. Finally, we verify the high performance of our ECC processor by the simulation using FPGA simulation tools and C++ language.

並列關鍵字

elliptic curve cryptosystem ； network Security

參考文獻

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[2] Sining Liu, Francis Bowen, Brian King, and Wei Wang, “Elliptic Curves Cryptosystem Implementation Based on A Look-Up Table Sharing Scheme,” 2006 IEEE International Symposium on Circuits and Systems Proceedings (ISCAS 2006), CD-ROM, pp.4, 21-24 May 2006.

[5] Xiaoyu Ruan and Rajendra S. Katti, “Left-to-Right Optimal Signed-Binary Representation of a Pair of Integers,” IEEE Transactions on Computers, Vol. 54, No. 2, pp.124-131, February 2005.

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[8] Nazar A. Saqib, Francisco Rodriguez-Henriquez, and Arturo Diaz-Perez, “A Parallel Architecture for Fast Computation of Elliptic Curve Scalar Multiplication over GF(2m),” 18th International Parallel and Distributed Processing Symposium (IPDPS 2004), Workshop 3, p.144a, 2004.