FPGA 實現GF(2^191)有限場之橢圓曲線點乘法

FPGA Implementation of Elliptic Curve Point Multiplication over GF(2^191)

湯智安(Chih-An Tang)

指導教授 ： 汪順祥

大同大學/電機資訊學院/電機工程學系所/碩士(2012年)

摘要

需要快速加密或解密的關鍵應用必須以硬體來實現。本論文發展一個有效率有限場運算的硬體並行架構以快速實現在橢圓曲線密碼系統中的純量乘法。這一個並行架構是由點加法和點加倍的模組所構成的。為求更快速的硬體實現，我們提出了一個點加法的修改模組，這一個點加法的修改模組是使用兩個有限場的乘法器。經由實驗的結果得知在使用Xilinx VirtexE3200下作實現，所提架構在有限場GF(2^191)運算之橢圓曲線純量乘法的運算時間為84.23μs。

關鍵字

純量乘法 ； 橢圓曲線密碼系統 ； 有限場

並列摘要

Hardware implementation is needed in critical applications requiring high encryption or decryption speeds. In this thesis, a parallel architecture with efficient hardware implementation of finite field operations is developed to realize high speed scalar multiplication which is the main operation in Elliptic Curve Cryptography (ECC) system. The parallel architecture consists of a point addition module and a point doubling module. For high speed realization, we present a modified point addition module using two finite field multipliers. The experimental results show that the proposed architecture is able to compute GF(2^191) elliptic curve scalar multiplication operations in 84.23 μs on Xilinx VirtexE 3200.

並列關鍵字

finite field ； scalar multiplication ； ECC

參考文獻

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