【摘要】：隨著計算機計算速度的飛速提升,對信息的加密強度也隨之提高。目前廣泛應用的RSA(Rivest-Shamir-Adleman)算法已經(jīng)不能滿足人們在安全性能上的要求。擁有更高加密強度的橢圓曲線加解密算法成了替代它的必然選擇。2010年12月,國家商用密碼管理辦公室發(fā)布了SM2橢圓曲線公鑰密碼算法,規(guī)定了基于橢圓曲線加密原理的SM2算法。橢圓曲線加密(Elliptic Curve Cryptography,ECC)理論于1985年提出,同RSA加密算法相比,ECC算法具有安全性能高、計算量小、處理速度快等特點。加解密運算常常應用在實時性要求較高的場合,快速的運算是必然的要求,因此,提高SM2算法的運算速度是非常重要的。在SM2算法中,需要執(zhí)行大量的加法與乘法運算。本文采用二位元擴域進行運算,在m次二位元擴域中,加法運算只需通過m個異或門即可實現(xiàn),而乘法運算則需要大量的與門和異或門來共同實現(xiàn),這極大地增加了運行時間。乘法器部分我們分析了傳統(tǒng)乘法器的架構形式,通過對其分析構思自己的乘法器。本文的設計目標是設計出一種具有更短計算時間的新型乘法器,應用在SM2算法上提高加解密過程的時間效率。本文提出了一種基于雙基底的新型乘法器,它結合PB(polynomial basis)基底和MPB(modified polynomial basis)基底,利用Toeplitz矩陣特性構建實現(xiàn)整個乘法器。實驗結果表明,本文提出的新型乘法器與傳統(tǒng)乘法器相比,可以節(jié)省約50%的乘法運算時間。提升了SM2算法加解密過程的效率。
[Abstract]:With the rapid improvement of computer computing speed, the encryption intensity of information is also improved. At present, the widely used RSA (Rivest-Shamir-Adleman) algorithm can not meet the requirements of security performance. The elliptic curve encryption and decryption algorithm with higher encryption intensity has become the inevitable choice to replace it. In December 2010, the National Office of Commercial Cryptography published the SM2 elliptic curve public key cryptography algorithm, which specifies the SM2 algorithm based on elliptic curve encryption principle. The theory of elliptic curve encryption (Elliptic Curve Cryptography,ECC) was put forward in 1985. Compared with the RSA encryption algorithm, the ECC algorithm has the advantages of high security performance, low computational cost and fast processing speed. Encryption and decryption operations are often used in situations where real-time requirements are high, and fast operation is a necessary requirement. Therefore, it is very important to improve the speed of SM2 algorithm. In the SM2 algorithm, a large number of addition and multiplication operations need to be performed. In this paper, the two-bit extension field is used to perform the operation. In the m-order binary extension domain, the addition operation can only be achieved through m XOR gates, while the multiplication operation needs a large number of gate and XOR gates to implement together, which greatly increases the running time. In the part of multiplier, we analyze the architecture of traditional multiplier, and conceive our multiplier by analyzing it. The aim of this paper is to design a new multiplier with shorter computing time, which can be used in SM2 algorithm to improve the efficiency of encryption and decryption. In this paper, a new multiplier based on double bases is proposed. It combines PB (polynomial basis) base with MPB (modified polynomial basis) base, and uses the characteristic of Toeplitz matrix to construct the whole multiplier. The experimental results show that the proposed new multiplier can save about 50% of the multiplication time compared with the traditional multiplier. Improve the efficiency of SM2 encryption and decryption process.
【學位授予單位】：哈爾濱工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TN918.4

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