基于双基底乘法器的SM2公钥密码算法研究与实现

发布时间：2018-09-04 07:19

【摘要】：随着计算机计算速度的飞速提升,对信息的加密强度也随之提高。目前广泛应用的RSA(Rivest-Shamir-Adleman)算法已经不能满足人们在安全性能上的要求。拥有更高加密强度的椭圆曲线加解密算法成了替代它的必然选择。2010年12月,国家商用密码管理办公室发布了SM2椭圆曲线公钥密码算法,规定了基于椭圆曲线加密原理的SM2算法。椭圆曲线加密(Elliptic Curve Cryptography,ECC)理论于1985年提出,同RSA加密算法相比,ECC算法具有安全性能高、计算量小、处理速度快等特点。加解密运算常常应用在实时性要求较高的场合,快速的运算是必然的要求,因此,提高SM2算法的运算速度是非常重要的。在SM2算法中,需要执行大量的加法与乘法运算。本文采用二位元扩域进行运算,在m次二位元扩域中,加法运算只需通过m个异或门即可实现,而乘法运算则需要大量的与门和异或门来共同实现,这极大地增加了运行时间。乘法器部分我们分析了传统乘法器的架构形式,通过对其分析构思自己的乘法器。本文的设计目标是设计出一种具有更短计算时间的新型乘法器,应用在SM2算法上提高加解密过程的时间效率。本文提出了一种基于双基底的新型乘法器,它结合PB(polynomial basis)基底和MPB(modified polynomial basis)基底,利用Toeplitz矩阵特性构建实现整个乘法器。实验结果表明,本文提出的新型乘法器与传统乘法器相比,可以节省约50%的乘法运算时间。提升了SM2算法加解密过程的效率。
[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.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.4

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