椭圆曲线标量乘算法的快速实现

发布时间：2017-12-28 06:17

本文关键词：椭圆曲线标量乘算法的快速实现　出处：《扬州大学》2017年硕士论文　论文类型：学位论文

【摘要】：椭圆曲线密码(ECC,Elliptic Curve Cryptography)是一种杰出的公钥密码体制,但在实现时仍有一些关键的问题需要进一步研究。由于标量乘法的效率决定了 ECC的实现效率,因此标量乘法的快速算法研究成为了许多密码学家关心的问题。本文主要工作有:(1)提出一种新的形如d(1/2)a3b5c7z的标量k的多基表示算法和相应的多基标量乘算法。在已有的二进制域椭圆曲线标量乘算法的基础上,新算法结合了扩展系数集和半点运算方法。在美国国家标准技术研究所推荐的椭圆曲线NIST B-163、NIST B-233和NIST B-283上进行实验,结果表明,新算法以增加少量预计算存储为代价,有效降地低了算法复杂度,提高了标量乘算法的效率,使标量乘法的运算更高效。相比于相关工作,提高了约14.4%～41.4%。因此,新算法可以较好地应用到计算资源、存储资源受限的领域中。(2)提出一种新的更高效的多标量乘算法。在已有的二进制域和素域的标量乘算法的基础上,新的多标量乘算法结合了滑动窗口技术、多基算法,有效地提高了多标量乘的效率。并对其进行了理论和实验分析,实验结果表明,新算法与传统Shamir算法和交错NAF算法相比,其所需的运算量更少。有效地提高了椭圆曲线多标量乘算法的效率,使多标量乘的运算更高效。相比于相关工作,新算法的计算效率比已有的多标量乘算法提高了约7.9%～20.6%。
[Abstract]:ECC (Elliptic Curve Cryptography) is an outstanding public key cryptosystem, but there are still some key problems to be further studied when it is implemented. The efficiency of ECC is determined by the efficiency of scalar multiplication, so the fast algorithm for scalar multiplication has become a concern for many cryptography. The main contents of this paper are: (1) a new form of D (1/2 K a3b5c7z) proposed the scalar mbns algorithm and the corresponding multi scalar multiplication algorithm. On the basis of the existing binary domain elliptic curve scalar multiplication algorithm, the new algorithm combines the extended coefficient set and the half point operation method. In the United States National Institute of standards and technology recommended by B-163, NIST elliptic curve NIST B-233 and NIST B-283 on the experimental results show that the new algorithm by adding a small amount of pre computation and storage cost, effectively reduce low algorithm complexity and improve the efficiency of scalar multiplication algorithm, the scalar multiplication is more efficient. Compared to the related work, the increase is about 14.4% ~ 41.4%. Therefore, the new algorithm can be applied to the domain of limited computing resources and storage resources. (2) a new and more efficient multiscalar multiplication algorithm is proposed. Based on the scalar multiplication algorithm for binary field and prime field on the new multi scalar multiplication algorithm with sliding window technique, multi algorithm, effectively improve the efficiency of multi scalar multiplication. The experimental results show that the new algorithm is less operational than the traditional Shamir algorithm and the interlaced NAF algorithm. The efficiency of the elliptic curve multiscalar multiplication algorithm is effectively improved, and the operation of multi scalar multiplication is more efficient. Compared with the related work, the computational efficiency of the new algorithm is about 7.9% to 20.6% higher than that of the existing multi scalar multiplication algorithm.
【学位授予单位】：扬州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN918.1

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