The key algorithms including point multiplication algorithms and multiple point multiplication algorithms of ECC are further investigated in chapter four. 第四章深入研究椭圆曲线密码体制的关键算法:点乘算法及多点乘算法。
Because the velocities of the encryption and decryption of the ECC are greatly affected by the point multiplication, the optimization FPGA algorithm of the point multiplication is designed. 由于点乘运算极大影响了椭圆曲线密码系统的加/解密速度,本文对点乘运算的FPGA设计进行了重点优化。
Simulation results show that the accelerator designed by the algorithm can rapidly complete ECC point multiplication operation. When 162 bits key and 192 bits key are selected, the point multiplication operation takes 0.22 ms and 0.43 ms respectively. 仿真结果表明,基于该算法设计的加速器能快速完成ECC点乘运算,取162位和192位的密钥,点乘运算时间分别为0.22ms和0.43ms。
Thirdly, the paper also proposes the algorithms for scalar multiplication and multi-scalar multiplication for an arbitrary point on Weierstrass elliptic curves over fields of characteristic Three. 再次,设计适宜于特征值为3的有限域F(3~m)上的Weierstrass曲线的任意基点的标量乘和多标量乘算法。
The Wushu, as one kind of dynamic culture, presented the basic cultural characteristics by Wushu are the multiplication, which is the point showing out the value of Wuhu. 作为一种动态文化,武术呈现出来的文化基本特征是多元的,这也正是武术文化的价值所在。
In elliptic curve cryptosystems, point multiplication kP is the core operation, where P is a point on the elliptic curve and P is an integer. 在椭圆曲线密码系统中,其核心操作是点乘运算kP,P是椭圆曲线上的点,k是整数。
This paper analyses some published fast algorithms for the point multiplication on elliptic curves. We define the factorial expansions of an integer, and present a new fast algorithm for point multiplication on elliptic curves using factorial expansions. 本文分析了已有的一些计算椭圆曲线上点乘运算的快速算法,定义了整数阶乘展开式,并提出一种新的基于阶乘展开式的计算椭圆曲线上点乘的快速算法。
Fifthly, we overview the current fast algorithm of point multiplication, improve the fix base point comb algorithm, advance the speed of the whole system and remark the advantages and disadvantages of the popular algorithms based upon the experimental datas; 第五,研究了目前流行的计算椭圆曲线标量乘法的快速算法,同时改进了固定基点梳形法,提高了整个系统的速度,并在实验的基础上分析研究了流行算法的优劣;
It's introduced the conception of floating point multiplication in the series of MCS-96 Single Chip Microcomputer in this paper. And the designing approach and programming points of floating point multiplication for 8089 Single Chip Microcomputer are illustrated in detail. 以MCS-96系列单片机为例,介绍了浮点乘法运算原理,详细阐述了8098单片机三字节浮点乘法运算的设计方法及编程要领。
Scalar multiplication and point addition in elliptic curves are core operations in elliptic curve cryptosystem. 椭圆曲线上点的标量乘和加法运算是椭圆曲线密码算法的核心运算。
By using stereographic projection of each point group, all symmetry operation and generating operation of the point groups are listed, and group multiplication table of maximal proper point group 822 is filled in. 运用八方晶系各点群的极赤投影图,列出了各点群的所有对称操作;填出了固有点群822的群乘表。
Scalar Multiplication of the Point on Elliptic Curve 椭圆曲线上点的标量乘法
All symmetry operation and generating operation of the point groups were listed, and their group multiplication table of maximal proper point group 10 22 was filled in. 填写出了最大的固有点群1022的群乘表。
The basic operation is scalar multiplication: taking a given integer multiple of a given point on the elliptic curve over finite fields. The cost of the protocols depends on that of the elliptic scalar multiplication operation. 其基本的操作是标量乘法:即用一整数乘以椭圆曲线上给定的点P.协议的主要开销在于椭圆曲线的标量乘操作上。
Then the structure of ECC is expatiated in detail, the algorithms of modular multiplication, modular squaring, modular inversion based on Galois field and point addition, point multiplication, double point based on finite group are focus on too. 接着详细阐述了椭圆曲线的结构,基于二进制有限域上的模乘、模平方、模逆运算和基于有限群上的点加、点乘、倍点运算。
Algorithms for Efficient Simultaneous Elliptic Curve Scalar Multiplication Using Point Halving 利用半点计算椭圆曲线双标量乘法算法
This is the most important improvement of the bottom of multiplication algorithm finite field and elliptic curve encrypted point by algorithm, this makes the system to accomplish the encryption process faster. 这当中最重要的是改进底层有限域乘法的算法以及椭圆曲线加密的点乘算法,这样使得系统完成加密的过程变快了。
The part of system control is developed by adopting the top-down design way. The floating-point multiplication is equivalent to multiplication of fixed point by transforming the DDS instruction words formula. 控制部分采用自顶向下的设计方法,对DDS控制字计算公式转换,有效的解决了浮点乘法运算等效成高精度的定点运算。
This paper is divided the chip circuit into point multiplication and point add double point and finite field operation module, and respectively the circuit optimization for three different operation on characteristics. 本文把芯片电路分为点乘模块、点加倍点模块和有限域运算模块,并且针对这三种模块的不同运算特点分别作了电路优化。
The cryptographic protocols and the point multiplication of ECC are computed by software programs, which are composed of main processer instructions and extended application specific ECC processing instructions. The ECC point addition and doubling are operated in ECC hardware coprocessor. ECC密码协议和点乘调度算法由主处理器指令和扩展的ECC专用指令编程实现;ECC点加、倍点等运算则由硬件加速协处理器实现。
First of all, this paper, from the aspect of algorithm, studies the parallel processing algorithm of public key algorithm based on multicore processor, including the parallelism of Montgomery modular multiplication, point addition and double point based on ECC. 首先在算法上,本论文研究了公钥密码在多核处理器上的并行处理算法,包括对蒙哥马利模乘,椭圆曲线上点加和倍点的并行性进行了开发。