一种双域Montgomery求逆算法与硬件实现

有限域上的求逆运算是椭圆曲线密码算法的关键运算之一。分别对GF（p）和GF（2ⁿ）域上的Montgomery模逆算法进行分析,并将GF（2ⁿ）域上的Montgomery模逆算法中对变量阶数的比较进行了改进,这样不仅利于GF（p）和GF（2ⁿ）域上的模逆运算在统一的硬件结构上实现,也解决了数据位数较大时进行阶数比较延迟较大的问题,在此基础上提出一种基于GF（p）和GF（2ⁿ）双域上统一的模逆算法,并根据算法,采用双域可伸缩运算单元,实现了一种可扩展的统一Montgomery模逆硬件结构。设计采用Verilog-HDL语言进行硬件描述,并基于0.18 μm工艺标准单元库进行了综合,结果表明该设计与其他设计相比具有灵活性好、性能高的特点。     

基于ECC的身份认证系统的设计与实现

本文从应用系统的安全性和高效性的要求出发,阐述了椭圆曲线密码体制的基本原理及其优点,设计了一个基于大素数域Fp椭圆曲线的身份认证系统,并对该系统进行了安全性分析。在椭圆曲线加密模块的实现中,大素数域中的模逆运算和椭圆曲线上的点乘运算经常是算法实现的瓶颈,本文采用模逆运算和点乘运算的改进算法来提高程序的运行效率。     

AES算法中模逆运算电路设计与实现

AES算法中字节替换和轮密钥扩展都需使用模逆运算.模逆运算是AES算法中最复杂的运算,也是AES算法中最关键的模块之一.本文分析二进制扩展的欧几里德算法,基于该算法使用Verilog HDL设计模逆运算电路,通过FPGA实现模逆运算.电路选用优先权编码器、比较器和移位寄存器等基本逻辑部件组成,使得两个多项式次数的计算、...     

有限域模乘专用指令设计

针对椭圆曲线密码算法中有限域模乘运算的需求,提出其专用模乘指令。利用指令域中的组参数实现算法多组模乘运算,通过对参数进行配置,使指令支持运算长度拓展,在模乘运算单元中实现Montgomery模乘算法,并设计素域和二进制域统一的硬件流水线,以及双域乘法器单元结构。实验结果表明,该有限域模乘指令和硬件运算单元具有较高的执行效率和较好的灵活性。     

基于FPGA的多项式基下二进制域ECC点乘设计

文中基于经典蒙哥马利点乘算法,通过算法改进,模乘采用部分并行设计,在射影坐标系下实现模逆算法。通过VHDL语言进行设计描述,完成了椭圆曲线底层的模乘、模逆的模块设计,并通过一系列的状态机调用各个模块组合,最终完成点乘运算的设计。整个系统结构进行了优化处理,最终在Cyclone系列的EP2C35F484C5上,利用QuartusⅡ平台分析得出时钟频率为50．3MHZ,逻辑单元个数为25044个。     

二进制域运算在DSP上的优化

主要研究二进制域运算在DSP上的实现。通过设置多个中间变量，实现了对数组的并行计算，将最佳正规基模乘算法提高到6级流水。重构almost inversion多项式基模逆算法结构，消除跳转语句，实现程序设计模块化。在TMS320C6204上执行113位和191位算法证实确实提高了模乘和模逆两种运算的速度。以循环移位取代乘法的模乘算法，限制了C6201的流水深度。     

一种通用ECC协处理器的设计与实现

提出一种能同时在素数域和二进制有限域下支持任意曲线、任意域多项式的高速椭圆曲线密码体系(ECC)协处理器。该协处理器可以完成ECC中的各种基本运算,根据指令调用基本运算单元完成ECDSA及其他改进算法。支持384位以下任意长度的ECC应用,采用基于字的模乘器、操作数分离、RAM阵列等技术提高系统性能。     

SM2算法模逆加速器的设计

SM2公钥密码在智能卡领域有广泛的应用,其运算中难以避免模逆运算,而模逆算法因为其具有幂指数级别的运算复杂度,成为制约SM2算法性能的一个重要瓶颈。以SM2算法公钥引擎为基础,巧妙地利用了已有的蒙哥马利乘法器结构,设计出了一种长度可伸缩的快速模逆算法。并复用已有模乘资源,给出了节省存储空间、不增加面积成本的硬件实现结构以及数据存储方案。其速度性能远远优于传统的费马小定理算法和扩展欧几里德算法,对比同类蒙哥马利模逆算法也有良好的性能。     

有限域GF(2m)模逆算法的改进与实现

在椭圆曲线密码体制中,有限域GF(2m)中模逆运算是最重要的运算之一。在分析一种通用有限域GF(2m)模逆算法的基础上,提出改进算法。改进算法减少了原算法快速实现时的缺点,能够有效地提高算法效率。基于FPGA分别实现了GF(283)和GF(2233)中模逆算法模块,并与2种已有实现结果进行了对比。结果表明,选取有限域GF(283)和GF(2233)时,改进算法效率提高率分别约为72.9%和59.5%。     

集成模乘求逆双重运算的抗击RSA协处理器

提出了一种集成模乘求逆双重运算的抗攻击RSA协处理器设计.在设计中引入了指数重编码和双位扫描的方法以提高模幂运算的速度,并采用数据屏蔽和随机重编码的方案来防御功耗分析攻击.基于字串行架构实现了模乘和求逆运算,并提出了相应的可伸缩蒙哥马利模乘算法,使基本运算具有数据通路小、可伸缩性强的特点.在VLSI设计上实现了模乘和求逆运算的硬件复用,大幅度地降低了成本.FPGA验证表明协处理器能够正确地完成所有预定的功能.TSMC0.25um工艺综合结果显示,协处理器的工作频率可达170MHZ,总的规模(包括核心电路与存储单元)约为26K等效门.因此本文RSA协处理器体现了多功能、可伸缩、抗攻击和低成本的综合优势.     

Partition Algorithm For Parallel Processing Of Array Multiplication In Gf(2m) Fields

The multiplication operations in GF(2m) fields are widely used in cryptosystems. However, the multiplication operations for public-key cryptosystems require very large operands with 512 bits or more, and then existing multipliers are not available for such multiplications. In this paper, we will present a partition algorithm to divide large operands into small operands such as 32 bits or 64 bits, and then existing multipliers can be employed. We also present a parallel version of the partition algorithm by employing an important natural property of the multiplication operations in GF(2m) fields.     

基于方程式逆序数的软件水印算法*

针对方程式重排序等算法存在的程序运行速度、信息隐藏量等问题,提出基于方程式操作数系数排列逆序数的软件水印算法。重新排列那些可以相互交换的操作数,使各操作数的系数按照一定次序排列。通过排列的逆序数和二进制数的一一对应关系来隐藏水印。这一方法无须向程序中添加任何代码,并且能有效提高隐藏数据的效率,程序的规模和速度并不受影响。     

Improvements to algorithms for computing the Minkowski sum of 3-polytopes

A Minkowski sum is a geometric operation that is equivalent either to the vector additions of all points in two operands or to the sweeping of one operand around the profile of the other without changing the relative orientation. Applications of Minkowski sums are found in computer graphics, robotics, spatial planning, and CAD. This paper presents two algorithms for computing Minkowski sum of convex polyhedron in three space (3-polytopes). Both algorithms are improvements on current ones found in the literature. One is based on convex hulls and the other on slope diagrams. The original convex hull based Minkowski algorithm is costly, while the original slope diagram based algorithms require the operation of stereographic projection from 3D to 2D for merging the slope diagrams of the two operands. Implementation of stereographic projection is complicated which increases the computation time and reduces the accuracy of the geometric information that is needed for constructing the resultant solid. This paper reports on improvements that have been made to these two algorithms and their implementation. These improvements include using vector operations to find the interrelations between points, arcs and regions on a unit sphere for the slope diagram algorithm, and addition of a pre-sorting procedure before constructing convex hull for convex hull based Minkowski sum algorithm. With these improvements, the computation time and complexity for both algorithms have been reduced significantly, and the computational accuracy of the slope diagram algorithm has been improved. This paper also compares these two algorithms to each other and to their original counterparts. The potential for extending these algorithms to higher dimensions is briefly discussed.     

An on-line arithmetic unit for bit-pipelined rational arithmetic

We derive a binary version of an algorithm of Gosper to compute the sum, difference, product, quotient, and certain rational functions of two rational operands applicable to integrated approximate and exact rational computation. The arithmetic unit we propose is an eight-register computation cell with bit-serial input and output employing a binary continued fraction representation of the rational operands. The operands and results are processed in a most-significant-bit first on-line fashion with bit level logic. Individual bits of the input/output in our binary continued fraction representation are shown to correspond in a one-to-one manner with primitive shift and shift-and-add/subtract operations on pairs of registers in the computation cell. Extension to a redundant signed-bit format is shown feasible toward the ultimate goal of achieving small on-line delay and near uniform throughput in cascaded pipelined computation with these computation cells.     

Montgomery逆算法的改进和应用

本文通过对Montgomery逆算法核心部分的改进，得到两种分别以4为基和8为基的优化算法。其中以4为基的算法，在基本不增加算法实现复杂度的情况下，使迭代次数的平均上限从2n降到7/6n，平均迭代次数也从3n/2降到了7/8n。而8基算法则相应分别下降到25/24和25/32n，但算法内部的比较和跳转稍有增多。由于新算法只要求两个关键操作数中有一个变成1，就可以结束操作（原算法要求两个都变为1），因此实际迭代次数可能还要少。本文提出的算法也可以运用在文[1，2，7]中求基本模逆的算法中。本文算法主要适用于软件实现，在RSA和ECC等公钥体制实现中有广泛的应用。     

Dataflow query execution in a parallel main-memory environment

In this paper, the performance and characteristics of the execution of various join-trees on a parallel DBMS are studied. The results of this study are a step into the direction of the design of a query optimization strategy that is fit for parallel execution of complex queries.Among others, synchronization issues are identified to limit the performance gain from parallelism. A new hash-join algorithm is introduced that has fewer synchronization constraints than the known hash-join algorithms. Also, the behavior of individual join operations in a join-tree is studied in a simulation experiment. The results show that the introduced Pipelining hash-join algorithm yields a better performance for multi-join queries. The format of the optimal join-tree appears to depend on the size of the operands of the join: A multi-join between small operands performs best with a bushy schedule; larger operands are better off with a linear schedule. The results from the simulation study are confirmed with an analytic model for dataflow query execution.     

一种128位高精度浮点乘加部件的研究与实现

高性能高精度的浮点数值处理一直是科学计算追求的目标。为此,本文研究并实现了一种128位浮点乘加融合计算单元。在乘法模块中,使用分块乘法,复用57位乘法模块,减小了数据宽度。采用三输入前导1预期技术,简化了预编码,缩短了预测电路的延时并减小面积。该模块单元使用Verilog语言实现,用Design Compiler进行逻辑综合,在simc0.13μm工艺下频率达202MHz,关键路径延时为4.93μs,面积约为191000门。     

The identical operands commutative encryption and watermarking based on homomorphism

Aiming at the requirement of comprehensive security protection for multimedia information, this paper proposes a new algorithm to realize the combination of encryption and watermarking based on the homomorphism. Under the proposed algorithm scheme, the plaintext watermark embedding operations are mapped to the ciphertext domain by homomorphism to achieve the plaintext watermark embedding in the ciphertext domain; at the same time, the embedded plaintext watermarks are also mapped to the ciphertext domain by homomorphism to achieve the ciphertext watermarking embedding. According to the experimental results, by the proposed algorithm, the order of watermark embedding and data encrypting does not affect the production of the same encrypted-watermarked data, meanwhile, whether the encrypted-watermarked data being decrypted or not does not affect the extraction of embedded watermark. For the operands of encryption and watermarking being the same data, the proposed algorithm has higher security compared with the existing mainstream independent operands based communicative encryption and watermarking.     

基于手指轮廓的手形验证算法

针对手形特点和现有的手形认证方法的不足,提出了一种新颖的基于有序手形轮廓点匹配的手形验证方法。摆脱了固定拴的束缚,运算量小。系统首先对预处理后的手形图像进行边界跟踪后提取手指的关键特征点分离手指,运用对有序边缘点进行运算的手指归一化算法进行图像标准化,最后,运用新型点匹配算法进行自动鉴别。通过小样本实验检测,该方法在鲁棒性、准确率、和运算量方面具有良好的综合性能。