椭圆曲线密码处理器的高效VLSI设计与实现

采用复合武硬件设计方法，通过数学公式推导和电路结构设计，完成了一款GF（2m）域椭圆曲线密码处理器的高效VLSI实现。以低成本为目标，对算术逻辑模块的乘法、约减、平方、求逆，以及控制电路模块都进行了优化设计。按照椭圆曲线密码的不同运算层次，设计了不同层次的控制电路。该处理器综合在中芯国际SMIC0．18μm标准工艺库上．比相关研究的芯片面积节省48％，同时保证了很快的速度。     

GF（2^m）域高速椭圆曲线加密处理器设计

针对高速椭圆曲线加密应用的要求,设计了一种多项式基表示的有限域GF(2m)上的高速椭圆加密处理器.为提高运算速度,点加和倍点模块并行运算,且分别采用全并行结构实现;为减少资源,初始化和最后的坐标变换求逆模块通过优化分解成一系列乘和加运算,合并在一个模块中用串行结构实现.Xilinx公司的VirtexEXCV2600 FPGA硬件实现结果表明,完成有限域GF(2163)上任意椭圆曲线上的一次点乘的全部运算时间消耗约为31.6μs,适合高速椭圆曲线加密应用的要求.     

Software Implementation of Elliptic Curve Encryption over Binary Field

The mathematical theory for elliptic curve encryption based on optimal normal basis(ONB) over F_2~m is introduced.Then an elliptic curve cryptography(ECC) based encryption scheme isanalyzed and designed.The mechanism for key exchange based on Diffie-Hellman is described in detailsfor further applications.Based on these theoretic foundations,the software based on ECC is developedand an application is provided.The software is characterized by excellent security as well as highefficiency.     

GF(2m)域椭圆曲线密码算法的高速实现

文章提出椭圆曲线密码中算术处理的几个快速算法及其实现,并在此基础上提出一个新的、高速的ECC芯片结构体系,具有高速、低功耗、面积小等优势。     

用替换标量加速椭圆曲线点乘的研究

在优化有限域上椭圆曲线点乘的研究中,寻找标量的等价表示形式以减少点加和倍点运算的数量一直是关注的热点。因为点乘运算在一个H阶有限群中,利用有限群的性质,Q=kP=（n-k）（-P）。对于椭圆曲线,n-k和-P容易计算,于是计算点乘的标量k可以替换为n-k。因此,计算点乘时可通过选取代价更小的标量来减少计算量。理论和实验研究表明,替换标量可在微小的开销下使通常的重复倍加点算法的点加次数平均减少约5％。     

椭圆曲线密码处理器的高效并行处理架构研究与设计

为了解决当前椭圆曲线密码处理器普遍存在灵活性低、资源占用大的问题,该文采用统计建模的方式,以面积-时间(AT)综合性能指标为指导,提出了一种面向椭圆曲线密码并行处理架构的量化评估方式,并确定3路异构并行处理架构可使处理器综合性能达到最优。其次,该文提出一个分离分级式存储结构和一个运算资源高度复用的模运算单元,可增强存储器的访问效率和运算资源的利用率。在90 nm CMOS工艺下综合,该文处理器的面积为1.62mm2,完成一次GF(2571)和GF(p521)上的点乘运算分别需要2.26 ms/612.4J和2.63 ms/665.4J。与同类设计相比,该文处理器不仅具有较高的灵活性、可伸缩性,而且其芯片面积和运算速度达到了很好的折中。     

基于边信道原子的椭圆曲线标量乘算法

提出了一种能够抵抗简单能量分析攻击的边信道原子结构,减少了椭圆曲线密码体制中标量乘的倍点和点加运算次数,从而节省了运算时间,最后通过调用Crypto++库函数,对于NIST提供的160 bit素域上椭圆曲线编程实现算法,发现此算法的效率比Montgomery Ladder算法提高了37.6%。     

高性能可扩展公钥密码协处理器研究与设计

 本文提出了一种高效的点乘调度策略和改进的双域高基Montgomery模乘算法,在此基础上设计了一种新型高性能可扩展公钥密码协处理器体系结构,并采用0.18μm 1P6M标准CMOS工艺实现了该协处理器,以支持RSA和ECC等公钥密码算法的计算加速.该协处理器通过扩展片上高速存储器和使用以基数为处理字长的方法,具有良好的可扩展性和较强的灵活性,支持2048位以内任意大数模幂运算以及576位以内双域任意椭圆曲线标量乘法运算.芯片测试结果表明其具有很好的加速性能,完成一次1024位模幂运算仅需197μs、GF(p)域192位标量乘法运算仅需225μs、GF(2^m)域163位标量乘法运算仅需200.7μs.     

椭圆曲线数字签名算法优化与设计

简单阐述经典椭圆曲线数字签名(ECDSA)的基本原理,并分析其时间复杂度.在文中列举两种已经改进ECDSA签名算法,同时也分析它们时间复杂度.从椭圆曲线数字签名的安全性和高效性出发,提出一种椭圆曲线数字签名新算法,并证明其理论正确性,讨论其安伞性和复杂度.研究结果表明,改进算法在签名和验证过程中避免求逆运算,并且在签名...     

一种网络安全协处理器的椭圆曲线密码模块设计

提出了一种网络安全协处理器的椭圆曲线密码(ECC)模块设计方法,可以两个核共同完成多种椭圆曲线数字签名算法,而且支持多倍点、点加和点验证运算.在0.18μmCMOS工艺下,综合后关键路径为3.42ns、面积为3.58mm2.时钟频率为250MHz时,每秒完成770多次参数长度为192位椭圆曲线数字签名算法(ECDSA)的签名或者验证.     

一类安全椭圆曲线的选取及其标量乘法的快速计算

安全椭圆曲线的选取和标量乘法的快速计算是有效实现椭圆曲线密码体制的两个主要问题.本文将二者结合起来考虑给出了一类适合普通PC机实现的安全椭圆曲线,并详细给出了选取这类曲线的具体步骤和基于"大步-小步法"思想构造了一种新的计算这类曲线上标量乘法的快速算法.这类曲线不仅选取容易而且利用本文所提出方法计算其标量乘法时能使所需椭圆曲线运算次数大大减少.此外,选用这类曲线后基域中元素不再需要专门的表示方法,各种运算能非常快地得到实现,从而能极大地提高体制的整体实现速度.     

High-performance Public-key Cryptoprocessor for Wireless Mobile Applications

We present a high-speed public-key cryptoprocessor that exploits three-level parallelism in Elliptic Curve Cryptography (ECC) over GF(2 ⁿ ). The proposed cryptoprocessor employs a Parallelized Modular Arithmetic Logic Unit (P-MALU) that exploits two types of different parallelism for accelerating modular operations. The sequence of scalar multiplications is also accelerated by exploiting Instruction-Level Parallelism (ILP) and processing multiple P-MALU instructions in parallel. The system is programmable and hence independent of the type of the elliptic curves and scalar multiplication algorithms. The synthesis results show that scalar multiplication of ECC over GF(2¹⁶³) on a generic curve can be computed in 20 and 16 μs respectively for the binary NAF (Non-Adjacent Form) and the Montgomery method. The performance can be accelerated furthermore on a Koblitz curve and reach scalar multiplication of 12 μs with the TNAF (τ-adic NAF) method. This fast performance allows us to perform over 80,000 scalar multiplications per second and to enhance security in wireless mobile applications.

基于DFT的全方向M型超声心动图运动曲线的频域滤波

介绍一种基于离散傅里叶变换(DFT)的全方向M型超声心动图运动曲线频域滤波技术。全方向M型心动图是利用B超获取的心脏各结构的序列图像,沿各个方向提取的心脏某结构部位灰度点位置变化在时间轴上展开得到的运动轨迹,其边缘线即全方向M型心动图边界代表了了该灰度点的运动方程。依据其特点及要求,通过对不同区域的频域滤波效果比较,提出了分段滤波方法,实现了消除噪声干扰及减弱阶梯效应的影响的目的,从而保证了对全方向M型心动图的动态信息进一步分析的可靠性。     

一种基于椭圆曲线的前向安全数字签名

具有前向安全的数字签名是一种重要的数字签名方案,其要求攻击者即使在 t 时段入侵系统获得签名密钥,也无法伪造 t 时段之前的签名。换句话说,前向安全数字签名确保了密钥泄露时段以前所有签名的有效性。基于椭圆曲线离散对数问题和大数分解问题,构造了一种基于椭圆曲线的前向安全数字签名方案,并且对方案的安全性和效率进行了系统的分析和证明。     

Novel Method for DNA-Based Elliptic Curve Cryptography for IoT Devices

Elliptic curve cryptography (ECC) can achieve relatively good security with a smaller key length, making it suitable for Internet of Things (IoT) devices. DNA-based encryption has also been proven to have good security. To develop a more secure and stable cryptography technique, we propose a new hybrid DNA-encoded ECC scheme that provides multilevel security. The DNA sequence is selected, and using a sorting algorithm, a unique set of nucleotide groups is assigned. These are directly converted to binary sequence and then encrypted using the ECC; thus giving double-fold security. Using several examples, this paper shows how this complete method can be realized on IoT devices. To verify the performance, we implement the complete system on the embedded platform of a Raspberry Pi 3 board, and utilize an active sensor data input to calculate the time and energy required for different data vector sizes. Connectivity and resilience analysis prove that DNA-mapped ECC can provide better security compared to ECC alone. The proposed method shows good potential for upcoming IoT technologies that require a smaller but effective security system.     

A Secure Key Predistribution Scheme for WSN Using Elliptic Curve Cryptography

Security in wireless sensor networks (WSNs) is an upcoming research field which is quite different from traditional network security mechanisms. Many applications are dependent on the secure operation of a WSN, and have serious effects if the network is disrupted. Therefore, it is necessary to protect communication between sensor nodes. Key management plays an essential role in achieving security in WSNs. To achieve security, various key predistribution schemes have been proposed in the literature. A secure key management technique in WSN is a real challenging task. In this paper, a novel approach to the above problem by making use of elliptic curve cryptography (ECC) is presented. In the proposed scheme, a seed key, which is a distinct point in an elliptic curve, is assigned to each sensor node prior to its deployment. The private key ring for each sensor node is generated using the point doubling mathematical operation over the seed key. When two nodes share a common private key, then a link is established between these two nodes. By suitably choosing the value of the prime field and key ring size, the probability of two nodes sharing the same private key could be increased. The performance is evaluated in terms of connectivity and resilience against node capture. The results show that the performance is better for the proposed scheme with ECC compared to the other basic schemes.     

关于椭圆曲线密码的实现

从实现的角度,讨论了椭圆曲线密码实现中的一些问题,涉及有限域的选择,高斯正规基,曲线的选择,点乘的计算方法,签名方案等实际问题。     

基于比特重组快速模约简的高面积效率椭圆曲线标量乘法器设计

针对现有椭圆曲线密码标量乘法器难以兼顾灵活性和面积效率的问题,该文设计了一种基于比特重组快速模约简的高面积效率标量乘法器。首先,根据椭圆曲线标量乘的运算特点,设计了一种可实现乘法和模逆两种运算的硬件复用运算单元以提高硬件资源使用率,并采用Karatsuba-Ofman算法提高计算性能。其次,设计了基于比特重组的快速模约简算法,并实现了支持secp256k1, secp256r1和SCA-256(SM2标准推荐曲线)快速模约简计算的硬件架构。最后,对点加和倍点的模运算操作调度进行了优化,提高乘法与快速模约简的利用率,降低了标量乘计算所需的周期数量。所设计的标量乘法器在55 nm CMOS工艺下需要275 k个等效门,标量乘运算速度为48309次/s,面积时间积达到5.7。