GF（2^n）域上的一种Ⅱ型优化正规基乘法器及其FPGA实现

有限域GF(2^n)上的椭圆曲线密码体制以其密钥短，安全强度高的优点正在获得广泛的重视和应用。该密码体制最主要的运算是有限域上的乘法运算。本文提出了一种基于Ⅱ型优化正规基的乘法器，该乘法器具有Massey-Omura乘法器的优点，又避免了其不足，易于编程，适合FPGA实现，实验表明，该算法简单，快速。     

小面积、低能耗的GF（2^m）域ECC模运算VLSI实现

以面积、能耗为优先准则,研究了GF(2m)域椭圆曲线密码(ECC)模运算VLSI的实现.选择GF(2163)上固定多项式基,引入了简单有效的快速模平方算法和改进的模逆算法,利用串行结构分别实现了模乘、模平方与模逆模块.基于UMC 0.25μm 1.8V工艺库的仿真结果表明,提出的串行模乘、快速组合逻辑模平方和快速模逆VLSI实现方式,通过牺牲域多项式灵活性,能够有效地减小面积、降低能耗,适合于资源受限的ECC系统.     

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。     

GF(2m)椭圆曲线密码体制在智能卡中的应用

介绍了特征2域上的椭圆曲线密码体制（ECC）的理论基础。分析了智能卡的安全机制，将椭圆曲线密码体制应用到智能卡中，给出了椭圆曲线密码算法在智能卡数据加密中的实现，并给出了在智能卡pin验证中的应用流程。最后，对ECC智能卡的性能进行了分析。     

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.     

Accelerated precomputation points–based scalar reduction on elliptic curve cryptography for wireless sensor networks

Sensor devices are limited resource power and energy, thus providing security services for sensor networks is very difficult. Elliptic curve cryptography (ECC) is one of the most famous asymmetric cryptographic schemes, which offers the same level of security with much shorter keys compared to the other widely used asymmetric cryptographic algorithm, RSA (Rivest, Shamir, and Adleman). In ECC, the main and most‐heavily used operation is the scalar multiplication kP , where the scalar value k is a private integer and must be secured. In this work, we present a new approach to accelerate the main scalar multiplication on ECC over prime fields for sensor networks. This approach uses an equivalent representation of points and can act as a support for existing schemes in a selected interval. The simulation results showed that the proposed technique increases the efficiency of the computation time. For example, on this scalar multiplication, we obtain a gain of 4 bits in 161 bits for 6.25% of the scalars. This gain can sometimes reach 100% in some cases. After this significant reduction of the scalar k , we present a fast precomputation algorithm in a distributed scalar multiplication on kP to avoid storage of precomputation points, which requires extra memory.     

有限域GF（q）上安全椭圆曲线的选取

椭圆曲线密码体制是安全性最高的公钥密码体制,它的安全性是基于椭圆曲线上的离散对数问题,同时椭圆曲线参数的选择对系统的安全性也至关重要。本文首先介绍了椭圆曲线密码体制的基本概念和相关数论知识,其次阐述了选择安全椭圆曲线的原则,最后详细介绍了如何通过选取合适的椭圆曲线参数来产生安全椭圆曲线,并对这些参数的合理性进行了验证。结果表明,按照这种方式所选取的椭圆曲线,抵御现有算法攻击能力大大增强。     

基于GF(2~m)上椭圆曲线点乘的实现

给出了椭圆曲线加密算法的点乘实现.在实现模乘运算时,把相乘过程和模约多项武过程结合起来,以改善运算效率.片外双口RAM的使用,加快了数据存取速度,同时通过预留RAM空间,增强了系统的可扩充性.本设计用VerilogHDL语言作为设计工具,在synopsys DC Z-2007 03 solaris9工作平台上,基于chartered 0.35 CMOS的综合库,50MHz约束下综合出结果约为18657门.     

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。     

一类有限域GF(2~n)上椭圆曲线密码体制的实现

本文首先分析了一类GF(2~n)上的算术运算,然后讨论了在这类GF(2~n)上实现椭圆曲线密码体制的方法,最后列出了我们在GF(2~(178))上实现的椭圆曲线密码体制的结果。     

面向椭圆曲线密码的处理器并行体系结构研究与设计

在研究椭圆曲线密码算法的处理特征以及有限域层上的并行调度算法基础上,采用指令级并行和数据级并行方法,提出了面向椭圆曲线密码的并行处理器体系结构模型,并就模型的存储结构进行了分析。基于该模型实现了一款验证原型,在FPGA上成功进行了验证测试并在0.18μm CMOS工艺标准单元库下进行逻辑综合以及布局布线。实验证明提出的并行处理器体系结构既能保证椭圆曲线密码算法应用的灵活性,又能够达到较高的性能。     

A secure and efficient identity‐based mutual authentication scheme with smart card using elliptic curve cryptography

The e‐commerce has got great development in the past decades and brings great convenience to people. Users can obtain all kinds of services through e‐commerce platform with mobile device from anywhere and at anytime. To make it work well, e‐commerce platform must be secure and provide privacy preserving. To achieve this goal, Islam et al. proposed a dynamic identity‐based remote user mutual authentication scheme with smart card using Elliptic Curve Cryptography(ECC). Islam et al claimed that the security of their scheme was good enough to resist various attacks. However, we demonstrate that their scheme is vulnerable to insider attack and suffers from off‐line password guessing attack if smart card is compromised. To overcome the deficiencies, we present an improved scheme over Islam's scheme. The security proof and analysis shows that our scheme can also provide user anonymity and mutual authentication, and the security is enough to against relay attack, impersonation attack, and other common secure attackers. The performance analysis shows that the proposed scheme is more efficient than Islam et al's scheme.