High-Performance Elliptic Curve Cryptography by Using the CIOS Method for Modular Multiplication
High-Performance Elliptic Curve Cryptography by Using the CIOS Method for Modular Multiplication
复制标题
使用 CIOS 模乘法的高性能椭圆曲线密码学
DOI：
10.1007/978-3-319-54876-0_15
复制
发表时间：
2016
影响因子：
2.8
通讯作者：
Mohsen Machhout
中科院分区：
文献类型：
--
作者：
Amine Mrabet;Nadia El Mrabet;Ronan Lashermes;J. Rigaud;B. Bouallegue;Sihem Mesnager;Mohsen Machhout
椭圆曲线密码体制(ECC)正变得不可避免，应该用于公钥协议。由于与RSA相比，在相同的安全级别下，操作数的位数要小得多，因此它在实践中得到了越来越多的接受。大多数基于ECC的协议都包含标量乘法的计算。ECC可以在仿射、投影、雅可比或其他坐标模型中执行。有限域上的算法构成了ECC公钥密码体制的核心。利用蒙哥马利模乘(MMM)的粗集成操作数扫描法(CIO)，结合一种有效的脉动结构，提出了一种在雅可比坐标下高效实现标量乘法的硬件实现方法。据我们所知，这是第一次在大型素数域上实现这样的设计。所提出的架构是为现场可编程门阵列(现场可编程门阵列)平台设计的。其目的是减少模乘运算的时钟周期数，这意味着ECC具有良好的性能。所给出的实现结果集中于对密码学有用的各种安全级别。该体系结构是为了在Xilinx现场可编程门阵列上使用灵活的DSP48而设计的。我们的MMM体系结构是可伸缩的，只依赖于单词的数量和大小。
Elliptic Curve Cryptography (ECC) is becoming unavoidable, and should be used for public key protocols. It has gained increasing acceptance in practice due to the significantly smaller bit size of the operands compared to RSA for the same security level. Most protocols based on ECC imply the computation of a scalar multiplication. ECC can be performed in affine, projective, Jacobian or others models of coordinates. The arithmetic in a finite field constitutes the core of ECC Public Key Cryptography. This paper discusses an efficient hardware implementation of scalar multiplication in Jacobian coordinates by using the Coarsely Integrated Operand Scanning method (CIOS) of Montgomery Modular Multiplication (MMM) combined with an effective systolic architecture designed with a two-dimensional array of Processing Elements (PE). As far as we know this is the first implementation of such a design for large prime fields. The proposed architectures are designed for Field Programmable Gate Array (FPGA) platforms. The objective is to reduce the number of clock cycles of the modular multiplication, which implies a good performance for ECC. The presented implementation results focuses on various security levels useful for cryptography. This architecture have been designed in order to use the flexible DSP48 on Xilinx FPGAs. Our architecture for MMM is scalable and depends only on the number and size of words.