RSD-based high-performance radix-4 Montgomery Modular Multiplication for Elliptic Curve Cryptography

IF 1.9 3区工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC

Microelectronics Journal Pub Date : 2024-10-10 DOI:10.1016/j.mejo.2024.106433

Shilei Zhao, Jiwen Zheng, Yutong Shao, Hai Huang, Zhiwei Liu, Bin Yu, Ziyue Zhang

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引用次数: 0

Abstract

This paper proposes a high-performance radix-4 Montgomery Modular Multiplication (MMM) algorithm and its corresponding hardware architecture for Elliptic Curve Cryptography (ECC), in which the quotient and the partial product accumulation are computed in parallel in each iteration. Additionally, in this MMM, the Redundant Signed Digit (RSD) representation and the Signed Digit Adder (SDA) are used to eliminate the long carry chain and achieve parallel computation, as well as remove pre-computation and integrate modular reduction operations. Our MMM algorithm is implemented in 256-bit and 1024-bit versions on Xilinx Virtex-6 and Virtex-7 FPGAs, respectively. It consumes only 1.55k/10.18k Look-Up Tables (LUTs), takes 133/517 clock cycles, and runs at maximum frequencies of 558.8/641.7 MHz. According to the comparison in terms of Area Time Product (ATP), our design can achieve the ATP of 0.369 over the 256-bit NIST prime domain, which is approximately half of that of the state-of-the-art works. The Scalar Point Multiplication (SPM) scheme using this MMM algorithm consumes 14.19k LUTs and completes a single Scalar Point Multiplication (SPM) operation in 0.217 ms, and it also has a lower ATP than most other SPM algorithms currently in existence.

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基于 RSD 的高性能弧度-4 蒙哥马利模块乘法椭圆曲线密码学

本文为椭圆曲线加密（ECC）提出了一种高性能radix-4蒙哥马利模块乘法（MMM）算法及其相应的硬件架构，其中商和部分积累加在每次迭代中并行计算。此外，在这种 MMM 算法中，冗余带符号数字（RSD）表示法和带符号数字加法器（SDA）被用来消除长进位链，实现并行计算，以及消除预计算和集成模块化还原操作。我们的 MMM 算法在 Xilinx Virtex-6 和 Virtex-7 FPGA 上分别实现了 256 位和 1024 位版本。该算法仅消耗 1.55k/10.18k 查找表（LUT），耗时 133/517 个时钟周期，最高运行频率为 558.8/641.7 MHz。根据面积时间乘积（ATP）的比较，我们的设计在 256 位 NIST 质域上的 ATP 为 0.369，约为最先进设计的一半。使用这种 MMM 算法的标量点乘法（SPM）方案消耗 14.19k LUT，在 0.217 ms 内完成一次标量点乘法（SPM）操作，其 ATP 也低于目前大多数其他 SPM 算法。

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来源期刊

Microelectronics Journal 工程技术-工程：电子与电气

CiteScore

4.00

自引率

27.30%

发文量

222

审稿时长

43 days

期刊介绍： Published since 1969, the Microelectronics Journal is an international forum for the dissemination of research and applications of microelectronic systems, circuits, and emerging technologies. Papers published in the Microelectronics Journal have undergone peer review to ensure originality, relevance, and timeliness. The journal thus provides a worldwide, regular, and comprehensive update on microelectronic circuits and systems. The Microelectronics Journal invites papers describing significant research and applications in all of the areas listed below. Comprehensive review/survey papers covering recent developments will also be considered. The Microelectronics Journal covers circuits and systems. This topic includes but is not limited to: Analog, digital, mixed, and RF circuits and related design methodologies; Logic, architectural, and system level synthesis; Testing, design for testability, built-in self-test; Area, power, and thermal analysis and design; Mixed-domain simulation and design; Embedded systems; Non-von Neumann computing and related technologies and circuits; Design and test of high complexity systems integration; SoC, NoC, SIP, and NIP design and test; 3-D integration design and analysis; Emerging device technologies and circuits, such as FinFETs, SETs, spintronics, SFQ, MTJ, etc. Application aspects such as signal and image processing including circuits for cryptography, sensors, and actuators including sensor networks, reliability and quality issues, and economic models are also welcome.