Highly Optimized Montgomery Multiplier for SIKE Primes on FPGA
Highly Optimized Montgomery Multiplier for SIKE Primes on FPGA
复制标题
DOI：
10.1109/arith48897.2020.00018
复制
发表时间：
2020-06
期刊：
影响因子：
--
通讯作者：
Rami Elkhatib;R. Azarderakhsh;Mehran Mozaffari Kermani
中科院分区：
文献类型：
--
作者：
Rami Elkhatib;R. Azarderakhsh;Mehran Mozaffari Kermani
在进一步的密码分析研究表明所选初始素数的安全级别被高估后，在NIST第二轮标准化过程中提出了新的素数用于超奇异同构密钥封装（SIKE）[1]，[2]。在本文中，我们开发了一个高度优化的$\mathbb{F}_p$蒙哥马利乘法算法和架构，进一步利用特殊形式的SIKE素数相比，以前的文献中的实现。然后，我们使用建议的乘法器在Xilinx Virtex 7上实现了所有第2轮NIST安全级别的SIKE（NIST安全级别1的SIKep 434，NIST安全级别2的SIKep 503，NIST安全级别3的SIKep 610和NIST安全级别5的SIKep 751）。我们最好的实现（NIST安全级别1）运行速度快29%，占用硬件资源少30%，与文献[3]中的领先同行相比，其他安全级别的实现也实现了类似的改进。
New primes were proposed for Supersingular Isogeny Key Encapsulation (SIKE) in NIST standardization process of Round 2 after further cryptanalysis research showed that the security levels of the initial primes chosen were over-estimated [1], [2]. In this paper, we develop a highly optimized $\mathbb{F}_p$ Montgomery multiplication algorithm and architecture that further utilizes the special form of SIKE prime compared to previous implementations available in the literature. We then implement SIKE for all Round 2 NIST security levels (SIKEp434 for NIST security level 1, SIKEp503 for NIST security level 2, SIKEp610 for NIST security level 3, and SIKEp751 for NIST security level 5) on Xilinx Virtex 7 using the proposed multiplier. Our best implementation (NIST security level 1) runs 29% faster and occupies 30% less hardware resources in comparison to the leading counterpart available in the literature [3] and implementations for other security levels achieved similar improvement.