A High-Efficiency Modular Multiplication Digital Signal Processing for Lattice-Based Post-Quantum Cryptography

IF 1.8 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Cryptography Pub Date : 2023-09-25 DOI:10.3390/cryptography7040046
Trong-Hung Nguyen, Cong-Kha Pham, Trong-Thuc Hoang
{"title":"A High-Efficiency Modular Multiplication Digital Signal Processing for Lattice-Based Post-Quantum Cryptography","authors":"Trong-Hung Nguyen, Cong-Kha Pham, Trong-Thuc Hoang","doi":"10.3390/cryptography7040046","DOIUrl":null,"url":null,"abstract":"The Number Theoretic Transform (NTT) has been widely used to speed up polynomial multiplication in lattice-based post-quantum algorithms. All NTT operands use modular arithmetic, especially modular multiplication, which significantly influences NTT hardware implementation efficiency. Until now, most hardware implementations used Digital Signal Processing (DSP) to multiply two integers and optimally perform modulo computations from the multiplication product. This paper presents a customized Lattice-DSP (L-DSP) for modular multiplication based on the Karatsuba algorithm, Vedic multiplier, and modular reduction methods. The proposed L-DSP performs both integer multiplication and modular reduction simultaneously for lattice-based cryptography. As a result, the speed and area efficiency of the L-DSPs are 283 MHz for 77 SLICEs, 272 MHz for 87 SLICEs, and 256 MHz for 101 SLICEs with the parameters q of 3329, 7681, and 12,289, respectively. In addition, the N−1 multiplier in the Inverse-NTT (INTT) calculation is also eliminated, reducing the size of the Butterfly Unit (BU) in CRYSTAL-Kyber to about 104 SLICEs, equivalent to a conventional multiplication in the other studies. Based on the proposed DSP, a Point-Wise Matrix Multiplication (PWMM) architecture for CRYSTAL-Kyber is designed on a hardware footprint equivalent to 386 SLICEs. Furthermore, this research is the first DSP designed for lattice-based Post-quantum Cryptography (PQC) modular multiplication.","PeriodicalId":36072,"journal":{"name":"Cryptography","volume":"36 1","pages":"0"},"PeriodicalIF":1.8000,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cryptography","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/cryptography7040046","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}
引用次数: 0

Abstract

The Number Theoretic Transform (NTT) has been widely used to speed up polynomial multiplication in lattice-based post-quantum algorithms. All NTT operands use modular arithmetic, especially modular multiplication, which significantly influences NTT hardware implementation efficiency. Until now, most hardware implementations used Digital Signal Processing (DSP) to multiply two integers and optimally perform modulo computations from the multiplication product. This paper presents a customized Lattice-DSP (L-DSP) for modular multiplication based on the Karatsuba algorithm, Vedic multiplier, and modular reduction methods. The proposed L-DSP performs both integer multiplication and modular reduction simultaneously for lattice-based cryptography. As a result, the speed and area efficiency of the L-DSPs are 283 MHz for 77 SLICEs, 272 MHz for 87 SLICEs, and 256 MHz for 101 SLICEs with the parameters q of 3329, 7681, and 12,289, respectively. In addition, the N−1 multiplier in the Inverse-NTT (INTT) calculation is also eliminated, reducing the size of the Butterfly Unit (BU) in CRYSTAL-Kyber to about 104 SLICEs, equivalent to a conventional multiplication in the other studies. Based on the proposed DSP, a Point-Wise Matrix Multiplication (PWMM) architecture for CRYSTAL-Kyber is designed on a hardware footprint equivalent to 386 SLICEs. Furthermore, this research is the first DSP designed for lattice-based Post-quantum Cryptography (PQC) modular multiplication.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
基于格子后量子密码的高效模乘法数字信号处理
在基于点阵的后量子算法中,数论变换(NTT)被广泛用于加速多项式乘法。所有NTT操作数都使用模块化运算,特别是模块化乘法,这对NTT硬件实现效率有很大影响。到目前为止,大多数硬件实现使用数字信号处理(DSP)来乘两个整数,并从乘法乘积中最佳地执行模计算。本文提出了一种基于Karatsuba算法、吠陀乘法器和模约简方法的模块化乘法定制栅格dsp (L-DSP)。所提出的L-DSP可以同时对基于格的密码进行整数乘法和模约简。因此,77片时,l - dsp的速度为283 MHz, 87片时为272 MHz, 101片时为256 MHz,参数q分别为3329、7681和12289。此外,还消除了逆ntt (INTT)计算中的N−1乘数,将CRYSTAL-Kyber中的蝴蝶单元(BU)的大小减少到约104片,相当于其他研究中的常规乘法。基于所提出的DSP,为CRYSTAL-Kyber设计了一个点向矩阵乘法(PWMM)架构,其硬件占用相当于386片。此外,该研究是第一个为基于晶格的后量子密码(PQC)模块化乘法设计的DSP。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Cryptography
Cryptography Mathematics-Applied Mathematics
CiteScore
3.80
自引率
6.20%
发文量
53
审稿时长
11 weeks
期刊最新文献
Locking-Enabled Security Analysis of Cryptographic Circuits Residue Number System (RNS) and Power Distribution Network Topology-Based Mitigation of Power Side-Channel Attacks Practical Certificate-Less Infrastructure with Application in TLS A Publicly Verifiable E-Voting System Based on Biometrics Garbled Circuits Reimagined: Logic Synthesis Unleashes Efficient Secure Computation
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1