利用低复杂度数论变换的长多项式模块乘法 [讲义]

IF 9.4 1区工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

IEEE Signal Processing Magazine Pub Date : 2024-01-01 DOI:10.1109/MSP.2024.3368239

Sin-Wei Chiu;Keshab K. Parhi

{"title":"利用低复杂度数论变换的长多项式模块乘法 [讲义]","authors":"Sin-Wei Chiu;Keshab K. Parhi","doi":"10.1109/MSP.2024.3368239","DOIUrl":null,"url":null,"abstract":"This tutorial aims to establish connections between polynomial modular multiplication over a ring to circular convolution and the discrete Fourier transform (DFT). The main goal is to extend the well-known theory of the DFT in signal processing (SP) to other applications involving polynomials in a ring, such as homomorphic encryption (HE).","PeriodicalId":13246,"journal":{"name":"IEEE Signal Processing Magazine","volume":"41 1","pages":"92-102"},"PeriodicalIF":9.4000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Long Polynomial Modular Multiplication Using Low-Complexity Number Theoretic Transform [Lecture Notes]\",\"authors\":\"Sin-Wei Chiu;Keshab K. Parhi\",\"doi\":\"10.1109/MSP.2024.3368239\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This tutorial aims to establish connections between polynomial modular multiplication over a ring to circular convolution and the discrete Fourier transform (DFT). The main goal is to extend the well-known theory of the DFT in signal processing (SP) to other applications involving polynomials in a ring, such as homomorphic encryption (HE).\",\"PeriodicalId\":13246,\"journal\":{\"name\":\"IEEE Signal Processing Magazine\",\"volume\":\"41 1\",\"pages\":\"92-102\"},\"PeriodicalIF\":9.4000,\"publicationDate\":\"2024-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Signal Processing Magazine\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10502128/\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Signal Processing Magazine","FirstCategoryId":"5","ListUrlMain":"https://ieeexplore.ieee.org/document/10502128/","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}

引用次数: 0

摘要

本教程旨在建立环上多项式模乘与环卷积和离散傅里叶变换（DFT）之间的联系。主要目的是将信号处理（SP）中著名的 DFT 理论扩展到涉及环上多项式的其他应用，如同态加密（HE）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Long Polynomial Modular Multiplication Using Low-Complexity Number Theoretic Transform [Lecture Notes]

This tutorial aims to establish connections between polynomial modular multiplication over a ring to circular convolution and the discrete Fourier transform (DFT). The main goal is to extend the well-known theory of the DFT in signal processing (SP) to other applications involving polynomials in a ring, such as homomorphic encryption (HE).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

IEEE Signal Processing Magazine 工程技术-工程：电子与电气

CiteScore

27.20

自引率

0.70%

发文量

123

审稿时长

6-12 weeks

期刊介绍： EEE Signal Processing Magazine is a publication that focuses on signal processing research and applications. It publishes tutorial-style articles, columns, and forums that cover a wide range of topics related to signal processing. The magazine aims to provide the research, educational, and professional communities with the latest technical developments, issues, and events in the field. It serves as the main communication platform for the society, addressing important matters that concern all members.