New algorithms for fully homomorphic matrix addition and multiplication

Basit Öğe Kaydı
dc.contributor.authorCi, Shang
dc.contributor.authorWang, Yihan
dc.contributor.authorHu, Sen
dc.contributor.authorGuan, Donghai
dc.contributor.authorKoc, Cetin Kaya
dc.date.accessioned2026-07-01T11:40:11Z
dc.date.available2026-07-01T11:40:11Z
dc.date.issued2025
dc.departmentDüzce Üniversitesi
dc.description.abstractNew algorithms are introduced for embedding matrices with integer or fixed-point real number entries into plaintexts and for performing matrix addition and multiplication on encrypted matrices. The encryption algorithms used for this purpose are fully homomorphic, such as BGV, BFV, and CKKS. These algorithms have the property of performing SIMD style parallel operations on plaintext values encrypted into a single ciphertext vector by a technique called ciphertext packing using the Chinese Remainder Theorem. This concept was introduced by Halevi and Shoup, and algorithms for homomorphic matrix operations were further improved by Jiang et al. (JKLS). Our algorithms improve both Halevi and Shoup and JKLS algorithms in terms of arithmetic and data rotation complexity. The proposed algorithms are designed on top of the BFV fully homomorphic encryption scheme. We describe our algorithms in detail step by step in this article, providing numerical examples in Appendix A. Experimental results demonstrate that our matrix multiplication algorithm achieves superior efficiency in terms of running time compared to JKLS algorithm. Real-world applications of FHE-based matrix computations often require matrix dimensions in the hundreds of thousands. Given typical FHE parameter settings (polynomial degree N=213\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N = 2<^>{13}$$\end{document}, plaintext modulus t=65537\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t = 65537$$\end{document}), the total number of arithmetic and data-rotation operations can easily reach the order of 1012\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10<^>{12}$$\end{document}. This scale necessitates state-of-the-art high-performance computing practices.
dc.description.sponsorshipJiangsu Province 100 Foreign Experts Introduction Plan [BX2022012] -- This research is supported in part by the Jiangsu Province 100 Foreign Experts Introduction Plan BX2022012. This research is also supported in part by TUB & Idot; TAK Projects 2232-118C332 and 1001-121F348.
dc.identifier.doi10.1007/s11227-025-08032-w
dc.identifier.issn0920-8542
dc.identifier.issn1573-0484
dc.identifier.issue16
dc.identifier.orcid0000-0001-5264-9272
dc.identifier.scopus2-s2.0-105021082733
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1007/s11227-025-08032-w
dc.identifier.urihttps://hdl.handle.net/20.500.12684/23666
dc.identifier.volume81
dc.identifier.wosWOS:001611683300008
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer
dc.relation.ispartofJournal of Supercomputing
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WOS_20260623
dc.subjectMatrix Addition And Multiplication
dc.subjectHomomorphic Encryption
dc.titleNew algorithms for fully homomorphic matrix addition and multiplication
dc.typeArticle

Dosyalar

Koleksiyon

WoS İndeksli Yayınlar Koleksiyonu
Scopus İndeksli Yayınlar Koleksiyonu