{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T04:57:23Z","timestamp":1775797043984,"version":"3.50.1"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T00:00:00Z","timestamp":1775779200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T00:00:00Z","timestamp":1775779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Fully Homomorphic Encryption (FHE) enables computation over encrypted data while preserving strong security and privacy guarantees. However, its high computational cost remains a major challenge. This study therefore evaluates the performance of homomorphic matrix multiplication using three Homomorphic Encryption (HE) libraries, Microsoft SEAL, HElib and OpenFHE, across two platforms with AMD EPYC and Intel Xeon CPUs, with a particular focus on the impact of different compiler flags. The results indicate that compiler configurations and hardware selection significantly influence runtime in libraries such as Microsoft SEAL, whereas HElib and OpenFHE show negligible variation under different compilation settings. Furthermore, the analysis reveals that SEAL makes more efficient use of memory bandwidth while OpenFHE achieves the highest overall performance, the lowest mean absolute error and the shortest execution time.<\/jats:p>","DOI":"10.1007\/s11227-026-08464-y","type":"journal-article","created":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T04:04:00Z","timestamp":1775793840000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Cross-platform characterisation and performance analysis of homomorphic matrix multiplication"],"prefix":"10.1007","volume":"82","author":[{"given":"Franklin","family":"Espinoza","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Justo","family":"Molina","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Darwin","family":"Quezada-Gaibor","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sandra","family":"Catal\u00e1n","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manuel F.","family":"Dolz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,4,10]]},"reference":[{"key":"8464_CR1","unstructured":"Albrecht M, Chase M, Chen H, Ding J, Goldwasser S, Gorbunov S, Halevi S, Hoffstein J, Laine K, Lauter K, Lokam S, Micciancio D, Moody D, Morrison T, Sahai A, Vaikuntanathan V (2019) Homomorphic encryption standard. Cryptology ePrint Archive, Paper 2019\/939 (https:\/\/eprint.iacr.org\/2019\/939"},{"key":"8464_CR2","doi-asserted-by":"crossref","unstructured":"Badawi AA, Alexandru A, Bates J, Bergamaschi F, Cousins DB, Erabelli S, Genise N, Halevi S, Hunt H, Kim A, Lee Y, Liu Z, Micciancio D, Pascoe C, Polyakov Y, Quah I, RV S, Rohloff K, Saylor J, Suponitsky D, Triplett M, Vaikuntanathan V, Zucca V (2022): OpenFHE: open-source fully homomorphic encryption library. Cryptology ePrint Archive, Paper 2022\/915 https:\/\/eprint.iacr.org\/2022\/915","DOI":"10.1145\/3560827.3563379"},{"key":"8464_CR3","doi-asserted-by":"publisher","first-page":"131406","DOI":"10.1109\/ACCESS.2022.3229892","volume":"10","author":"S Behera","year":"2022","unstructured":"Behera S, Prathuri JR (2022) Design of novel hardware architecture for fully homomorphic encryption algorithms in fpga for real-time data in cloud computing. IEEE Access 10:131406\u2013131418. https:\/\/doi.org\/10.1109\/ACCESS.2022.3229892","journal-title":"IEEE Access"},{"key":"8464_CR4","unstructured":"Benedict D, Giwa T, Usman O, Ezenduka C (2024) A review of open-source fully homomorphic encryption libraries: Zama. AI concrete compiler, applications and vulnerability. Univ Ibadan J Sci Log ICT Res11(2), 24\u201335"},{"key":"8464_CR5","doi-asserted-by":"crossref","unstructured":"Brakerski Z (2012) Fully homomorphic encryption without modulus switching from classical gapsvp. IACR Cryptology ePrint Arch 2012: 78. http:\/\/dblp.uni-trier.de\/db\/journals\/iacr\/iacr2012.html#Brakerski12","DOI":"10.1007\/978-3-642-32009-5_50"},{"key":"8464_CR6","doi-asserted-by":"publisher","unstructured":"Brakerski Z, Gentry C, Vaikuntanathan V (2012): (leveled) fully homomorphic encryption without bootstrapping. In: Proceedings of the 3rd innovations in theoretical computer science conference, ITCS \u201912, pp 309\u2013325. Association for Computing Machinery, New York, NY, USA. https:\/\/doi.org\/10.1145\/2090236.2090262","DOI":"10.1145\/2090236.2090262"},{"key":"8464_CR7","doi-asserted-by":"publisher","unstructured":"Chen M, Chen Y, Jiang ZL (2023) Simd bootstrapping in fhew scheme. In: 2023 IEEE 22nd international conference on trust, security and privacy in computing and communications (TrustCom), pp. 1006\u20131013. https:\/\/doi.org\/10.1109\/TrustCom60117.2023.00141","DOI":"10.1109\/TrustCom60117.2023.00141"},{"key":"8464_CR8","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/978-3-319-70694-8_15","volume-title":"Advances in Cryptology - ASIACRYPT 2017","author":"JH Cheon","year":"2017","unstructured":"Cheon JH, Kim A, Kim M, Song Y (2017) Homomorphic encryption for arithmetic of approximate numbers. In: Takagi T, Peyrin T (eds) Advances in Cryptology - ASIACRYPT 2017. Springer International Publishing, Cham, pp 409\u2013437"},{"key":"8464_CR9","doi-asserted-by":"crossref","unstructured":"Chillotti I, Gama N, Georgieva M, Izabach\u00e8ne M (2016) Faster fully homomorphic encryption: bootstrapping in less than 0.1 seconds. Cryptology ePrint Archive, Paper 2016\/870. https:\/\/eprint.iacr.org\/2016\/870","DOI":"10.1007\/978-3-662-53887-6_1"},{"key":"8464_CR10","unstructured":"Chillotti I, Gama N, Georgieva M, Izabach\u00e8ne M (2018) TFHE: fast fully homomorphic encryption over the torus. Cryptology ePrint Archive, Paper 2018\/421. https:\/\/eprint.iacr.org\/2018\/421"},{"key":"8464_CR11","doi-asserted-by":"publisher","unstructured":"Fan G, Zhang M, Zheng F, Fan S, Zhou T, Deng X, Tang W, Kong L, Song Y, Yan S (2025) Warpdrive: Gpu-based fully homomorphic encryption acceleration leveraging tensor and cuda cores. In: 2025 IEEE international symposium on high performance computer architecture (HPCA), pp 1187\u20131200. https:\/\/doi.org\/10.1109\/HPCA61900.2025.00091","DOI":"10.1109\/HPCA61900.2025.00091"},{"key":"8464_CR12","doi-asserted-by":"publisher","unstructured":"Fan G, Zheng F, Wan L, Gao L, Zhao Y, Dong J, Song Y, Wang Y, Lin J (2023) Towards faster fully homomorphic encryption implementation with integer and floating-point computing power of gpus. In: 2023 IEEE international parallel and distributed processing symposium (IPDPS), pp 798\u2013808 . https:\/\/doi.org\/10.1109\/IPDPS54959.2023.00085","DOI":"10.1109\/IPDPS54959.2023.00085"},{"key":"8464_CR13","doi-asserted-by":"publisher","unstructured":"Faneela Ahmad J, Ghaleb B, Jan SU, Buchanan WJ (2025) Cross-platform benchmarking of the fhe libraries: Novel insights into seal and openfhe. In: 2025 International conference on new trends in computing sciences (ICTCS), pp. 219\u2013226. https:\/\/doi.org\/10.1109\/ICTCS65341.2025.10989417","DOI":"10.1109\/ICTCS65341.2025.10989417"},{"key":"8464_CR14","unstructured":"Halevi S, Shoup V (2020) Design and implementation of HElib: a homomorphic encryption library. Cryptology ePrint Archive, Paper 2020\/1481. https:\/\/eprint.iacr.org\/2020\/1481"},{"key":"8464_CR15","doi-asserted-by":"publisher","unstructured":"Jiang X, Kim M, Lauter K, Song Y (2018) Secure outsourced matrix computation and application to neural networks. Cryptology ePrint Archive, Paper 2018\/1041. https:\/\/doi.org\/10.1145\/3243734.3243837. https:\/\/eprint.iacr.org\/2018\/1041","DOI":"10.1145\/3243734.3243837"},{"key":"8464_CR16","doi-asserted-by":"publisher","unstructured":"Khan MJ, Fang B, Cimino G, Cirillo S, Yang L, Zhao D (2024): Privacy-preserving artificial intelligence on edge devices: a homomorphic encryption approach. In: 2024 IEEE international conference on web services (ICWS), pp 395\u2013405. https:\/\/doi.org\/10.1109\/ICWS62655.2024.00061","DOI":"10.1109\/ICWS62655.2024.00061"},{"key":"8464_CR17","unstructured":"Lattigo v6. Online: https:\/\/github.com\/tuneinsight\/lattigo (2024). EPFL-LDS, Tune Insight SA"},{"key":"8464_CR18","doi-asserted-by":"publisher","unstructured":"Lee Y, Micciancio D, Kim A, Choi R, Deryabin M, Eom J, Yoo D (2022) Efficient FHEW bootstrapping with small evaluation keys, and applications to threshold homomorphic encryption. Cryptology ePrint Archive, Paper 2022\/198. https:\/\/doi.org\/10.1007\/978-3-031-30620-4_8. https:\/\/eprint.iacr.org\/2022\/198","DOI":"10.1007\/978-3-031-30620-4_8"},{"key":"8464_CR19","doi-asserted-by":"publisher","unstructured":"Man D, Tai H (2024) Research on data encryption and privacy protection technologies in cloud computing environments. In: 2024 International conference on information technology, comunication ecosystem and management (ITCEM), pp 145\u2013150.https:\/\/doi.org\/10.1109\/ITCEM65710.2024.00035","DOI":"10.1109\/ITCEM65710.2024.00035"},{"key":"8464_CR20","unstructured":"McCalpin JD (1995) Stream: sustainable memory bandwidth in high performance computers . https:\/\/www.cs.virginia.edu\/stream\/. Accessed 06 Oct 2025"},{"key":"8464_CR21","unstructured":"Pal S, Swaminathan K, Aharoni E, Kushnir E, Drucker N, Schaul H, Buyuktosunoglu A, Soceanu O, Bose P (2023) Fully homomorphic encryption for computer architects: a fundamental characterization study. In: Annual IEEE\/ACM international symposium on microarchitecture"},{"key":"8464_CR22","doi-asserted-by":"publisher","unstructured":"Rahman T, Osmani AMIM, Rahman MS, Shibly MMA, Islam S (2025) Benchmarking fully homomorphic encryption libraries in iot devices. In: Proceedings of the 11th International conference on networking, systems, and security, NSysS \u201924, pp 16\u201323. Association for Computing Machinery, New York, NY, USA . https:\/\/doi.org\/10.1145\/3704522.3704546","DOI":"10.1145\/3704522.3704546"},{"key":"8464_CR23","unstructured":"Microsoft SEAL (release 4.1). (2023). Microsoft Research, Redmond, WA. https:\/\/github.com\/Microsoft\/SEAL"},{"key":"8464_CR24","doi-asserted-by":"crossref","unstructured":"Shivdikar K, Bao Y, Agrawal R, Shen M, Jonatan G, Mora E, Ingare A, Livesay N, Abell\u00e1n JL, Kim J, Joshi A, Kaeli D (2023) : Gme: Gpu-based microarchitectural extensions to accelerate homomorphic encryption. In: 2023 56th IEEE\/ACM international symposium on microarchitecture (MICRO), pp 670\u2013684","DOI":"10.1145\/3613424.3614279"},{"key":"8464_CR25","unstructured":"Takeshita J, Koirala N, McKechney C, Jung T (2024): HEProfiler: an in-depth profiler of approximate homomorphic encryption libraries. Cryptology ePrint Archive, Paper 2024\/1059. (https:\/\/eprint.iacr.org\/2024\/1059"},{"issue":"4","key":"8464_CR26","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1145\/1498765.1498785","volume":"52","author":"S Williams","year":"2009","unstructured":"Williams S, Waterman A, Patterson D (2009) Roofline: an insightful visual performance model for multicore architectures. Commun ACM 52(4):65\u201376. https:\/\/doi.org\/10.1145\/1498765.1498785","journal-title":"Commun ACM"},{"key":"8464_CR27","doi-asserted-by":"publisher","unstructured":"Ye T, Kannan R, Prasanna VK (2022) Fpga acceleration of fully homomorphic encryption over the torus. In: 2022 IEEE high performance extreme computing conference (HPEC), pp 1\u20137. https:\/\/doi.org\/10.1109\/HPEC55821.2022.9926381","DOI":"10.1109\/HPEC55821.2022.9926381"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-026-08464-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-026-08464-y","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-026-08464-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T04:04:17Z","timestamp":1775793857000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-026-08464-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,10]]},"references-count":27,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["8464"],"URL":"https:\/\/doi.org\/10.1007\/s11227-026-08464-y","relation":{},"ISSN":["1573-0484"],"issn-type":[{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,10]]},"assertion":[{"value":"15 October 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 March 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 April 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"341"}}