Triple-Hoisted Baby-Step Giant-Step Linear Transformation over CKKS Homomorphic Encryption and Hardware Accelerator

Computer Science > Cryptography and Security [Submitted on 17 May 2026] Triple-Hoisted Baby-Step Giant-Step Linear Transformation over CKKS Homomorphic Encryption and Hardware Accelerator Sajjad Akherati, Xinmiao Zhang Computations can be directly carried out over ciphertexts using homomorphic encryption (HE), which is indispensable for privacy-preserving cloud computing. Linear transformation is widely used in neural networks, including large language models. However, the implementation of linear transformation over HE requires a large number of ciphertext rotations, which incur significant memory and hardware overhead despite existing simplification techniques. This paper proposes a triple-hoisted baby-step giant-step algorithm that decomposes the baby step further to substantially reduce the number of ciphertext rotations needed for the CKKS HE evaluation of linear transformation. Moreover, to reduce off-chip memory access, which contributes to the majority of the latency, a memory-optimized data path is proposed by partitioning the algorithm into multiple phases. Furthermore, an efficient FPGA-based hardware accelerator with an optimized permutation circuit for message routing is designed for the proposed scheme. For a set of typical parameters, the proposed design reduces the off-chip memory access by 2.9x compared to the best prior design. Synthesized for Xilinx Virtex UltraScale+ devices, the proposed design achieves a 5.8x reduction in computational latency compared with the baseline design. Comments: 11 pages, 6 figures, 7 tables, 34 refrences, and journal paper Subjects: Cryptography and Security (cs.CR) Cite as: arXiv:2605.17222 [cs.CR]   (or arXiv:2605.17222v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2605.17222 Focus to learn more Submission history From: Sajjad Akherati [view email] [v1] Sun, 17 May 2026 01:57:35 UTC (455 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-05 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)