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

Sajjad Akherati; Xinmiao Zhang

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arXiv · 2605.17222

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

Sajjad Akherati·Xinmiao Zhang

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Abstract

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.

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BibTeX RIS

Sajjad Akherati, Xinmiao Zhang. 2026-05-17. Triple-Hoisted Baby-Step Giant-Step Linear Transformation over CKKS Homomorphic Encryption and Hardware Accelerator. https://arxiv.org/abs/2605.17222

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