Revisiting the Slot-to-Coefficient Transformation for BGV and BFV
Authors
Robin Geelen
Robin Geelen
COSIC, KU Leuven, Leuven, Belgium
robin dot geelen at esat dot kuleuven dot be
robin dot geelen at esat dot kuleuven dot be
Abstract
Numerous applications in homomorphic encryption require an operation that moves the slots of a ciphertext to the coefficients of a different ciphertext. For the BGV and BFV schemes, the only efficient algorithms to implement this slot-to-coefficient transformation were proposed in the setting of non-power-of-two cyclotomic rings. In this paper, we devise an FFT-like method to decompose the slot-to-coefficient transformation (and its inverse) for power-of-two cyclotomic rings. The proposed method can handle both fully and sparsely packed slots. Our algorithm brings down the computational complexity of the slot-to-coefficient transformation from a linear to a logarithmic number of FHE operations, which is shown via a detailed complexity analysis.
The new procedures are implemented in Microsoft SEAL for BFV. The experiments report a speedup of up to 44 times when packing 2^12 elements from GF(8191^8). We also study a fully packed bootstrapping operation that refreshes 2^15 elements from GF(65537) and obtain an amortized speedup of 12 times.
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History
Submitted: 2024-07-08
Accepted: 2024-09-02
Published: 2024-10-07
Accepted: 2024-09-02
Published: 2024-10-07
How to cite
Robin Geelen, Revisiting the Slot-to-Coefficient Transformation for BGV and BFV. IACR Communications in Cryptology, vol. 1, no. 3, Oct 07, 2024, doi: 10.62056/a01zogy4e-.
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