Abstract
Lattice-based homomorphic encryption (HE) schemes are based on the noisy encryption technique, where plaintexts are masked with some random noise for security. Recent advanced HE schemes rely on a decomposition technique to manage the growth of noise, which involves a conversion of a ciphertext entry into a short vector followed by multiplication with an evaluation key. Prior to this work, the decomposition procedure turns out to be the most time-consuming part, as it requires discrete Fourier transforms (DFTs) over the base ring for efficient polynomial arithmetic. In this paper, an expensive decomposition operation over a large modulus is replaced with relatively cheap operations over a ring of integers with a small bound. Notably, the cost of DFTs is reduced from quadratic to linear with the level of a ciphertext without any extra noise growth. We demonstrate the implication of our approach by applying it to the key-switching procedure. Our experiments show that the new key-switching method achieves a speedup of 1.2–2.3 or 2.1–3.3 times over the previous method, when the dimension of a base ring is \(2^{15}\) or \(2^{16}\), respectively.
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Notes
- 1.
Here we assume for simplicity that two inputs have the same modulus, but a more general case will be discussed later.
- 2.
The original CKKS scheme enables to encode a vector of complex numbers to a plaintext in R. For the sake of brevity, we assume that an input of the encryption function is given as a plaintext polynomial.
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Acknowledgement
This work was supported by Samsung Research Funding & Incubation Center of Samsung Electronics under Project Number SRFC-TB2103-01.
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Kim, M., Lee, D., Seo, J., Song, Y. (2023). Accelerating HE Operations from Key Decomposition Technique. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14084. Springer, Cham. https://doi.org/10.1007/978-3-031-38551-3_3
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