Low-Latency Bootstrapping for CKKS using Roots of Unity

Jean-Sébastien Coron; Robin Köstler

Paper 2025/651

Low-Latency Bootstrapping for CKKS using Roots of Unity

Jean-Sébastien Coron, University of Luxembourg

Robin Köstler, University of Luxembourg

Abstract

We introduce a new bootstrapping equation for the CKKS homomorphic encryption scheme of approximate numbers. The original bootstrapping approach for CKKS consists in homomorphically evaluating a polynomial that approximates the modular reduction modulo q. In contrast, our new bootstrapping equation directly embeds the additive group modulo q into the complex roots of unity, which can be evaluated natively in the CKKS scheme. Due to its reduced multiplicative depth, our new bootstrapping equation achieves a 7x latency improvement for a single slot compared to the original CKKS bootstrapping, though it scales less efficiently when applied to a larger number of slots.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Fully Homomorphic Encryption CKKS scheme
Contact author(s): jscoron @ gmail com
robin koestler @ uni lu
History: 2025-04-13: approved; 2025-04-09: received; See all versions
Short URL: https://ia.cr/2025/651
License: CC BY

BibTeX

@misc{cryptoeprint:2025/651,
      author = {Jean-Sébastien Coron and Robin Köstler},
      title = {Low-Latency Bootstrapping for {CKKS} using Roots of Unity},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/651},
      year = {2025},
      url = {https://eprint.iacr.org/2025/651}
}