Exploring General Cyclotomic Rings in Torus-Based Fully Homomorphic Encryption: Part I - Prime Power Instances

Philippe Chartier; Michel Koskas; Mohammed Lemou

Paper 2025/488

Exploring General Cyclotomic Rings in Torus-Based Fully Homomorphic Encryption: Part I - Prime Power Instances

Philippe Chartier

, French Institute for Research in Computer Science and Automation

Michel Koskas, Ravel Technologies

Mohammed Lemou, Centre National de la Recherche Scientifique

Abstract

In the realm of fully homomorphic encryption on the torus, we investigate the algebraic manipulations essential for handling polynomials within cyclotomic rings characterized by prime power indices. This includes operations such as modulo reduction, computation of the trace operator, extraction, and the blind rotation integral to the bootstrapping procedure, all of which we reformulate within this mathematical framework.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: fully homomorphic encryption residue number system trace operator extraction bootstrapping
Contact author(s): philippe chartier @ inria fr
michel koskas @ raveltech io
mohammed lemou @ univ-rennes fr
History: 2025-03-17: approved; 2025-03-14: received; See all versions
Short URL: https://ia.cr/2025/488
License: CC BY

BibTeX

@misc{cryptoeprint:2025/488,
      author = {Philippe Chartier and Michel Koskas and Mohammed Lemou},
      title = {Exploring General Cyclotomic Rings in Torus-Based Fully Homomorphic Encryption: Part I - Prime Power Instances},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/488},
      year = {2025},
      url = {https://eprint.iacr.org/2025/488}
}