I want to ride my BICYCL: BICYCL Implements CryptographY in CLass groups

Cyril Bouvier; Guilhem Castagnos; Laurent Imbert; Fabien Laguillaumie

Paper 2022/1466

I want to ride my BICYCL: BICYCL Implements CryptographY in CLass groups

Cyril Bouvier, Montpellier Laboratory of Informatics, Robotics and Microelectronics

Guilhem Castagnos, Institut de Mathématiques de Bordeaux

Laurent Imbert, Montpellier Laboratory of Informatics, Robotics and Microelectronics

Fabien Laguillaumie, Montpellier Laboratory of Informatics, Robotics and Microelectronics

Abstract

We introduce BICYCL an Open Source C++ library that implements arithmetic in the ideal class groups of imaginary quadratic fields, together with a set of cryptographic primitives based on class groups. It is available at https://gite.lirmm.fr/crypto/bicycl under GNU General Public License version 3 or any later version. BICYCL provides significant speed-ups on the implementation of the arithmetic of class groups. Concerning cryptographic applications, BICYCL is orders of magnitude faster than any previous pilot implementation of the CL linearly encryption scheme, making it faster than Paillier’s encryption scheme at any security level. Linearly homomorphic encryption is the core of many multi-party computation protocols, sometimes involving a huge number of encryptions and homomorphic evaluations: class group-based protocols become the best solution in terms of bandwidth and computational efficiency to rely upon.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published by the IACR in JOC 2023
DOI: 10.1007/s00145-023-09459-1
Keywords: class group cryptography quadratic form arithmetic implementation library linearly homomorphic encryption
Contact author(s): cyril bouvier @ lirmm fr
guilhem castagnos @ math u-bordeaux fr
laurent imbert @ lirmm fr
Fabien Laguillaumie @ lirmm fr
History: 2023-09-13: last of 2 revisions; 2022-10-26: received; See all versions
Short URL: https://ia.cr/2022/1466
License: CC BY

BibTeX

@misc{cryptoeprint:2022/1466,
      author = {Cyril Bouvier and Guilhem Castagnos and Laurent Imbert and Fabien Laguillaumie},
      title = {I want to ride my BICYCL: BICYCL Implements CryptographY in CLass groups},
      howpublished = {Cryptology ePrint Archive, Paper 2022/1466},
      year = {2022},
      doi = {10.1007/s00145-023-09459-1},
      note = {\url{https://eprint.iacr.org/2022/1466}},
      url = {https://eprint.iacr.org/2022/1466}
}