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 cryptographyquadratic form arithmeticimplementation librarylinearly 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
Creative Commons Attribution
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},
      url = {https://eprint.iacr.org/2022/1466}
}
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