I Want to Ride My BICYCL : BICYCL Implements CryptographY in CLass Groups

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...

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Bibliographic Details
Published in:Journal of cryptology Vol. 36; no. 3; p. 17
Main Authors: Bouvier, Cyril, Castagnos, Guilhem, Imbert, Laurent, Laguillaumie, Fabien
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2023
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Arithmetic
Coding and Information Theory
Combinatorics
Communications Engineering
Computational Mathematics and Numerical Analysis
Computer Science
Computing on Encrypted Data
Cryptography
Cryptography and Security
Encryption
Fields (mathematics)
Libraries
Networks
Number theory
Probability Theory and Stochastic Processes
Research Article
Multi-party computation
Implementation library
Class group cryptography
Quadratic form arithmetic
Linearly homomorphic encryption
implementation library
linearly homomorphic encryption
class group cryptography
quadratic form arithmetic
multi-party computation
ISSN:0933-2790, 1432-1378
Online Access:Get full text
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Summary: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.
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ISSN:0933-2790
1432-1378
DOI:10.1007/s00145-023-09459-1