Summary: ``We introduce {\tt 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. {\tt BICYCL} provides significant speed-ups on the implementation of the arithmetic of class groups. Concerning cryptographic applications, {\tt BICYCL} is orders of magnitude faster than any previous pilot implementation of the $\ssf{CL}$ 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.''