Towards a generalized Regev's cryptosystem and its related signing cryptosystem: An implementation for hashes and simple ASCII texts in Python

Abstract Quantum computing makes most of nowadays protocols breakable. Fortunately, this technology is still too expensive to be used by anybody. The cryptosystems relying on the LWE problem are still an excellent choice to prepare for the democratization of quantum computing. The motivation of this work is to implement a post-quantum complete and complex asymmetric cryptosystem using the learning with error (LWE) problem. In fact, it is impossible or hard to find a cryptosystem in Python in the literature like the implemented one. As a contribution, this work proposes an implementation of a generalized Regev's Cryptosystem and its related signature and verification functions for achieving the quantum-safety property.\\ It also tests the validity of a list of primes for specified values. Finally, this work completes the cryptosystem with the signing and verification algorithms. These algorithms are news for the scientific community. Errors and omissions excepted. These implementations are based on hard problems related to lattices