Trade-off between Performance and Security for Coding and Ring Learning With Errors-based Diffie-Hellman Cryptosystems

In this work, we provide a complexity analysis of the trade-off between performance and security for two post-quantum key exchange cryptosystems: a protocol based on coding theory (Ouroboros) and the lattice-based ring learning with errors key exchange (RLWE). Ouroboros is considered secure because, according to the general belief, the Quasi-Cyclic Syndrome Decoding (QCSD) problem is NP-hard. The RLWE cryptosystem is considered secure due to the hardness of the Learning With Errors problem, that is proven to be as hard as the Shortest Vector Problem (SVP). We analyze the tradeoff between performance and security for those cryptosystems in comparison with the Discrete Logarithm Problem (DLP) and the Integer Factorization Problem (IFP). Regarding key lengths, RLWE outperforms Ouroboros for desired security levels.