Comparison analysis and efficient implementation of reconciliation-based RLWE key exchange protocol

Error reconciliation is an important technique for Learning With Error (LWE) and Ring-LWE (RLWE)-based constructions. In this paper, we present a comparison analysis on two error reconciliation-based RLWE key exchange protocols: Ding et al. in 2012 (DING12) and Bos et al. in 2015 (BCNS15). We take them as examples to explain core idea of error reconciliation, building key exchange over RLWE problem, implementation, real-world performance and compare them comprehensively. We also analyse a LWE key exchange “Frodo” that uses an improved error reconciliation mechanism in BCNS15. To the best of our knowledge, our work is the first to present at least 128-bit classic (80-bit quantum) and 256-bit classic (>200-bit quantum) secure parameter choices for DING12 with efficient portable C/C++ implementations. Benchmark shows that our efficient implementation is 11x faster than BCNS15 and one key exchange execution only costs 0.07ms on a 4-year-old middle range CPU. Error reconciliation is 1.57x faster than BCNS15