Information- and Coding-Theoretic Analysis of the RLWE/MLWE Channel

Several cryptosystems based on the Ring Learning with Errors (RLWE) problem have been proposed within NIST post-quantum cryptography standardization process, e.g., NewHope. Furthermore, there are systems like Kyber which closely related MLWE assumption. Both previously mentioned schemes result in a non-zero decryption failure rate (DFR). The combination of encryption and for these kinds algorithms can be interpreted as data transmission over noisy channel. To best our knowledge this paper is first work that analyzes capacity We show how to modify such input alphabets corresponding channels increased. In particular, we present lower bounds their capacities significantly increased compared standard proposals literature. under common assumption stochastically independent coefficient failures, give achievable rates both Gilbert-Varshamov bound concrete code constructions using BCH codes. By means constructions, either increase total bitrate (by factor 1.84 by 7 NewHope) while guaranteeing same DFR or bitrate, reduce all considered (e.g., NewHope from 2?216 2?12769).