Coding with Cyclic PAM and Vector Quantization for the RLWE/MLWE Channel

In some lattice-based cryptosystems, the encryption and decryption processes can be interpreted as a noisy communication channel. In this work, we focus on cryptosystems based on the ring learning with errors (RLWE) and module learning with errors (MLWE) problems, e.g. Kyber. We provide new coding schemes for the communication channel involved in these cryptosystems. For encoding we use an error-correction code (ECC) along with modulo Q pulse amplitude modulation (PAM) (for some fixed small prime power Q), and vector dequantization. For decoding we perform vector quantization followed by hard/soft decision decoding (HDD/SDD) for the ECC. This construction provides remarkable reduction in the decryption failure rate (DFR), compared to some earlier proposed coding schemes for the same bitrate. For example, in Kyber encryption scheme, we reduce the DFR from 2−174 (uncoded) to 2−1325 (using HDD) or 2−1414 (using SDD).