MDPC Code-Based Constructions and Their Decoding in Post-Quantum Cryptosystems

Abstract

Quantum computers pose a threat to most of the popular public-key cryptosystems. This has prompted a search for good quantum-safe cryptographic protocols. Codebased cryptography is one promising approach, as its security relies on coding theory problems which are thought to be hard for both classical and quantum computers. The McEliece cryptosystem is the oldest code-based cryposystem and it is thought to be secure to this day. National Institute of Standards and Technology has started a project for standardizing quantum-resistant public-key cryptosystems. Among the candidates are three code-based cryptosystems, one of which is based on a McEliece variant which uses quasi-cyclic moderate-density parity-check (QC-MDPC) codes. We analyze a novel decoder in application to this McEliece variant and compare it to the existing decoders. Our results indicate that this decoder can be a viable alternative to the existing decoders, offering a trade-off between computational complexity and key and ciphertext lengths. We also analyze a new tail-biting unit memory convolutional QC-MDPC code construction as an alternative to the standard QC-MDPC codes used in this variant of the McEliece cryptosystem. We show that this code construction can be a better choice in settings where ephemeral keys are used.