Cryptosystem for Post-Quantum Age Based on Moderate-Density Parity-Check (MDPC) Codes

Abstract

With the technology for quantum computers being actively developed by researchers worldwide, new methods for encrypting of sensitive data are needed. As a consequence of invention of Shor’s algorithm, all cryptographic schemes based on finding the prime factors will become insecure, which include various asymmetric cryptosystems used today. The McEliece cryptosystem is based on the difficulty to distinguish structured linear codes from random linear codes. As it is believed to be immune to known attacks possible with a quantum computer, the McEliece cryptosystem is one of the main candidates for ensuring the confidentiality of sensitive data in a post-quantum environment. However, the construction of McEliece suffers from a large key size which makes using the scheme inefficient. There have been numerous variations to the original construction of the McEliece cryptosystem, but most of them have been proven to be insecure. One of the best candidates is the McEliece cryptosystem variation based on moderate density parity-check codes and its quasi-cyclic variant, which has not been successfully attacked while reducing the key size drastically. In this work, an overview of both the original construction of the McEliece cryptosystem and its modern variant is given, and iterative decoding algorithms used in decrypting messages in the cryptosystem are presented and analyzed.