A Joint Encryption-Encoding Scheme Using QC-LDPC Codes Based on Finite Geometry

TL;DR

This paper introduces a joint encryption-encoding scheme utilizing QC-LDPC codes based on finite geometry, achieving reduced key size, high transmission rates, and strong security against known cryptanalyses, with low computational complexity.

Contribution

The paper presents a novel joint encryption-encoding scheme using finite geometry-based QC-LDPC codes that significantly reduces key size and enhances transmission flexibility.

Findings

Key size reduced to 1/5 of previous systems

Achieves a wide range of transmission rates

Remains secure against known cryptanalyses

Abstract

Joint encryption-encoding schemes have been released to fulfill both reliability and security desires in a single step. Using Low Density Parity Check (LDPC) codes in joint encryption-encoding schemes, as an alternative to classical linear codes, would shorten the key size as well as improving error correction capability. In this article, we present a joint encryption-encoding scheme using Quasi Cyclic-Low Density Parity Check (QC-LDPC) codes based on finite geometry. We observed that our proposed scheme not only outperforms its predecessors in key size and transmission rate, but also remains secure against all known cryptanalyses of code-based secret key cryptosystems. We subsequently show that our scheme benefits from low computational complexity. In our proposed joint encryption-encoding scheme, by taking the advantage of QC-LDPC codes based on finite geometries, the key size decreases to 1/5 of that of the so far best similar system. In addition, using our proposed scheme a wide range of desirable transmission rates are achievable. This variety of codes makes our cryptosystem suitable for a number of different communication and cryptographic standards.