A joint encryption-encoding scheme using QC-LDPC codes based on finite geometry

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, a joint encryption-encoding scheme using Quasi-Cyclic Low Density Parity-Check (QC-LDPC) codes based on finite geometry is presented. It is 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. In this paper, we have proposed an idea to make QC-LDPC based cryptosystems secure against reaction attacks. It is subsequently shown that our scheme benefits from low computational complexity. By taking the advantage of QC-LDPC codes based on finite geometry, the key size of our scheme is very close to its target security level. In addition, using the 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 such as Wireless Personal Area Networks (WPAN) and Digital Video Broadcasting (DVB). (c) 2024 Sharif University of Technology. All rights reserved.