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

Joint encryption-encoding schemes has 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 in its 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 plenty of different desirable transmission rates is achievable. The wide variety of codes proposed here makes our cryptosystem applicable on a number of different communication and cryptographic standards.