A Joint encryption system based on McEliece and RLWE

To enhance cryptographic security in the post-quantum era, this paper proposes a hybrid encryption system that combines the strengths of the McEliece and Ring-Learning With Errors (RLWE) algorithms. The system leverages the generalized logistic map to establish a mapping between the public keys of both systems. Inspired by their similar encryption mechanisms, a novel encryption formula is introduced. The Joint McEliece and RLWE Cryptosystem (JMRC) is an asymmetric cryptosystem designed to offer maximum security. Its integrated approach leverages the error correction capabilities of McEliece, reducing the decryption failure rate (DFR) and enhancing performance in Additive White Gaussian Noise (AWGN) channels, ultimately leading to a lower bit error rate (BER). When the signal-to-noise ratio (SNR) reaches 3.4 dB, the BER of the JMRC system drops to 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup>.