Network Security by Merging two Robust Tools from the Mathematical Firmament

Significant advances in wireless detection, networking, and IoT technologies presuppose network security and confidentiality demand. Therefore, we develop a novel text encryption framework that has provable security against attacks on cryptosystems. The framework is based on fundamental mathematics and specifically on the Pell-Lucas sequence in conjunction with elliptic curves. We elaborate the plain text by the implementation of three basic steps. Initially, by applying a cyclic shift on the symbol set, we obtain a meaningless plain text. After that, we conceal the elements of the scattered plain text from the adversaries by using the Pell-Lucas sequence, a weight function, and a binary sequence. The binary sequence encodes each component of the diffused plain text into real numbers. In the final step, the encoded scattered plain text is confused by creating permutations over elliptic curves. We then prove that the proposed encryption framework has provable security against brute-force and known-plaintext attack. It is also extremely secure compared with fundamental spacing analysis.