Novel Standard Polynomial as New Mathematical Basis for Digital Information Encryption Process

[Objective] The proposed approach is based on producing new irreducible polynomials that help reduce the drawbacks of traditional cryptosystems. This work demonstrates the proposed model's efficiency and applicability, which could help researchers and practitioners investigate the proposed model in different cryptosystems and other related systems. In addition, the structure of the proposed polynomial function can be implemented in different cryptosystems with lightweight processing. The primary objective of this work is to present an efficient irreducible polynomial equation that can be implemented with lightweight cryptosystems. [Methodology] The proposed work is based on computing an irreducible polynomial, which is no more than two power multiplications. The structure of the proposed irreducible polynomial is carried out by using the exhaustive search approach and experiment. The mathematical function of the new standard polynomial is applied to generate a vital sequence of the proposed cipher algorithm. Various quantitative and statistical methods are applied to decision sciences at the individual and population levels. [Findings] The generated sequence keys are examined and analyzed using different statistical tests. The analysis output showed a significant random behavior of the generated sequence keys of the proposed cipher algorithm compared with the original cipher algorithm. [Novelty] This work considers a new approach based on the results, the proposed model's originality, and uniqueness in the literature. This work introduced a new standard polynomial function for a lightweight cipher algorithm that was implemented to develop a new lightweight cryptosystem for the digital information encryption process. The current cryptosystems suffer from computational complexity, which exceeds the quadratic power multiplication. Thus, this work presented a new design of the digital information encryption process, which contributed to solving traditional cryptosystems' cost and performance problems.