A Cryptographic Algorithm using Polynomial Interpolations for Mitigating Key-Size Based Attacks

Abstract

Confidentiality is one of the fundamental aspects to consider while securing wireless communication. Endeavouring current developments will catch up with the conventional cryptographic methods soon than expected; therefore, a new path is indispensable. In this context, this article presents an innovative idea of using polynomials to achieve a higher level of data privacy. Polynomials' strength lies in their irreducible property, which makes them plausibly appropriate for cryptography. Thenceforth, two novel schemes are proposed based on root-finding polynomial interpolations such as Bisection, Newton-Raphson, and Secant. Relying on these techniques, while the first scheme performs substitution, the BI-New scheme performs substitution, rotation, replacement, and substitution. Hence, both schemes provide confusion and diffusion, a fundamental security aspect. Besides, these algorithms utilise initial points to extract the exact root of the polynomial p1(y) =0. On the basis thereof, an algorithm is developed to retrieve the initial data points. Consequently, the decryption is accomplished in reverse order by evaluating a function. The proposed scheme has unique characteristics, including non-linear interpolating polynomials, roots of non-linear algebraic equations, and non-linear functions. Due to the amalgamation of various non-linear methods and randomised variables, the methods are one-way functions that can endure several assaults. Lastly, the algorithm's security is illustrated by multiple state-of-the-art quantitative metrics such as time complexity, accuracy, memory usage, key space analysis, key sensitivity analysis, robustness analysis, and statistical analysis.