Constructions of plateaued correctors with high correction order and good nonlinearity via Walsh spectral neutralization technique

Abstract

A corrector is a critical component of True Random Number Generators (TRNGs), serving as a post-processing function to reduce statistical weaknesses in raw random sequences. It is important to note that a \(\textit{t}\)-resilient Boolean function is a \(\textit{t}\)-corrector, while the converse is not necessarily true. Building upon the pioneering method introduced by Zhang in 2023 for constructing nonlinear correctors with correction order one greater than resiliency order, this paper presents for the first time two approaches for constructing nonlinear plateaued correctors with correction order at least two greater than resiliency order via Walsh spectral neutralization technique, and the resulting correctors have algebraic degree at least \(\text {2}\). The first approach yields \(\textit{n}\)-variable plateaued correctors with correction order \(\textit{n}-\text {2}\) and resiliency order approximately \(\textit{n}- \text {log}_\text {2} \textit{n}\). The nonlinearity and algebraic degree of the resulting correctors are also analyzed, demonstrating that they meet both Siegenthaler’s and Sarkar-Maitra’s bounds. Another approach based on Walsh spectral neutralization technique for constructing \(\textit{n}\)-variable plateaued correctors is proposed. This approach facilitates the design of semi-bent correctors with algebraic degree \(\lceil \frac{\textit{n}}{\text {2}} \rceil \), correction order \(\lfloor \frac{\textit{n}}{\text {2}} \rfloor -\text {1}\) and resiliency order approximately \( \frac{\textit{n}}{\text {4}} \).