Construction of Odd-Variable Strictly Almost Optimal Resilient Boolean Functions with Higher Resiliency Order via Modifying High-Meets-Low Technique*

Construction of resilient Boolean functions in odd vari-ables having strictly almost optimal (SAO) nonlinearity appears to be a rather difficult task in stream cipher and coding theory. In this paper, based on the modified High-Meets-Low technique, a general construction to ob-tain odd-variable SAO resilient Boolean functions without directly using PW functions or KY functions is presented. It is shown that the new class of functions possess higher resiliency order than the known functions while keeping higher SAO nonlinearity, and in addition the resiliency order increases rapidly with the variable number n.

Automated summary

This paper presents a general construction method to obtain odd-variable SAO resilient Boolean functions using the modified High-Meets-Low technique, without directly using PW functions or KY functions. It is shown that the new class of functions has higher resiliency order and higher SAO nonlinearity than the known functions, with the resiliency order increasing rapidly with the variable number n.