On the algebraic immunity of multiplexer Boolean functions

Abstract

Abstract A multiplexer generator is a device that accepts two or more inputs and based on some logic sends one of them as output. In a special case when inputs to a multiplexer generator are 2 k {2}^{k} bits and one of them is selected according to the value of a k k -bit number, a multiplexer generator can be regarded as a Boolean function in 2 k + k {2}^{k}+k variables. We call this generator a multiplexer Boolean function. Boolean functions serve as combiners and filters in cryptographic designs. The study of their cryptographic strength attracts the cryptographer because of the extremely simple and cost effective of their design. The study of algebraic attacks on multiplexer generators is another major concern to judging the suitability for its use in cryptographic designs. In this article, we calculate the algebraic immunity of the multiplexer Boolean function, which is not an obvious task in the case of a Boolean function like a multiplexer generator.