Correlation Immunity of Boolean Functions

Abstract

The concept of correlation immunity was proposed by Siegenthaler in 1984. It is a security measure to the correlation attack of nonlinear combiners. This chapter first briefly describes the correlation attack of nonlinear combiners, which gives the rationale about why correlation immunity is a reasonable security measure, and then the correlation immunity of Boolean functions is studied. Different approaches to the constructions of Boolean functions are introduced, which yields a way in theory to exhaustively construct all the correlation immune Boolean functions, and such an example is given for the correlation immune Boolean functions in four variables. Correlation immune Boolean function with some other cryptographic properties are also studied in brief. In the end, the concept of correlation immunity is introduced to reflect the resistance against correlation attack when the Boolean function is not correlation immune in the traditional sense.