A parallel approach in computing correlation immunity up to six variables

Abstract

We show the use of a reconfigurable computer in computing the correlation immunity of Boolean functions of up to 6 variables. Boolean functions with high correlation immunity are desired in cryptographic systems because they are immune to correlation attacks. The SRC-6 reconfigurable computer was programmed in Verilog to compute the correlation immunity of functions. This computation is performed at a rate that is 190 times faster than a conventional computer. Our analysis of the correlation immunity is across all n-variable Boolean functions, for 2 ⦤ n ⦤ 6, thus obtaining, for the first time, a complete distribution of such functions. We also compare correlation immunity with two other cryptographic properties, nonlinearity and degree.