Improved Cost Function in the Design of Boolean Functions Satisfying Multiple Criteria

We develop an improved cost function to be used in simulated annealing followed by hill-climbing to find Boolean functions satisfying multiple desirable criteria such as high nonlinearity, low autocorrelation, balancedness, and high algebraic degree. Using this cost function that does not necessitate experimental search for parameter tuning, the annealing-based algorithm reaches the desired function profiles more rapidly. Some Boolean functions of eight and nine variables have been found, which are unattained in the computer search based literature, in terms of joint optimization of nonlinearity and autocorrelation. Global characteristics of eight-variable Boolean functions generated by algebraic construction or computer search are compared with respect to the sum-of-squared-errors in their squared spectra, which is also proportional to the sum-of-squared-errors in their autocorrelation function, the term ‘error’ denoting the deviation from bent function characteristics. Preliminar...

• Type: Conference
• Year: 2003
• Where: INDOCRYPT
• Authors: Selçuk Kavut, Melek D. Yücel
• Keywords: Boolean Functions, Cost Function, Improved Cost Function, INDOCRYPT 2003