Improved S-box construction from binomial power functions

Abstract

Substitution boxes with strong cryptographic properties are commonly used in block ciphers to provide the crucial property of nonlinearity. This is important to resist standard attacks such as linear and differential cryptanalysis. A cryptographically-strong s-box must have high nonlinearity, low differential uniformity and high algebraic degree. In this paper, we improve previous s-box construction based on binomial operation on two power functions over the finite field F2 8. By widening the scope of the power function and introducing new manipulation techniques, we managed to obtain cryptographically-strong s-boxes which are better than the previous construction.