Resistance of Balanced s-Boxes to Linear and Differential Cryptanalysis

In this letter, we study the marginal density of the XOR distribution table, and the linear approximation table entries of regular substitution boxes (s-boxes). Based on this, we show that the fraction of good s-boxes (with regard to immunity against linear and differential cryptanalysis) increases dramatically with the number of input variables. Introduction Differential cryptanalysis [1], and linear cryptanalysis [3] are currently the most powerful cryptanalytic attacks on private-key block ciphers. The complexity of differential cryptanalysis depends on the size of the largest entry in the XOR table, the total number of zeroes in the XOR table, and the number of nonzero entries