A Recursive Construction Method of S-boxes Satisfying Strict Avalanche Criterion

S(ubstitution)-boxes are quite important components of modern symmetric cryptosystems. S-boxes bring nonlinearity to cryptosystems and strengthen their cryptographic security. An S-box satisfies the strict avalanche criterion (SAC), if and only if for any single input bit of the S-box, the inversion of it changes each output bit with probability one half. We present some interesting properties of S-boxes and propose an efficient and systematic means of generating arbitrary input size bijective S-boxes satisfying the SAC by applying simple rules recursively given 3-bit input bijectective S-box(es) satisfying the SAC.