Abstract

S(ubstitution)-boxes are quite important components of modern symmetric cryptosystems (in particular, block ciphers) in the sense that S-boxes bring nonlinearity to block ciphers and strengthen their cryptographic security. An S-box is said to satisfy 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. In this thesis, with the concrete proof of cryptographical properties of S-boxes satisfying the SAC, we propose a variety of provable construction methods for S-boxes satisfying the SAC. For Boolean S-boxes satisfying the SAC, we can construct and enlarge them by using concatenation, Kronecker (or direct) product, and dyadic shift. For bijective S-boxes satisfying the SAC, when an n-bit input Boolean function and an n-bit input bijective function satisfying the SAC are given, the combined function is proved to become an (n+1)-bit bijective function satisfying the SAC as well. A...

Citations