Extended SAC: A Review on DC and SAC of 4-bit BFs and S-Boxes and a New Algorithm on DC of S-Boxes based on Various Types of SAC including the Extended Higher Order SAC

Abstract

Bitwise-Xor of two 4-bit patterns is the 4-bit difference between them which carries useful information in Cryptography. The method to analyze cryptographic ciphering algorithms or 4-bit Substitution boxes (S-boxes) with 4-bit differences is known as Differential Cryptanalysis (DC). An analysis of DC of 4-bit bijective Crypto S-boxes based on Differential Distribution Table (DDT) is reviewed including the Strict Avalanche Criteria (SAC) of 4-bit BFs and corresponding S-Boxes categorizing SAC in two orders, namely Simple Order (SO) and Higher Order (HO). A new algorithm of adding an extension of HO-SAC is proposed and considering the comprehensive SAC, which considers SO-SAC, HO-SAC and extended HO-SAC together, the properties of whole set of 65536 4-bit BFs including the comprehensive SAC are analyzed. Another new algorithm to analyze comprehensive SAC properties of 4-bit S-boxes is elaborated based on Differential Analysis Table (DAT) which turns out to be a better tool than DDT in analyzing DC of 4-bit S-boxes.