A smart review and two new techniques using 4-bit Boolean functions for cryptanalysis of 4-bit crypto S-boxes

Abstract

ABSTRACT 4-bit linear relations play an important role in cryptanalysis of 4-bit crypto S-boxes. 4-bit finite differences have also been a major concern in cryptanalysis of 4-bit S-boxes. In linear cryptanalysis of the concerned 4-bit crypto S-box the existences of all 4-bit linear relations have been counted for all 16 input and corresponding 16 output 4-bit bit patterns and noted in linear approximation table (LAT). The count of existing finite differences from each element of output S-boxes to distant output S-boxes has been noted at the difference distribution table in differential cryptanalysis of 4-bit S-boxes. In this paper, a brief review of these two cryptanalytic methods for 4-bit S-boxes has been introduced in a very lucid and conceptual manner. A new cryptanalysis technique to search for the existing 4-bit linear relations for a particular S-box in which the search is limited to find the existing linear relations out of total 256, 4-bit linear relations has been reported in this paper. Another is to find the number of balanced difference BFs in difference output S-boxes of a 4-bit output S-box. The better the number of balanced BFs, the better the security.