Paper 2017/1161

A Review of Existing 4-bit Crypto S-box cryptanalysis Techniques and Two New Techniques with 4-bit Boolean Functions for Cryptanalysis of 4-bit Crypto S-boxes.

Sankhanil Dey and Ranjan Ghosh

Abstract

4-bit Linear Relations play an important role in Cryptanalysis of 4-bit Bijective Crypto S-boxes. 4-bit finite differences also a major part of cryptanalysis of 4-bit substitution boxes. Count of existence of all 4-bit linear relations, for all of 16 input and 16 output 4-bit bit patterns of 4-bit bijective crypto S-boxes said as S-boxes has been reported in Linear Cryptanalysis of 4-bit S-boxes. Count of existing finite differences from each element of output S-boxes to distant output S-boxes have been noted in Differential Cryptanalysis of S-boxes. In this paper a brief review of these cryptanalytic methods for 4-bit S-boxes has been introduced in a very lucid and conceptual manner. Two new Analysis Techniques, one to search for the existing Linear Approximations among the input Boolean Functions (BFs) and output BFs of a particular 4-bit S-Box has also been introduced in this paper. The search is limited to find the existing linear relations or approximations in the contrary to count the number existent linear relations among all 16 4-bit input and output bit patterns within all possible linear approximations. Another is to find number of balanced 4-bit BFs in difference output S-boxes. Better the number of Balanced BFs, Better the security.

Note: This is an original and exhaustive work on Cryptanalysis of s-boxes used in public key cryptography.