TITLE:
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*
AUTHORS:
Sankhanil Dey, Ranjan Ghosh
KEYWORDS:
Linear Cryptanalysis, Differential Cryptanalysis, Substitution Boxes, S-Boxes, Cryptography, Cryptanalysis
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.8 No.3,
March
22,
2018
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 part of cryptanalysis of 4-bit S-boxes. Existence of all 4-bit
linear relations have been counted for all of 16 input and 16 output 4-bit bit
patterns of 4-bit 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
two 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 vectors (IPVs) and output
Boolean functions (BFs) of a particular 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 of 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 BFs in difference output S-boxes. Better
the number of Balanced BFs, Better the security.