Secure communication through reliable S-box design: A proposed approach using coset graphs and matrix operations

Abstract

Protection of sensitive information has been always the major security concern since decades to withstand against illegitimate access and usage. Substitution-boxes (S-boxes) are vital components of any modern day cryptographic system that allows us to ensure its resistance to attacks. The prime problem with creating S-box is that we are generally unable to discover a consistent distribution among its numerous features to withstand diverse cryptanalysis attacks. The majority of S-boxes investigated in the literature has good cryptographic defenses against some attacks but are susceptible to others. Keeping these considerations in mind, this paper proposes a novel approach for S-box design based on a pair of coset graphs and a newly defined operation of row and column vectors on a square matrix. Several standard performance assessment criteria are used to evaluate the reliability of proposed approach, and the results demonstrate that the developed S-box satisfies all criterions for being robust for secure communication and encryption.

Keywords: Block cipher; Coset graphs; Image encryption; Substitution-box.

Fig. 1

Coset graph of M over $F_{23}\cup \left\{\infty \right\}$.

Fig. 2

One of the patches $P_i$ of $D_1$.

Fig. 3

The patch $P_7$ of $D_1$.

Fig. 4

Some part of $D_2$.

Fig. 5

Graphical version of the arrangement 1.

Fig. 6

Graphical version of the arrangement 2.

Fig. 7

Graphic of the row vector's operation on the initial S-box.

Fig. 8

Graphic of the column vector's operation on the initial S-box.

Fig. 9

Block diagram describing the suggested S-box construction.

Fig. 10

Original image and the encrypted images using two rounds of encryption a) Cameraman, b) Pepper and c) Baboon.