A highly nonlinear S-box based on a fractional linear transformation.

Shabieh Farwa,Lubna Idrees,Tariq Shah

doi:10.1186/s40064-016-3298-7

Shabieh Farwa, Lubna Idrees + Show 1 more

Open Access

https://doi.org/10.1186/s40064-016-3298-7

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Abstract

We study the structure of an S-box based on a fractional linear transformation applied on the Galois field GF(2^{8}). The algorithm followed is very simple and yields an S-box with a very high ability to create confusion in the data. The cryptographic strength of the new S-box is critically analyzed by studying the properties of S-box such as nonlinearity, strict avalanche, bit independence, linear approximation probability and differential approximation probability. We also apply majority logic criterion to determine the effectiveness of our proposed S-box in image encryption applications.

Highlights

The advanced encryption standard (AES) (Daemen and Rijmen 2002) is based on the substitution permutation network (SPN) which applies several layers of substitution and permutation
Motivated by some recently presented designs, we in this paper propose an algorithm to structure an 8 × 8 substitution box (S-box) using fractional linear transformation applied on the Galois field GF (28 )
In “Statistical analyses of S-box” section we perform some statistical analysis based on the image encryption application of the S-box and in “Conclusion” section we present conclusion regarding the significance of the new S-box when critically observed in comparison with the previously known models

Summary

Introduction

The advanced encryption standard (AES) (Daemen and Rijmen 2002) is based on the substitution permutation network (SPN) which applies several layers of substitution and permutation. Motivated by some recently presented designs, we in this paper propose an algorithm to structure an 8 × 8 S-box using fractional linear transformation applied on the Galois field GF (28 )

Results

Conclusion