Abstract
Substitution box (S-box), being the only nonlinear component, contributes to the confusion creating capability of a cryptosystem. Keeping in view the predominant role of S-box, many design algorithms to synthesize cryptographically stronger S-boxes have gained pivotal attention. A quick review of these algorithms shows that all these ideas mainly concentrate on the choice of bijective Boolean functions, with nonobservance to the irreducible polynomial that generates the Galois field. In this paper, we propose that the selection of irreducible polynomial has a deep influence on the highly desirable features of an S-box such as nonlinearity, strict avalanche, bit independence, linear approximation probability, and differential approximation probability. We underpin our claim by investigating a detailed model, which deploys the same algorithm but different polynomials and produces unusual changes in the results regarding the performance parameters of S-box.
Highlights
Electronic exchange of data has undoubtedly revolutionized the communication in recent years but, on the other hand, the secure transfer of confidential material over Internet has become the biggest challenge nowadays
To achieve the desired level of security, many techniques such as cryptography, watermarking, and steganography have been the major focus of research for past few years [1,2,3,4,5]
The symmetric key cryptography can be further split into two types: block ciphers and the stream ciphers
Summary
Electronic exchange of data has undoubtedly revolutionized the communication in recent years but, on the other hand, the secure transfer of confidential material over Internet has become the biggest challenge nowadays. The indispensable involvement of S-box to induce complexity and nonlinearity motivates studying the properties and algorithms for safer and more reliable S-boxes In this regard, many advanced structural developments are witnessed in literature. An S-box is the salient component used to produce confusion in the data, it is worth studying that the confusion creating ability is associated with the choice of the irreducible polynomial used to form the background Galois field. In [9], Hussain et al presented an algorithm for generating S-box through the application of a linear fractional transformation on the Galois field GF(28 ), structured by the polynomial X8 + X4 + X3 + X2 + 1.
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