An algorithm for construction of substitution box based on subfield of galois field GF(216) and dynamic linear fractional transformation

• Published in: Multimedia tools and applications Vol. 83; no. 19; pp. 56347 - 56368
• Main Authors: Zafar, Sohail, Idrees, Bazgha, Rashid, Tabasam
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2024; Springer Nature B.V
• Subjects: Algebra; Algorithms; Computer Communication Networks; Computer Science; Construction; Cryptography; Data encryption; Data Structures and Information Theory; Diffusion barriers; Multimedia; Multimedia Information Systems; Nonlinearity; Polynomials; Special Purpose and Application-Based Systems; Substitutes; Image encryption; S-Box; Galois field; Linear fractional transformation
• ISSN: 1573-7721; 1380-7501; 1573-7721
• DOI: 10.1007/s11042-023-17763-y

In block encryption algorithms the only nonlinear component, which creates confusion and diffusion, is substitution box (S-Box). Therefore, carefully selection of S-Box is an important task. In this article, an algorithm is presented for the construction of 8 × 8 S-Box based on all subfields of Galois Field G F 2 16 and linear fractional transformation. Proposed algorithm is easy and simple but significantly complex for the attackers as it utilizes all subfields of G F ( 2 16 ) corresponding to all primitive irreducible polynomials for making G F ( 2 16 ) . An illustrating S-Box is also developed which is showing good structural characteristics such as it has no fixed point with 108.5 nonlinearity and 0.5020 strict avalanche. In the last, illustrated S-Box is applied on images for checking the performance under various criteria available in the literature. Obtained results of analyses are compared to well-known S-Boxes and found better in the comparison.