S-Box on Subgroup of Galois Field

Abstract

In substitution−permutation network as a cryptosystem, substitution boxes play the role of the only nonlinear part. It would be easy for adversaries to compromise the security of the system without them. 8-bit S-boxes are the most used cryptographic components. So far, cryptographers were constructing 8-bit S-boxes used in cryptographic primitives by exhaustive search of permutations of order 256. However, now for cryptographic techniques with 8-bit S-boxes as confusion layers, researchers are trying to reduce the size of S-box by working with a small unit of data. The aim is to make the techniques compact, fast and elegant. The novelty of this research is the construction of S-box on the elements of the multiplicative subgroup of the Galois field instead of the entire Galois field. The sturdiness of the proposed S-box against algebraic attacks was hashed out by employing the renowned analyses, including balance, nonlinearity, strict avalanche criterion, and approximation probabilities. Furthermore, the statistical strength of the S-box was tested by the majority logic criterion. The fallouts show that the S-box is appropriate for applications for secure data communications. The S-box was also used for watermarking of grayscale images with good outcomes.

Keywords

• data communication
• S-box
• encryption
• image processing
• watermarking