Construction of Substitution Boxes Using Finite Fields

Abstract

Substitution boxes (S-boxes) play a crucial role in modern cryptographic algorithms, providingnon-linear transformations that enhance the security of data encryption. S-boxes are essentialcomponents of symmetric key ciphers, such as Advanced Encryption Standard (AES) and DataEncryption Standard (DES). Non-linearity is a fundamental property that resists linear attacksand enhances the cryptographic strength of S-boxes. Constructing secure and efficient S-boxeswith high non-linearity is a critical challenge in cryptography. The problem of this research isto develop a systematic approach for constructingsubstitution boxes (S-boxes) using finite fields,with a particular focus on achieving optimal non-linearity to enhance the security of cryptographicalgorithms.