A Novel Algebraic Technique for Design of Computational Substitution-Boxes Using Action of Matrices on Galois Field

• Main Authors: Nasir Siddiqui, Hira Khalid, Fiza Murtaza, Muhammad Ehatisham-Ul-Haq, Muhammad Awais Azam
• Format: Article
• Language: English
• Published: IEEE 2020-01-01
• Series: IEEE Access
• Subjects: Advanced encryption standard; confusion; cryptography; Galois field; image encryption; substitution-box
• Online Access: https://ieeexplore.ieee.org/document/9243939/

Cryptography entails the practice of designing mathematical algorithms to secure data communication over insecure networks in the presence of adversaries. In this aspect, a cryptographic algorithm encrypts the confidential data and converts it into a non-readable text for adversaries. Advanced Encryption Standard (AES) is the most effective encryption algorithm proposed till now. Substitution-box (S-box) is the most crucial and only nonlinear component in AES (or any cryptographic algorithm), which provides data confusion. A highly nonlinear S-box offers high confidentiality and security against cryptanalysis attacks; hence, the design of S-box is very crucial in any encryption algorithm. To address this challenge, we propose the action of matrices (conforming to the basis of P₇ [Z₂]) on the Galois field GF (2⁸). Consequently, a novel algebraic technique for S-box construction to generate highly nonlinear 8 × 8 S-boxes based on by our proposed algorithm, we obtain 1.324×10¹⁴ different S-boxes. Standard S-box tests analyze the cryptographic strength of our proposed S-boxes. The examined results show that the proposed S-boxes possess state-of-the-art cryptographic properties. Moreover, we also demonstrate the effectiveness of the proposed S-boxes in image encryption applications using the majority logic criterion.