One of the most crucial elements in the design of a block cipher is the substitution box or S-box. Its cipher strength directly impacts the cipher algorithm's security, and the block cipher algorithm requires a good S-box. According to the cryptanalysis result of the S-box construction in AES: (1) the number of irreducible polynomials can be increased to 30; (2) the affinity transformation constant c can be chosen from all elements if the existence of fixed points and reverse fixed points in an S-box is ignored; and (3) the S-box in AES is fixed, which poses possible security risks to the AES algorithm. The study above led us to build a non-degenerate 2D enhanced quadratic map (2D-EQM) with unpredictability and ergodicity. From there, we generated affine transformation constants and affine transformation matrices, which were then applied to seed S-boxes to create a batch of strongly nonlinear S-boxes. Finally, we assessed the performance of suggested S-boxes using six criteria. Security and statistical research showed that the suggested S-box batch generation procedure was practical and effective.

Cryptography serves as the cornerstone for safe communication and data security in today's digital environment. Because they feature substitution boxes, substitution-permutation networks (SPNs) are crucial for cryptographic algorithms such as the popular Advanced Encryption Standard (AES). The structure and properties of S-boxes have a significant impact on the overall security of cryptographic systems. This article aims to improve cryptographic security through unique S-box construction methodologies. The proposed S-boxes improve the security features by employing chaotic maps and Galois fields, which go beyond traditional design approaches. The S-boxes were analyzed and the weaknesses were removed to design strong candidate S-boxes. The efficiency of the proposed S-boxes in increasing cryptographic resilience is thoroughly explored thereby taking nonlinearity, strict avalanche requirements, bit independence constraints, linear approximation, and differential approximation into account. The dynamic S-boxes have average scores of nonlinearity, strict avalanche criteria(SAC), nonlinearity of Bit Independence Criteria (BIC Nonlinearity), SAC of Bit Independence Criteria (BIC SAC), Linear Approximation Probability (LAP) and Differential Approximation Probability (DAP) is 111.1025, 111.1022, 0.5014, 0.5024, 111.1082, 111.0964, 0.5024, 0.5022, 0.0726, 0.0729 and 0.0214, 0.0219, respectively. Furthermore, given the prevalence of images in modern communication and data storage, this work studies the seamless incorporation of advanced S-boxes into image encryption systems. With its thorough research, the paper contributes to the current discussion on cryptographic security by providing theoretical understandings and practical solutions to improve digital communication and data security in an era of rising cyber dangers and ubiquitous connectivity.