A substitution box generator, its analysis, and applications in image encryption

•We proposed some necessary tests to analyze the cryptographic properties of an S-box generator.•Presented a new S-box generator based on elliptic curves and characterized its cryptographic properties.•Compared to several existing S-box generators over different mathematical structures, our proposed generator is cryptographically secure.•We proposed an image encryption scheme based on the proposed generator that can create a highly confused ciphertext. A substitution box (S-box) is the only non-linear component in many cryptosystems. Recently, S-box generators have been used intensively in many modern cryptosystems to obtain ciphertext that is secure against modern cryptanalysis. The purpose of these generators is to (i) efficiently generate (ii) dynamic S-boxes (iii) with optimal cryptographic properties (iv) that can be used as a group to create a secure ciphertext. However, no formal methods have been introduced that can analyze if an S-box generator can satisfy conditions (i), (ii) and (iv). The aim of this paper is fourfold: we formally discuss five methods to test if an S-box generator satisfies (i), (ii) and (iv). In the second part, we propose a new S-box generator based on isomorphic ordered elliptic curves that satisfies conditions (i)-(iv). In the third part, we conduct a detailed comparison of our S-box generator with some of the state-of-the-art S-box generators. From the comparison, we conclude that our generator is more secure and suitable for encryption. In the fourth part, we discuss an application of the proposed S-box generator for image encryption. Experimental results reveal that our S-box generator can generate a highly secure ciphertext for a plain text with a high correlation.