A fast and secure public-key image encryption scheme based on Mordell elliptic curves

•Proposed a fast image encryption scheme by generating a substitution box and random numbers over elliptic curves.•The computational complexity of the scheme is independent of the point computation over elliptic curves.•Secrete keys are highly sensitive to plain text, and hence the scheme is highly secure.•Generated highly secure ciphertexts for all standard images in the USC-SIPI image database.•The scheme has high security against modern cryptanalyses such as differential attacks, statistical attacks, brute-force attacks, and known plain text and chosen plain text attacks.•The scheme has low computational complexity and high security as compared to state-of-the-art schemes over elliptic curves and chaotic systems. Encryption schemes based on elliptic curves (ECs) have shown high resistance against modern cryptanalysis. However, these schemes involve heavy computation for the generation of points over ECs, and therefore they are not suitable for communication systems such as sensor networks and Internet of Things. Thus, we propose a fast and secure public-key image encryption scheme. In this scheme, the sender and receiver agree on a public EC. Then the scheme performs pixel-masking and pixel-scrambling procedures using random numbers and a dynamic substitution box over ECs that are isomorphic to the public EC. For a fixed public EC, we prove that our scheme has a computational complexity that is a polylogarithmic function of the size of the plain text. In other words, the computational complexity of our scheme is independent of the point generation over ECs. We tested the security of our scheme against modern attacks by encrypting all standard images in the USC-SIPI image database. Compared to some state-of-the-art cryptosystems, our scheme is fast and has high security.