Designing an Efficient and Highly Dynamic Substitution-Box Generator for Block Ciphers Based on Finite Elliptic Curves

Abstract

Developing a substitution-box (S-box) generator that can efficiently generate a highly dynamic S-box with good cryptographic properties is a hot topic in the field of cryptography. Recently, elliptic curve (EC)-based S-box generators have shown promising results. However, these generators use large ECs to generate highly dynamic S-boxes and thus may not be suitable for lightweight cryptography, where the computational power is limited. The aim of this paper is to develop and implement such an S-box generator that can be used in lightweight cryptography and perform better in terms of computation time and security resistance than recently designed S-box generators. To achieve this goal, we use ordered ECs of small size and binary sequences to generate certain sequences of integers which are then used to generate S-boxes. We performed several standard analyses to test the efficiency of the proposed generator. On an average, the proposed generator can generate an S-box in 0.003 seconds, and from 20,000 S-boxes generated by the proposed generator, $93\%$ S-boxes have at least the nonlinearity 96. The linear approximation probability of 1000 S-boxes that have the best nonlinearity is in the range [0.117, 0.172] and more than 99% S-boxes have algebraic complexity at least 251. All these S-boxes have the differential approximation probability value in the interval [0.039, 0.063]. Computational results and comparisons suggest that our newly developed generator takes less running time and has high security against modern attacks as compared to several existing well-known generators, and hence, our generator is suitable for lightweight cryptography. Furthermore, the usage of binary sequences in our generator allows generating plaintext-dependent S-boxes which is crucial to resist chosen-plaintext attacks.