Efficient and Secure Montgomery Curve Based Substitution Box Generator With Optimal Nonlinearity
Ikram Ullah, Shahzaib Arif, Fazal Abbas, Umar Hayat · Security and Privacy · 2025
ABSTRACT Rapid technological advancements have made it essential to develop new approaches for designing dynamic substitution boxes (S‐boxes) to secure valuable data. These S‐boxes are controlled by input parameters to acquire the desired cryptographic strength. For this purpose, the S‐box generators with favorable cryptographic strength are intensively developed; however, they suffer from high computational overhead to generate a large number of dynamic S‐boxes with the desired degree of security, limiting their capability to efficiently generate the required number of secure S‐boxes. The key findings of this study are counting, generation of optimal and dynamic S‐boxes, and low computational time. This is done by unconventionally taking the Montgomery elliptic curve, imaginary quadratic field, and defining an ordering on the points of the underlying curve. Then we apply a linear fractional transformation on the ordered points to enhance the required S‐boxes and their security against the key‐related attacks. On detailed analysis, the presented algorithm shows high capability to generate dynamic S‐boxes, providing high security with optimal nonlinearity in minimal time and energy consumption.