Conception of efficient key-dependent binary diffusion matrix structures for dynamic cryptographic algorithms

Abstract

The existing static cryptographic algorithms suffer from different performance and security challenges. These limitations are attributed to their fixed structure, where the substitution and diffusion primitives maintain the same values throughout the process. In this paper, we present a new framework of a dynamic binary diffusion matrix with flexible dimensions (n×n). The proposed solution replaces the static diffusion primitives, in existing symmetric and un-keyed cryptographic algorithms, with dynamic primitives. We define six different dynamic and flexible binary diffusion forms, four that are invertible, and two that are non-invertible, and hence, they could be used for different security services. However, using a single diffusion form does not always guarantee the required cryptographic properties. To that effect, we propose a binary multiplication scheme of a dynamic primary matrix and its transposed form, which yields the desired efficiency, and provides good resistance against recent implementation attacks, yet without degrading the system performance. We conduct security and performance analyses to validate the effectiveness of the proposed solution. The results confirm the cryptographic performance in terms of the linear branch number and the number of fixed points. In this context, the best-obtained branch number is 4 for n=8 and 5 for n=12 for the invertible forms, while for the non-invertible ones, the best branch number is 3 for n=8 and 4 for n=12. Moreover, in terms of the number of fixed points, the obtained numbers are very close to 0 for the invertible and non-invertible forms.