Efficient binary diffusion matrix structures for dynamic key-dependent cryptographic algorithms

Abstract

In this paper, we propose a new mechanism for the generation of dynamic binary diffusion matrices, with a flexible dimension (n×n), to be used in the design of new symmetric cryptographic algorithms. The proposed framework defines four primary invertible and non-invertible binary diffusion matrix forms. The advantages of these forms stem from the dynamic key approach, where each primary matrix requires the construction of two pseudo-random sub-matrices (Mu and Mv) with a size that depends on two variables (m and l). A cryptographic analysis was carried out to detect the optimal size of m and l for the construction of the matrices to achieve the best possible cryptographic performance and thus, to provide better immunity against different types of attacks. The results showed that the optimal size for m is ∈{n2−1,n2,n2+1}, and for l=n−m. Accordingly, the proposed scheme was designed with an optimal size of m and l, which resulted an acceptable linear branch number and low fixed numbers. In comparison to the existing static diffusion techniques, the proposed solution offers a higher security level since the diffusion matrices are constantly changing and they depend of the dynamic key, which is unknown to attackers.