Linear Layer Architecture Based on Cyclic Shift and XOR

Abstract

One of the nodes of a block symmetric encryption algorithm is represented by a linear layer, the purpose of which is to distribute the mutual influence of bits within the processed data block. Several methods exist for constructing a linear layer, the most common of which are matrix multiplication operations and the permutation of bits. Both approaches have high computational complexity and are not equally effective for both hardware and software implementations. This paper presents an approach for constructing linear functions for block symmetric encryption algorithms utilizing cyclic shift, and bitwise addition operations are formulated. We provide a preliminary assessment of certain properties of such functions, including the branch number. This linear operation can accommodate binary words of any length, allowing for the design of an optimal linear layer for software or hardware architectures with any word size. Furthermore, the developed architecture allows for balancing the laboriousness of linear operations and related branch numbers. The proposed novel linear layer architecture facilitates the creation of fast lightweight encryption algorithms as well as robust classical algorithms with a high level of cryptographic strength. For efficient implementation on software and hardware platforms, no additional optimizations are required, as the proposed linear layer allows for achieving high performance in both cases.