Abstract
This paper presents an automated method for generating the parameters of linear functions used in the diffusion layer of block symmetric encryption algorithms. The focus is on designing linear layers constructed solely from cyclic shift operations and bitwise XORs, which are both efficient and hardware-friendly. Such layers play a critical role in achieving strong diffusion, a fundamental cryptographic requirement. The proposed method evaluates candidate configurations by exhaustively enumerating shift values, calculating their branch number, and assessing their avalanche characteristics. A set of quantitative diffusion metrics is introduced to guide the selection process, including single- and multi-round avalanche effects and activation rates at the byte level. An aggregated quality function is formulated to allow comparative assessment. The developed software tool identified optimal shift parameters for 128-bit blocks processed as four 32-bit words, achieving a branch number of 5 with only 12 XOR operations. The proposed approach contributes to the practical synthesis of lightweight and secure cryptographic primitives suitable for both classical and constrained platforms.