An STP-based model toward designing binary diffusion layers with the lowest latency

Abstract In the realm of lightweight cryptography, the construction of efficient and secure diffusion layers constitutes a critical component in block cipher design. The evaluation of diffusion layers primarily focuses on their cryptographic properties and circuit implementation costs. We propose an automatic model based on the g-XOR metric to design optimal binary diffusion layers with the lowest latency. The model employs graph theory, and from a circuit implementation perspective, translates branch number, invertibility, circuit area and depth into mathematical problems. Under these constraints, it explores improved implementations of Maximum Distance Binary Linear (MDBL) matrices (achieving maximum branch number) across different dimensions from 4 to 16 under the minimum latency. We find the tight lower bound for the implementation area of matrices with dimensions 4, 6, and 8, all with branch number of 4. We present matrices with dimensions 8 and 10, and branch numbers 5 and 6, whose implementation cost outperform existing results. For the first time, we provide optimized experimental results for dimensions 12, 14, and 16 with a branch number of 8 under the minimum depth of 3. Our work achieves the lowest latency, facilitating the design of highly efficient lightweight block ciphers.