Designing Binary Linear Diffusion Layers with Low-Depth Implementations
Shengyuan XU , Jian LIU , Da LIN , Xiutao FENG , Bo YU , Bing SUN
Binary diffusion layers are widely used in lightweight symmetric-key cryptography, where they provide diffusion through linear transformations over 𝔽2. Their design must balance cryptographic strength and implementation efficiency, usually measured by branch number, XOR count, and circuit depth. Existing studies mainly focus on constructing high-branch matrices with small XOR count or optimizing the implementation of a given matrix, while the depth of the XOR circuit is rarely treated as a primary constraint during matrix construction. In this paper, we propose an implementation-aware synthesis framework for constructing high-branch binary diffusion matrices under a prescribed depth bound. The framework generates candidate matrices from structured families and low-depth XOR circuits, filters them by rank and branch-number constraints, and then synthesizes bounded-depth XOR implementations by selecting row decompositions that share intermediate linear forms. A fixed-matrix resynthesis step is further applied to reduce the XOR count while preserving the depth bound. Applying the framework to dimensions from 4 to 64, we obtain a new set of binary diffusion matrices attaining the best reported depths for several branch-number targets. In particular, we obtain 32 × 32 matrices with branch number 12 and depth 4, and 64 × 64 matrices with branch number 18 and depth 5. These results demonstrate that jointly considering matrix construction and XOR synthesis can improve the diffusion–area–latency tradeoff of binary diffusion layers.
binary diffusion layer / branch number / low latency / lightweight cryptography
Higher Education Press 2026
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