Lightweight block cipher design has largely focused on incremental optimization of established paradigms such as substitution--permutation networks, Feistel structures, and ARX constructions, where security derives from the algebraic complexity of individual components. We propose a different approach based on \emph{expander-graph interaction networks}, where diffusion and security arise from sparse structural connectivity rather than component sophistication. We present \textbf{ExpanderGraph-128 (EGC128)}, a 128-bit block cipher constructed as a 20-round balanced Feistel network. Each round applies a 64-bit nonlinear transformation governed by a 3-regular expander graph whose vertices execute identical 4-input Boolean functions on local neighborhoods. Security analysis combines MILP-based differential bounds, proven optimal through 10 rounds via SCIP, establishing 147.3-bit differential security and conservatively extrapolating to 413 bits for the full cipher. Linear analysis provides MILP bounds of $\geq 2^{145}$, while related-key evaluation shows no free rounds for any nonzero key difference. Additional tests confirm rapid algebraic degree growth and the absence of invariant affine subspaces. Implementation results demonstrate practical efficiency. FPGA synthesis on Xilinx Artix-7 achieves 261~Mbps at 100~MHz using only 380 LUTs, while ARM Cortex-M4F software requires 25.8~KB Flash and 1.66~ms per encryption. These results show that expander-graph-driven diffusion provides a promising design methodology for lightweight cryptography.

翻译：轻量级分组密码的设计主要集中于对已有范式的渐进式优化，例如代换-置换网络、Feistel结构和ARX构造，其安全性源于各独立组件的代数复杂性。我们提出一种基于**扩展图交互网络**的不同方法，其扩散与安全性源于稀疏的结构连通性，而非组件的复杂程度。我们提出**ExpanderGraph-128 (EGC128)**，一种构建为20轮平衡Feistel网络的128位分组密码。每一轮应用一个由3-正则扩展图控制的64位非线性变换，该图的顶点在局部邻域上执行相同的4输入布尔函数。安全性分析结合了基于MILP的差分界限（通过SCIP证明前10轮达到最优），确立了147.3位的差分安全性，并对完整密码保守外推至413位。线性分析给出的MILP界限为 $\geq 2^{145}$，而相关密钥评估表明对于任何非零密钥差分均不存在自由轮次。附加测试证实了代数度的快速增长以及不变仿射子空间的不存在性。实现结果证明了其实际效率。在Xilinx Artix-7上的FPGA综合实现了100 MHz下261 Mbps的吞吐率，仅使用380个LUT；而ARM Cortex-M4F软件实现需要25.8 KB Flash，每次加密耗时1.66 ms。这些结果表明，扩展图驱动的扩散为轻量级密码学提供了一种有前景的设计方法。