In distributed computing with untrusted workers, the assignment of evaluation indices plays a critical role in determining both privacy and robustness. In this work, we study how the placement of unreliable workers within the Numerically Stable Lagrange Coded Computing (NS-LCC) framework influences privacy and the ability to localize Byzantine errors. We derive analytical bounds that quantify how different evaluation-index assignments affect privacy against colluding curious workers and robustness against Byzantine corruption under finite-precision arithmetic. Using these bounds, we formulate optimization problems that identify privacy-optimal and robustness-optimal index placements and show that the resulting assignments are fundamentally different. This exposes that index choices that maximizes privacy degrade error-localization, and vice versa. To jointly navigate this trade-off, we propose a low-complexity greedy assignment strategy that closely approximates the optimal balance between privacy and robustness.

翻译：在不可信工作节点的分布式计算中，评估索引的分配对隐私性和鲁棒性的确定起着关键作用。本研究探讨了在数值稳定拉格朗日编码计算（NS-LCC）框架中，不可靠工作节点的布局如何影响隐私性及拜占庭错误的定位能力。我们推导出解析界，量化了不同评估索引分配方案在有限精度算术下对合谋好奇节点的隐私保护效果及对拜占庭破坏的鲁棒性影响。基于这些界限，我们构建了优化问题以确定隐私最优和鲁棒性最优的索引布局方案，并证明这两种优化方案产生的分配结果存在本质差异。这表明最大化隐私性的索引选择会降低错误定位能力，反之亦然。为协同应对这种权衡关系，我们提出了一种低复杂度的贪心分配策略，该策略能紧密逼近隐私性与鲁棒性之间的最优平衡点。