Analog Lagrange Coded Computing (ALCC) is a recently proposed coded computing paradigm wherein certain computations over analog datasets can be efficiently performed using distributed worker nodes through floating point implementation. While ALCC is known to preserve privacy of data from the workers, it is not resilient to adversarial workers that return erroneous computation results. Pointing at this security vulnerability, we focus on securing ALCC from a wide range of non-colluding and colluding adversarial workers. As a foundational step, we make use of error-correction algorithms for Discrete Fourier Transform (DFT) codes to build novel algorithms to nullify the erroneous computations returned from the adversaries. Furthermore, when such a robust ALCC is implemented in practical settings, we show that the presence of precision errors in the system can be exploited by the adversaries to propose novel colluding attacks to degrade the computation accuracy. As the main takeaway, we prove a counter-intuitive result that not all the adversaries should inject noise in their computations in order to optimally degrade the accuracy of the ALCC framework. This is the first work of its kind to address the vulnerability of ALCC against colluding adversaries.

翻译：模拟拉格朗日编码计算（ALCC）是一种近期提出的编码计算范式，它通过浮点实现在分布式工作节点上高效处理模拟数据集上的特定计算任务。尽管已知ALCC能保护数据免受工作节点窥探，但其无法抵御返回错误计算结果的有敌意工作节点。针对这一安全漏洞，我们致力于保护ALCC免受多种非共谋与共谋敌手的攻击。作为基础步骤，我们利用离散傅里叶变换（DFT）码的纠错算法构建新型算法，以消除敌手返回的错误计算结果。此外，在实际环境中实现此类鲁棒ALCC时，我们证明系统存在的精度误差可被敌手利用，提出新颖的共谋攻击以降低计算精度。核心结论是，我们证明了一个反直觉的结果：并非所有敌手都需要向计算中注入噪声才能最优地降低ALCC框架的精度。这是首项解决ALCC面对共谋敌手脆弱性的研究工作。