Title: On Securing Analog Lagrange Coded Computing from Colluding Adversaries

Abstract: 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.