Coded Computing for Boolean Functions

The growing size of modern datasets necessitates splitting a large scale computation into smaller computations and operate in a distributed manner for improving overall performance. However, adversarial servers in a distributed computing system deliberately send erroneous data in order to affect the computation for their benefit. Computing Boolean functions is the key component of many applications of interest, e.g., classification problem, verification functions in the blockchain and the design of cryptographic algorithm. In this paper, we consider the problem of computing a Boolean function in which the computation is carried out distributively across several workers with particular focus on security against Byzantine workers. We note that any Boolean function can be modeled as a multivariate polynomial which can have high degree in general. Hence, the recently proposed Lagrange Coded Computing (LCC) can be used to simultaneously provide resiliency, security, and privacy. However, the security threshold (i.e., the maximum number of adversarial workers that can be tolerated) provided by LCC can be extremely low if the degree of the polynomial is high. Our goal is to design an efficient coding scheme which achieves the optimal security threshold. We propose two novel schemes called coded Algebraic normal form (ANF) and coded Disjunctive normal form (DNF). Instead of modeling the Boolean function as a general polynomial, the key idea of the proposed schemes is to model it as the concatenation of some linear functions and threshold functions. The proposed coded ANF and coded DNF outperform LCC by providing the security threshold which is independent of the polynomial's degree.