List-Decodable Coded Computing: Breaking the Adversarial Toleration Barrier

Abstract

We consider the problem of coded computing where a computational task is performed in a distributed fashion in the presence of adversarial workers. We propose techniques to break the adversarial toleration threshold barrier previously known in coded computing. More specifically, we leverage list-decoding techniques for folded Reed-Solomon (FRS) codes and propose novel algorithms to recover the correct codeword using side information. In the coded computing setting, we show how the master node can perform certain carefully designed extra computations in order to obtain the side information. This side information will be then utilized to prune the output of list decoder in order to uniquely recover the true outcome. We further propose folded Lagrange coded computing, referred to as folded LCC or FLCC, to incorporate the developed techniques into a specific coded computing setting. Our results show that FLCC outperforms LCC by breaking the barrier on the number of adversaries that can be tolerated. In particular, the corresponding threshold in FLCC is improved by a factor of two compared to that of LCC.

Secure Private and Adaptive Matrix Multiplication Beyond the Singleton Bound

“…For a very recent survey on private distributed computing and its connections we refer the reader to [40]. Security against malicious workers is considered in [28], [41]- [44]. The works of [41] and [28] design codes in which each malicious worker can inflict a double damage.…”

“…The master can thus use this fact to alleviate the assumption of limited knowledge of the malicious workers. In [43] and [44] variants of Reed-Solomon codes are used to half the damage of the malicious workers when the workers introduce random noise and when the workers introduce any kind of noise, respectively. The disadvantage of [44] is the high computational complexity incurred by the master.…”

“…In [43] and [44] variants of Reed-Solomon codes are used to half the damage of the malicious workers when the workers introduce random noise and when the workers introduce any kind of noise, respectively. The disadvantage of [44] is the high computational complexity incurred by the master. Concurrently and independently of our work, the authors of [50] present a scheme to tolerate malicious workers in coded computing with low computational complexity.…”

“…The ideas used in [50] are similar to the ideas used in this work. However, [28], [41], [43], [44] and [50] consider security in settings where the workers are assumed to have similar resources. In addition, a maximum amount of stragglers is assumed.…”

“…We build on the scheme introduced in [32] to achieve our goal. It is worth mentioning that the schemes presented in this work and in [42]- [44] allow the master to detect the presence of malicious workers and remove their corrupted computation with arbitrarily high probability.…”