We consider the setting of a Master server, M, who possesses confidential data (e.g., personal, genomic or medical data) and wants to run intensive computations on it, as part of a machine learning algorithm for example. The Master wants to distribute these computations to untrusted workers who have volunteered or are incentivized to help with this task. However, the data must be kept private and not revealed to the individual workers. Some of the workers may be stragglers, e.g., slow or busy, and will take a random time to finish the task assigned to them. We are interested in reducing the delays experienced by the Master. We focus on linear computations as an essential operation in many iterative algorithms such as principal component analysis, support vector machines and other gradient-descent based algorithms. A classical solution is to use a linear secret sharing scheme, such as Shamir's scheme, to divide the data into secret shares on which the workers can perform linear computations. However, classical codes can provide straggler mitigation assuming a worst-case scenario of a fixed number of stragglers. We propose a solution based on new secure codes, called Staircase codes, introduced previously by two of the authors. Staircase codes allow flexibility in the number of stragglers up to a given maximum, and universally achieve the information theoretic limit on the download cost by the Master, leading to latency reduction. Under the shifted exponential model, we find upper and lower bounds on the Master's mean waiting time. We derive the distribution of the Master's waiting time, and its mean, for systems with up to two stragglers. For systems with any number of stragglers, we derive an expression that can give the exact distribution, and the mean, of the waiting time of the Master. We show that Staircase codes always outperform classical secret sharing codes.
Communication Efficient Secret Sharing in the Presence of Malicious Adversary
考虑通信有效的秘密共享问题。经销商希望与$n$方共享秘密，使得任何$k\leq n$方都可以重建秘密，并且窃听其份额的任何$z<k$方都得不到关于秘密的信息。此外，合法用户联系任何$d$、$k\leq d \leq n$方来解码秘密可以通过读取和下载所需的最小量的信息来进行。我们感兴趣的是通信效率的秘密共享方案，容忍存在的恶意方积极破坏他们的份额和数据交付给用户。恶意方对秘密的了解仅限于他们获得的份额。我们描述的能力，即可以共享的秘密的最大大小。我们推导出需要被读取的最小信息量，并传达给一个合法的用户解码的秘密从$d$各方，$k\leq d \leq n$。在此设置下，纠错码无法实现容量。我们构造的代码，实现容量和实现最小的读取和通信成本的所有可能的值$d$。我们的代码是基于阶梯码，以前介绍的通信效率的秘密共享，并使用一个成对的散列方案，用于分布式数据存储和网络编码设置，以检测错误插入一个有限的知识对手。
ByzSecAgg: A Byzantine-Resistant Secure Aggregation Scheme for Federated Learning Based on Coded Computing and Vector Commitment
Department of Electrical Engineering and Computer Science, Technische Universität Berlin（电气工程与计算机科学系，柏林技术大学）；Department of Electrical and Computer Engineering, University of Minnesota Twin Cities（电气与计算机工程系，明尼苏达大学双城分校）
