Due to the large-scale availability of data, machine learning (ML) algorithms
are being deployed in distributed topologies, where different nodes collaborate
to train ML models over their individual data by exchanging model-related
information (e.g., gradients) with a central server. However, distributed
learning schemes are notably vulnerable to two threats. First, Byzantine nodes
can single-handedly corrupt the learning by sending incorrect information to
the server, e.g., erroneous gradients. The standard approach to mitigate such
behavior is to use a non-linear robust aggregation method at the server.
Second, the server can violate the privacy of the nodes. Recent attacks have
shown that exchanging (unencrypted) gradients enables a curious server to
recover the totality of the nodes' data. The use of homomorphic encryption
(HE), a gold standard security primitive, has extensively been studied as a
privacy-preserving solution to distributed learning in non-Byzantine scenarios.
However, due to HE's large computational demand especially for high-dimensional
ML models, there has not yet been any attempt to design purely homomorphic
operators for non-linear robust aggregators. In this work, we present SABLE,
the first completely homomorphic and Byzantine robust distributed learning
algorithm. SABLE essentially relies on a novel plaintext encoding method that
enables us to implement the robust aggregator over batching-friendly BGV.
Moreover, this encoding scheme also accelerates state-of-the-art homomorphic
sorting with larger security margins and smaller ciphertext size. We perform
extensive experiments on image classification tasks and show that our algorithm
achieves practical execution times while matching the ML performance of its
non-private counterpart.

SABLE 是第一种完全同态和拜占庭鲁棒分布式学习算法，基于新颖的明文编码方法，在图像分类任务上通过实验证明了其在实际执行时间方面的实用性和匹配非隐私算法的机器学习性能。