  Due to the widespread availability of data, machine learning (ML) algorithms
are increasingly being implemented in distributed topologies, wherein various
nodes collaborate to train ML models via the coordination of a central server.
However, distributed learning approaches face significant vulnerabilities,
primarily stemming from two potential threats. Firstly, the presence of
Byzantine nodes poses a risk of corrupting the learning process by transmitting
inaccurate information to the server. Secondly, a curious server may compromise
the privacy of individual nodes, sometimes reconstructing the entirety of the
nodes' data. Homomorphic encryption (HE) has emerged as a leading security
measure to preserve privacy in distributed learning under non-Byzantine
scenarios. However, the extensive computational demands of HE, particularly for
high-dimensional ML models, have deterred attempts to design purely homomorphic
operators for non-linear robust aggregators. This paper introduces SABLE, the
first homomorphic and Byzantine robust distributed learning algorithm. SABLE
leverages HTS, a novel and efficient homomorphic operator implementing the
prominent coordinate-wise trimmed mean robust aggregator. Designing HTS enables
us to implement HMED, a novel homomorphic median aggregator. Extensive
experiments on standard ML tasks demonstrate that SABLE achieves practical
execution times while maintaining an ML accuracy comparable to its non-private
counterpart.
