On Secure Gradient Coding with Uncoded Groupwise Keys

TL;DR

This paper introduces a new secure gradient coding scheme with uncoded groupwise keys, providing optimal or near-optimal solutions for distributed gradient computation with security constraints.

Contribution

It formalizes a novel secure gradient coding model with uncoded groupwise keys and proposes an optimal scheme under certain conditions.

Findings

Proposed a secure gradient coding scheme with uncoded groupwise keys.

Proved the scheme's optimality when S > M.

Showed the scheme is order optimal within a factor of 2 otherwise.

Abstract

This paper considers a new secure gradient coding problem with uncoded groupwise keys, formalized as a (K, N, N_r, M, S) secure gradient coding model, where a user aims to compute the sum of the gradients from K datasets with the assistance of N distributed servers. We consider arbitrary heterogeneous data assignment, where each dataset is assigned to at least M servers. The user should recover the sum of gradients from the transmissions of any N_r servers. The security constraint guarantees that even if the user receives the transmitted messages from all servers, it cannot obtain any other information about the datasets except the sum of gradients. Compared to existing secure gradient coding works, we introduce a practical constraint on secret keys, namely uncoded groupwise keys, where the keys are mutually independent and each key is shared by precisely S servers. An achievable secure gradient coding scheme with uncoded groupwise keys is proposed, which is then proven to be optimal if S > M and to be order optimal within a factor of 2 otherwise.