On Secure Gradient Coding with Uncoded Groupwise Keys

2026-04-14

AI Summary

This work addresses a fundamental security challenge in distributed gradient computation: enabling users to recover only the sum of gradients without revealing any individual participant’s private data, under the constraint of using only non-encoded group keys. The paper introduces, for the first time, a non-encoded group key model, wherein each key is shared by exactly S servers and is mutually independent across groups. Building upon this model, the authors devise a secure gradient coding scheme that guarantees information-theoretic security and ensures the gradient sum can be recovered from any N_r server responses, even under heterogeneous data distributions. Theoretical analysis demonstrates that the scheme achieves optimal communication overhead when S > M, and is within a factor of two of optimal otherwise, thereby effectively balancing security and efficiency.

Technology Category

• Search and Optimization: Distributed Search
• Machine Learning: Distributed Machine Learning & Federated Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Applications of cryptography
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• secure gradient coding
• uncoded groupwise keys
• distributed servers
• gradient sum
• information-theoretic security

Innovation

• secure gradient coding
• uncoded groupwise keys
• distributed computing
• information-theoretic security
• coded distributed learning