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.

翻译：本文考虑了一个新的安全梯度编码问题，其中采用未编码群组密钥，形式化为(K, N, N_r, M, S)安全梯度编码模型。在该模型中，用户旨在借助N个分布式服务器的协助，计算来自K个数据集的梯度之和。我们考虑任意异构数据分配，其中每个数据集至少分配给M个服务器。用户应从任意N_r个服务器的传输中恢复梯度之和。安全约束保证，即使用户接收到来自所有服务器的传输消息，除了梯度之和外，也无法获取有关数据集的任何其他信息。与现有的安全梯度编码工作相比，我们引入了对密钥的一种实用约束，即未编码群组密钥，其中密钥相互独立，且每个密钥恰好由S个服务器共享。本文提出了一种采用未编码群组密钥的可实现安全梯度编码方案，并证明该方案在S > M时最优，否则在2倍因子内达到阶最优。