Secure aggregation is a vital component for mitigating gradient leakage in federated learning, but its communication cost conventionally scales with the gradient dimension. This becomes prohibitive for large models and even more pronounced in decentralized federated learning with limited bandwidth and unreliable nodes. Top-K gradient sparsification is an effective approach to reduce communication by transmitting only a few entries of the full gradient, while maintaining competitive model accuracy. Nevertheless, the top-K entries selected by each user are unpredictable and vary across users, which poses a challenge for efficient sparse secure aggregation. This paper studies information-theoretic secure aggregation with top-K sparsification in decentralized federated learning under user dropouts and user collusion. We propose a communication-efficient sparse secure aggregation scheme that offloads dimension-dependent overhead to an offline phase and protects private gradients using random masks and permutations. Experimental results demonstrate that our scheme preserves accuracy comparable to full-gradient aggregation even with only 1% gradient sparsification, while substantially reducing the communication cost.

We consider the problem of evaluating arbitrary multivariate polynomials over a massive dataset containing multiple inputs, on a distributed computing system with a leader node and multiple worker nodes. Generalized Lagrange Coded Computing (GLCC) codes are proposed to simultaneously provide resiliency against stragglers who do not return computation results in time, security against adversarial workers who deliberately modify results for their benefit, and information-theoretic privacy of the dataset amidst possible collusion of workers. GLCC codes are constructed by first partitioning the dataset into multiple groups, then encoding the dataset using carefully designed interpolating polynomials, and sharing multiple encoded data points to each worker, such that interference computation results across groups can be eliminated at the leader. Particularly, GLCC codes include the state-of-the-art Lagrange Coded Computing (LCC) codes as a special case, and exhibit a more flexible tradeoff between communication and computation overheads in optimizing system efficiency. Furthermore, we apply GLCC to distributed training of machine learning models, and demonstrate that GLCC codes achieve a speedup of up to$2.5-3.9\times $over LCC codes in training time, across experiments for training image classifiers on different datasets, model architectures, and straggler patterns.