Publicly verifiable privacy-preserving aggregation is widely regarded as an effective approach to protect user privacy and ensure the integrity of the aggregated model published by the aggregator in Federated Learning (FL). State-of-the-art solutions either fail to guarantee unforgeability when the aggregator colludes with malicious users or require costly cryptographic operations during the online aggregation phase and lack fault tolerance. In this work, we propose eVTPA, the first online-efficient, publicly verifiable, and fault-tolerant privacy-preserving aggregation protocol considering malicious users and aggregators for FL. We introduce a novel collusion-resistant symmetric masking technique to conceal users' local gradients while ensuring the correctness of the aggregated model through a publicly verifiable aggregation signature algorithm. To improve the efficiency of online signature generation, we design a specialized precomputation-based acceleration method and leverage the randomness of masking to enable batch processing. Furthermore, eVTPA adopts a dynamic mask update mechanism that tolerates user dropouts without affecting the validation of the aggregated model. Security analysis shows that eVTPA meets FL's confidentiality, integrity, and authenticity requirements. Experimental results demonstrate that our scheme maintains model classification accuracy while achieving at least a 7.85× faster online aggregation than related solutions at the same security level.

Energy consumption data collected by smart meters (SMs) is increasingly used by various subscribers in the smart grid for load management, energy monitoring, and policy planning. To protect user privacy, edge-assisted privacy-preserving data aggregation (PPDA) techniques are commonly employed. However, existing methods face several challenges: 1) limited scalability, 2) strict trust requirements, and 3) the risk of revealing unique consumption patterns to data collectors. To address these challenges, we propose a privacy-preserving threshold aggregation method that is easily scalable and facilitates efficient energy data sharing under limited trust assumptions. Specifically, we design VFP-NTRU, a quantum-resistant homomorphic proxy re-encryption scheme with fault tolerance and re-encryption verification. In VFP-NTRU, SMs can encrypt data with a public key without the need for prior negotiation of decryption keys with multiple subscribers. Additionally, we develop a privacy threshold collection protocol that uses a verifiable oblivious pseudorandom function to provide privacy guarantees similar to k-anonymity for SM data collection. We further introduce an energy consumption model to determine optimal collection strategies, improving system responsiveness. We provide correctness analysis and prove the security of our scheme. Experimental results demonstrate that our approach outperforms existing PPDA methods, making it particularly suitable for resource-constrained SMs and central servers managing large-scale energy data.

Privacy-preserving data aggregation (PDA) enables an edge server to securely perform aggregation tasks on data generated by terminal devices in edge intelligence (EI) systems, revealing only the result without exposing individual inputs. However, most existing solutions, such as homomorphic encryption and federated learning, support only basic functions (e.g., SUM or AVG). They often fail to achieve privacy protection, fault tolerance, and lightweight terminal-side operations when the server colludes with compromised devices. In this work, we propose PrivEI, a practical PDA scheme for EI systems. It uses a proposed collusion-resistant symmetric masking scheme that enables an untrusted edge server to collect and decode masked inputs from$n$terminal devices while supporting arbitrary computations. The scheme allows the server to collude with$k \leq n - 2$terminal devices and has a lightweight mechanism to tolerate device dropouts during aggregation. PrivEI further leverages the Chinese Remainder Theorem to avoid frequent mask updates when aggregating multi-dimensional data, and ensures data integrity using a signer-efficient multiple-time elliptic curve signature algorithm. We formally prove that PrivEI ensures input privacy and achieves$(n-k)$-source anonymity. Both theoretical analysis and experimental results confirm that it offers superior functionality with performance comparable to existing approaches. We have open-sourced the implementation.