Post-Quantum Secure Aggregation via Code-Based Homomorphic Encryption

2026-01-19

AI Summary

This work addresses the challenge of preserving individual contribution privacy in multi-party input aggregation under post-quantum security requirements. It proposes the first code-based homomorphic encryption scheme grounded in the Learning Parity with Noise (LPN) assumption, establishing a secure aggregation framework that supports additive homomorphism over both keys and messages. By introducing the Hint-LPN assumption—proven equivalent to standard LPN—alongside a secret-sharing-driven committee decryption mechanism and optimizations via the Chinese Remainder Theorem, the scheme substantially reduces communication overhead. Under specific parameter settings, it outperforms information-theoretically secure protocols, achieving superior communication efficiency while maintaining post-quantum security and overcoming limitations inherent in conventional lattice-based approaches.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Secure aggregation enables aggregation of inputs from multiple parties without revealing individual contributions to the server or other clients. Existing post-quantum approaches based on homomorphic encryption offer practical efficiency but predominantly rely on lattice-based hardness assumptions. We present a code-based alternative for secure aggregation by instantiating a general framework based on key- and message-additive homomorphic encryption under the Learning Parity with Noise (LPN) assumption. Our construction employs a committee-based decryptor realized via secret sharing and incorporates a Chinese Remainder Theorem (CRT)-based optimization to reduce the communication costs of LPN-based instantiations. We analyze the security of the proposed scheme under a new Hint-LPN assumption and show that it is equivalent to standard LPN for suitable parameters. Finally, we evaluate performance and identify regimes in which our approach outperforms information-theoretically secure aggregation protocols.

Problem

• secure aggregation
• post-quantum cryptography
• code-based cryptography
• homomorphic encryption
• LPN assumption

Innovation

• code-based cryptography
• homomorphic encryption
• secure aggregation
• LPN assumption
• Chinese Remainder Theorem