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.

翻译：安全聚合允许多方输入在服务器或其他客户端不暴露个体贡献的情况下进行聚合。现有的基于同态加密的后量子方法虽具备实际效率，但主要依赖于基于格的困难性假设。本文提出一种基于编码的安全聚合替代方案，通过在带噪声学习奇偶性（LPN）假设下实例化一种基于密钥与消息可加性同态加密的通用框架来实现。我们的构建采用基于秘密共享实现的委员会式解密器，并结合基于中国剩余定理（CRT）的优化以降低基于LPN实例的通信开销。我们在新的Hint-LPN假设下分析了所提方案的安全性，并证明在适当参数下其与标准LPN假设等价。最后，我们评估了方案性能，并确定了本方法优于信息论安全聚合协议的应用场景。