Post-Quantum Secure Aggregation via Code-Based Homomorphic Encryption

TL;DR

This paper introduces a code-based homomorphic encryption scheme for secure aggregation that is post-quantum secure, efficient, and relies on the Learning Parity with Noise assumption, offering an alternative to lattice-based methods.

Contribution

It presents a novel code-based secure aggregation framework using LPN assumptions, with optimizations and security analysis demonstrating practical advantages over existing protocols.

Findings

Scheme is secure under the Hint-LPN assumption

Achieves reduced communication costs with CRT optimization

Outperforms some information-theoretic protocols in specific regimes

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.