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Towards Quantum-Safe Federated Learning via Homomorphic Encryption: Learning with Gradients

Guangfeng Yan, Shanxiang Lyu, Hanxu Hou, Zhiyong Zheng, Linqi Song

TL;DR

This work addresses gradient leakage and quantum-era security in federated learning by proposing FLAG, a post-quantum, private-key encryption framework for encrypted gradient aggregation. The core idea is to use lattice-based LWE encryption with per-client secret keys and a half-dithered, randomized gradient quantization that cancels the LWE error term, enabling exact aggregation without exposing raw gradients. The paper proves CPA security under LWE with uniform errors, analyzes overflow probability, and derives communication-cost bounds, while demonstrating practical performance through MNIST experiments where accuracy remains close to unencrypted baselines as the quantization bit-width increases. Overall, FLAG offers scalable, post-quantum secure FL with low communication overhead and strong privacy guarantees for honest-but-curious servers.

Abstract

This paper introduces a privacy-preserving distributed learning framework via private-key homomorphic encryption. Thanks to the randomness of the quantization of gradients, our learning with error (LWE) based encryption can eliminate the error terms, thus avoiding the issue of error expansion in conventional LWE-based homomorphic encryption. The proposed system allows a large number of learning participants to engage in neural network-based deep learning collaboratively over an honest-but-curious server, while ensuring the cryptographic security of participants' uploaded gradients.

Towards Quantum-Safe Federated Learning via Homomorphic Encryption: Learning with Gradients

TL;DR

This work addresses gradient leakage and quantum-era security in federated learning by proposing FLAG, a post-quantum, private-key encryption framework for encrypted gradient aggregation. The core idea is to use lattice-based LWE encryption with per-client secret keys and a half-dithered, randomized gradient quantization that cancels the LWE error term, enabling exact aggregation without exposing raw gradients. The paper proves CPA security under LWE with uniform errors, analyzes overflow probability, and derives communication-cost bounds, while demonstrating practical performance through MNIST experiments where accuracy remains close to unencrypted baselines as the quantization bit-width increases. Overall, FLAG offers scalable, post-quantum secure FL with low communication overhead and strong privacy guarantees for honest-but-curious servers.

Abstract

This paper introduces a privacy-preserving distributed learning framework via private-key homomorphic encryption. Thanks to the randomness of the quantization of gradients, our learning with error (LWE) based encryption can eliminate the error terms, thus avoiding the issue of error expansion in conventional LWE-based homomorphic encryption. The proposed system allows a large number of learning participants to engage in neural network-based deep learning collaboratively over an honest-but-curious server, while ensuring the cryptographic security of participants' uploaded gradients.
Paper Structure (11 sections, 4 theorems, 28 equations, 1 figure, 3 tables, 1 algorithm)

This paper contains 11 sections, 4 theorems, 28 equations, 1 figure, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Quantum-Safe Federated Learning
  4. The Encryption Scheme
  5. On randomized quantization
  6. CPA Security
  7. Probability of Overflow
  8. Communication Cost
  9. Algorithmic Complexity
  10. Experiments
  11. Conclusion

Key Result

Lemma 1

Let $\bm{x}_{total} = \sum_{i=1}^Nw_i\bm{x}_i$, where $\bm{x}_i \sim N(\bm{0}, \sigma_x^2\bm{I})$ are i.i.d. Gaussian random vectors with zero mean and variance $\sigma_x^2$, and $w_i$ be weights. The tail of $\bm{x}_{total}$ can be approximated as:

Figures (1)

  • Figure 1: Model Performance of Different Bits.

Theorems & Definitions (7)

  • Definition 1: The LWE problem
  • Lemma 1
  • proof
  • Lemma 2: Increased Communication Factor
  • Theorem 1
  • proof
  • Lemma 3: abdi2019nested