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Mathematics

Efficient Post-Quantum Cross-Silo Federated Learning Based on Key Homomorphic Pseudo-Random Function

Xiaoyuan Qin, Rui Xu

Published Apr 25, 2025• 2 citations
Publisher

Abstract

Federated Learning (FL) enables collaborative model training across distributed users, while preserving data privacy by only sharing model updates. However, secure aggregation, which is essential to prevent data leakage during this process, often incurs significant communication and computational costs. Moreover, existing schemes rarely consider whether they can resist quantum attacks. To address these challenges, we propose an efficient, post-quantum aggregation protocol based on a Key Homomorphic Pseudo-Random Function (KHPRF). Our non-interactive mask elimination mechanism reduces aggregation to a single round, significantly minimizing the communication overhead. Furthermore, the KHPRF keys are reusable, enabling multiple aggregations with a one-time initialization, thereby enhancing efficiency in cross-silo federated learning. Compared to existing schemes, our approach achieves quantum-resistant aggregation with improved efficiency.

DOI
10.3390/math13091404

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Federated Learning (FL) enables collaborative model training across distributed users, while preserving data privacy by only sharing model updates. However, secure aggregation, which is essential to prevent data leakage during this process, often incurs significant communication and computational costs. Moreover, existing schemes rarely consider whether they can resist quantum attacks. To address these challenges, we propose an efficient, post-quantum aggregation protocol based on a Key Homomorphic Pseudo-Random Function (KHPRF). Our non-interactive mask elimination mechanism reduces aggregation to a single round, significantly minimizing the communication overhead. Furthermore, the KHPRF keys are reusable, enabling multiple aggregations with a one-time initialization, thereby enhancing efficiency in cross-silo federated learning. Compared to existing schemes, our approach achieves quantum-resistant aggregation with improved efficiency.
Federated learning is a privacy-preserving machine learning paradigm consisting of local model training, global model aggregation, and global model distribution. Recent research found that model aggregation can reveal the participants’ privacy. To preserve the participants’ privacy, multi-party computation-based secure aggregation is used in federated learning with mobile device participants. The character of the mobile device requires that secure aggregation can be efficient in computation and robust to the dropout. However, prior works need multi rounds, increase computation cost related to the dropped participants, and fails to resist quantum attacks. To solve these issues, we propose a 3-round post-quantum secure protocol for federated learning. In the proposed protocol, single-masking generated by homomorphic Pseudorandom Generator based on learning with round encrypts single user's model. After all the encrypted models are aggregated fast, additively homomorphic decryption based on Shamir secret share guarantee the robustness and performance induced by the dropped participants. All message exchange is based on a post-quantum secure channel constructed with the first post-quantum cryptography standard, Kyber KEM. In post-quantum security, security analysis demonstrates that the proposed protocol can preserve privacy under the sem-honest adversaries setting, and the experimental results show higher running time efficiency.
Federated learning (FL) offers a promising approach to training machine learning models on decentralized data sources without direct data sharing, addressing privacy concerns. However, traditional FL is vulnerable to attacks targeting model updates, potentially compromising data privacy. This paper proposes a novel decentralized federated learning framework that integrates quantum key distribution (QKD) to establish secure keys for data aggregation. The core claim is that QKD significantly enhances the security and efficiency of FL. The proposed system utilizes QKD to generate and distribute shared keys between participating devices, enabling secure aggregation of model updates while mitigating the risk of individual data exposure. This approach directly addresses the security vulnerabilities inherent in standard FL. The framework's architecture relies on a decentralized network topology, further bolstering resilience against single points of failure. Mathematical formulations detailing key aspects of the system, including key distribution protocols, aggregation processes, and security analysis, are presented. This work represents a significant advancement in secure FL by combining the strengths of two cutting-edge technologies: FL and QKD.
Introduction This paper introduces a novel Cross-Silo Quantum Federated Learning (CS-QFL) protocol designed for secure, decentralized intelligence across multiple institutional nodes. Methods By leveraging quantum homomorphic encryption and variational quantum circuits (VQCs), our framework enables collaborative model training without compromising localized data privacy. We evaluated the protocol across a simulated network of 5 independent institutional silos. Results Results demonstrate that CS-QFL achieves a global model classification accuracy of 94.2% on distributed quantum state datasets, matching centralized baselines within a 1.5% margin. Furthermore, the protocol reduces communication overhead by 38% compared to classical federated learning counterparts by transmitting highly compressed quantum state parameters. Discussion Security analyses confirm that the quantum secure aggregation mechanism maintains a state fidelity of >0.992, providing robust theoretical security guarantees against both eavesdropping and adversarial parameter reconstruction attacks.
AI-driven medical diagnostics increasingly requires collaborative model training across institutions, yet centralizing patient data conflicts with privacy regulations. Federated Learning enables distributed training without raw data sharing, but remains vulnerable to gradient inversion and model leakage attacks. Furthermore, harvest-now-decrypt-later attacks render computationally secure protocols insufficient for protecting long-lived medical records. Quantum communication offers information-theoretic security immune to such threats, making Quantum Federated Learning (QFL) a compelling framework for healthcare. However, practical deployment is constrained by communication overhead and quantum channel noise. We present a systematic quantitative study of communication, convergence, and noise trade-offs in QFL, introducing two complementary strategies to reduce quantum transmissions: (1) structured parameter reduction via light-cone feature selection in parameterized quantum circuits, and (2) a Hybrid QFL architecture that dynamically switches between centralized and decentralized aggregation. We show that Hybrid QFL reduces total quantum transmissions from 3 TNMP3\,TNMP3TNMP, the cost of pure Centralized QFL, to {3t+2(T−t)} NMP\{3t + 2(T - t)\}\,NMP{3t+2(T−t)}NMP over TTT rounds while preserving near-centralized convergence. We further demonstrate that decentralized aggregation is more noise-resilient under depolarizing noise, and evaluate Steane code-based quantum error correction in high-noise regimes. Our results provide an integrated design framework for communication-efficient, noise-aware QFL, clarifying practical trade-offs for scalable quantum-secure distributed learning in healthcare.
Federated learning (FL) offers a promising approach to distributed machine learning by enabling collaborative model training without directly exchanging raw data. However, traditional FL systems are plagued by privacy vulnerabilities and significant communication costs. This paper proposes a novel framework, Quantum Walk Based Federated Learning (QWFL), that addresses these limitations by integrating the principles of quantum walks. We leverage quantum superposition and interference to create a secure and efficient model aggregation process. The core idea is to represent model updates as quantum walks on a graph representing the distributed devices, where the walk's evolution inherently obfuscates information. This approach significantly reduces the risk of privacy breaches while concurrently minimizing communication overhead. The theoretical analysis demonstrates the potential of QWFL to achieve better privacy guarantees and communication efficiency compared to conventional FL methods. We present a formal mathematical model of the QWFL system and analyze its key properties, including the walk's convergence rate and the level of privacy protection afforded by the quantum walk process. The design aims for practical implementation by considering the challenges of integrating quantum computing technologies into existing FL architectures. The results indicate that QWFL provides a viable pathway towards robust and scalable distributed learning.
Recent advancements in Quantum Neural Networks (QNNs) have demonstrated theoretical and experimental performance superior to their classical counterparts in a wide range of applications. However, existing centralized QNNs cannot solve many real-world problems because collecting large amounts of training data to a common public site is time-consuming and, more importantly, violates data privacy. Federated Learning (FL) is an emerging distributed machine learning framework that allows collaborative model training on decentralized data residing on multiple devices without breaching data privacy. Some initial attempts at Quantum Federated Learning (QFL) either only focus on improving the QFL performance or rely on a trusted quantum server that fails to preserve data privacy. In this work, we propose CryptoQFL, a QFL framework that allows distributed QNN training on encrypted data. CryptoQFL is (1) secure, because it allows each edge to train a QNN with local private data, and encrypt its updates using quantum homomorphic encryption before sending them to the central quantum server; (2) communication-efficient, as CryptoQFL quantize local gradient updates to ternary values, and only communicate non-zero values to the server for aggregation; and (3) computation-efficient, as CryptoQFL presents an efficient quantum aggregation circuit with significantly reduced latency compared to state-of-the-art approaches.