Post-quantum security is critical in the quantum era. Quantum computers, along with quantum algorithms, make the standard cryptography based on RSA or ECDSA over FL or Blockchain vulnerable. The implementation of post-quantum cryptography (PQC) over such systems is poorly understood as PQC is still in its standardization phase. In this work, we propose a hybrid approach to employ PQC over blockchain-based FL (BFL), where we combine a stateless signature scheme like Dilithium (or Falcon) with a stateful hash-based signature scheme like the extended Merkle Signature Scheme (XMSS). We propose a linearbased formulaic approach to device role selection mechanisms based on multiple factors to address the performance aspect. Our holistic approach of utilizing a verifiable random function (VRF) to assist in the blockchain consensus mechanism shows the practicality of the proposed approaches. The proposed method and extensive experimental results contribute to enhancing the security and performance aspects of BFL systems.

翻译：后量子安全在量子时代至关重要。量子计算机及量子算法使基于RSA或ECDSA的联邦学习或区块链上的标准密码学变得脆弱。由于后量子密码学仍处于标准化阶段，其在上述系统中的实现方式尚不明确。本研究提出一种混合方法，将Dilithium（或Falcon）等无状态签名方案与扩展默克尔签名方案（XMSS）等基于哈希的有状态签名方案相结合，在基于区块链的联邦学习（BFL）中部署后量子密码学。我们提出一种基于线性公式的多因素设备角色选择机制，以解决性能问题。通过利用可验证随机函数（VRF）辅助区块链共识机制的整体方案，验证了所提方法的实用性。所提出的方法及大量实验结果有助于增强BFL系统的安全性与性能表现。