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 linear-based 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。量子计算机与量子算法使得基于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尚不明确。本文提出一种混合方法，将后量子密码学应用于基于区块链的联邦学习，该方法结合了无状态签名方案（如Dilithium或Falcon）与有状态哈希基签名方案（如扩展默克尔签名方案）。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。采用可验证随机函数辅助区块链共识机制的整体方案，证明了所提方法的实用性。所提方法及广泛的实验结果有助于提升区块链联邦学习系统的安全性与性能。