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.

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