  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.
