A Maliciously Secure and Fully Decentralized Threshold FHE Scheme with Native RNS Acceleration
: Threshold fully homomorphic (ThFHE) encryption, as a communication encryption protocol, ensures that no third party participates in generating or knows any parameters. Compared to multi-key fully homomorphic encryption, it avoids excessive noise expansion caused by too many users participating in the calculation. However, current ThFHE algorithms focus on reducing computational overhead, thereby neglecting integrity verification of participating nodes’ behavior in distributed collaborative environments, leaving the system vulnerable to malicious actors. Without an effective verification mechanism, malicious nodes can manipulate the final result without breaking the protocol flow by injecting biased noise or providing forged partial decryption values, compromising data integrity. This research proposes an enhanced ThFHE encryption scheme based on a Full Remainder System (Full-RNS) architecture. This scheme integrates Distributed Key Generation (DKG) and Multi-Party Computation Relinearized Key (MPC RLK) techniques to achieve fully decentralized parameter initialization. To combat malicious attacks, we introduce a Non-Interactive Zero-Knowledge (NIZK) proof that incorporates smudging noise, ensuring that the computational trajectory at each stage can be publicly verified without leaking private key information. The results of the experiment show that this scheme maintains efficient homomorphic computation of the BFV algorithm while effectively resisting node fraud, providing more robust security for voting systems and medical privacy computations.