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However, communications in UAVN confront many security issues, for example, malicious entities may launch impersonate attacks. In UAVN, the command center (CMC) needs to perform mutual authentication with unmanned aerial vehicles in clusters. The aggregator (AGT) can verify the authenticity of authentication request from CMC; then, the attested authentication request is broadcasted to the reconnaissance unmanned aerial vehicle (UAV) in the same cluster. The authentication responses from UAVs can be verified and aggregated by AGT before being sent to CMC for validation. Also, existing solutions cannot resist malicious key generation center (KGC). To address these issues, this paper proposes a pairing-free authentication scheme (CLAS) for UAVNs based on the certificateless signature technology, which supports batch verification at both AGT and CMC sides so that the verification efficiency can be improved greatly. Security analysis shows that our CLAS scheme can guarantee the unforgeability for (attested) authentication request and (aggregate) responses in all phases. 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