Provably Secure Identity-Based Multi-Proxy Signature Scheme in the Standard Model for UAV-Assisted Rescue

Identity-based multi-proxy signatures (IBMPS) enable an original signer to delegate signing authority to multiple proxy signers, who jointly sign a common message on the original signer’s behalf using their identity-associated private keys. This supports authenticated collaborative reporting in unmanned aerial vehicle (UAV)-assisted rescue. We propose an IBMPS scheme for this application and a security model that captures adaptive queries and signer collusion. Under the computational Diffie–Hellman (CDH) assumption and the collision resistance of H^2 and H^3, we prove unforgeability for the three forgery scenarios of Game 1 in the standard model (SM), with explicit reduction bounds and no public-key replacement. We also analyze long-term private-key recovery under proxy signing-key exposure, assuming an honestly generated target public key that remains unchanged. The scheme verifies individual partial signatures before aggregation, while final verification requires a constant number of pairings and scalar multiplications; signer-list processing still depends on group size. Under historical benchmark timings and the adopted operation counts, with ten proxy signers, the estimated total computational cost is 19.34–44.00% lower than that of five of the six baseline schemes, and the estimated final verification cost is 50.26–74.06% lower than that of all six. Under the adopted encoding assumptions, the 20-byte long-term private-key representation is the smallest among the compared schemes, the 276-byte per-proxy delegation ties for the smallest, and the 532-byte final signature matches that of Shin et al.’s scheme. The cost figures are model-based estimates, and the byte counts are per-object representation sizes rather than complete end-to-end communication costs.