Identity‐Based Strong Designated Verifier Fully Homomorphic Signature Scheme From Lattices

ABSTRACT Identity‐based fully homomorphic signature (IBFHS) allows untrusted servers to conduct homomorphic evaluations on outsourced data to obtain a new valid signature, ensuring the evaluated output's correctness while significantly simplifying key management. However, the public composability of IBFHS limits its applicability in scenarios requiring restricted verification rights. For example, in cloud storage data audit systems, introducing a designated verifier mechanism ensures that only authorized third‐party auditors (TPAs) can verify data integrity, preventing malicious auditors from tampering with or forging results. To address this limitation, we propose an identity‐based strong designated verifier fully homomorphic signature (IBSDVFHS) scheme, where only an authorized entity can verify the validity of homomorphically evaluated signatures. We establish formal security definitions for IBSDVFHS, including unforgeability, nontransferability, privacy of the signer's identity, and robustness. Furthermore, we propose a specific design of IBSDVFHS with provable security under the small integer solution (SIS) assumption and the learning with errors (LWE) assumption in the random oracle model.