A quantum homomorphic signature scheme with verifiable identity based on four-particle Cluster states

With the development of cloud computing in recent years, homomorphic signatures have become a research hotspot in modern cryptography. This article proposes a quantum homomorphic signature scheme with verifiable identity based on four-particle Cluster states, starting from the identity verification of the signers. Compared with Shang's scheme (Shang et al 2015 Quantum Inf. Process. 14 393-410), our scheme uses four-particle Cluster states as quantum channels and achieves identity verification of the signers through the use of X operation and quantum measurement techniques. Meanwhile, our scheme extends the length of message M to 2n bits and uses random numbers during the signature process, which makes the scheme more secure. Security analysis shows that our scheme can ensure the security of the keys and the unforgeability of the signatures.