Quantum homomorphic signature

Quantum signature which concerns about the authenticity and non-repudiation of messages on insecure quantum channels is an important research topic in quantum cryptography. So far, a few quantum signature schemes have been proposed. Inspired by entanglement swapping, we first propose a new quantum homomorphic signature scheme which can be used to authenticate data packets of multiple streams for quantum networks. After combining two quantum signatures by entanglement swapping, it can generate a new homomorphic signature at the intermediate node. The proposed homomorphic quantum signature scheme can effectively guarantee the security of secret key and verify the identity of different data sources in a quantum network. In order to authenticate the identity of data source in a network, homomorphic signature scheme is considerably paid attention to instead of standard signature schemes in classical cryptography. However, homomorphic signature schemes of classical information are inapplicable in quantum networks. It is believed that homomorphic signature of quantum information is more meaningful and difficult than its counterpart in classical cryptography. Particularly, homomorphic signature in form of quantum states is desired for quantum networks. On one hand, the main problem is how to design a signature operation for quantum states. On the other hand, the authentication of different data sources is also a very hard problem for classical networks, so it is necessary to explore whether it is a hard problem for quantum networks or not. If quantum homomorphic signature scheme is feasible, it will be very helpful to enhance the security of quantum networks. However, a solution to quantum homomorphic signature still remains open. It is crucial to find an equivalent quantum homomorphic operation to realize signature computing in form of quantum states. Until now, there is no obvious way to combine two quantum signatures from the senders to realize a homomorphic operation due to the properties of quantum mechanics.