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Modern Physics Letters B

Quantum homomorphic aggregation signature scheme based on GHZ states

Xingjia Wei, Zhihui Li, Haozhe Duan, Kexin Hu

Published May 7, 2024• 3 citations
Publisher

Abstract

A quantum homomorphic aggregation signature scheme is proposed based on GHZ states, combined with homomorphic aggregation techniques. The scheme has the following features: Firstly, by changing the existing quantum homomorphic signature scheme which generally uses Bell state as the signature particle, and choosing GHZ state as the signature particle, it can realize the signature of the multi-bit messages by preparing fewer quantum resources; Secondly, the idea of classical aggregated signature is introduced, where multiple message signatures are aggregated into a single signature by quantum entanglement swapping technique, and the verifier can determine the validity of all signatures by only one verification; At the same time, the verification of individual signatures by the aggregator is realized, and dishonest behaviors among the signature members can be detected in time; Finally, the whole signature process satisfies the basic homomorphic property. Compared with the existing quantum homomorphic signature scheme, this scheme can effectively reduce the consumption of quantum resources, improving the efficiency of signature verification and enhancing the reliability of the signature. The security analysis shows that the scheme has the verifiability, unforgeability and non-repudiation.

DOI
10.1142/s0217984924503871

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A quantum homomorphic aggregation signature scheme is proposed based on GHZ states, combined with homomorphic aggregation techniques. The scheme has the following features: Firstly, by changing the existing quantum homomorphic signature scheme which generally uses Bell state as the signature particle, and choosing GHZ state as the signature particle, it can realize the signature of the multi-bit messages by preparing fewer quantum resources; Secondly, the idea of classical aggregated signature is introduced, where multiple message signatures are aggregated into a single signature by quantum entanglement swapping technique, and the verifier can determine the validity of all signatures by only one verification; At the same time, the verification of individual signatures by the aggregator is realized, and dishonest behaviors among the signature members can be detected in time; Finally, the whole signature process satisfies the basic homomorphic property. Compared with the existing quantum homomorphic signature scheme, this scheme can effectively reduce the consumption of quantum resources, improving the efficiency of signature verification and enhancing the reliability of the signature. The security analysis shows that the scheme has the verifiability, unforgeability and non-repudiation.
Abstract With the rapid development of computer and internet technology, quantum signature plays an extremely important role in modern secure communication. Quantum homomorphic aggregate signature, as an important guarantee of quantum signature, plays a significant role in reducing storage, communication, and computing costs. This article draws on the idea of quantum multi-party summation and proposes a quantum homomorphic aggregate signature scheme based on quantum Fourier transform. Our scheme uses nnn-particle entangled states as quantum channels, with different particles of each entangled state sent separately. This ensures secure transmission of signatures and messages with fewer entangled particles during transmission, further improving the efficiency of quantum signatures. Meanwhile, our scheme generates private keys for each participating party by randomly constructing key generation matrixes. Different signers perform quantum Fourier transforms and basis exchange operations on entangled particles based on different messages and private keys to generate signatures. In addition, the aggregator does not need to measure and verify the signature particles after receiving signatures from different signers, and the group addition operation process has additive homomorphism. Security analysis shows that our scheme has unforgeability, non-repudiation, and can resist various attacks such as entanglement measurement attacks, intercept-resend attacks, private key sequence attacks, and internal attacks by aggregator.
Quantum multi-signature has attracted extensive attention since it was put forward. Beside its own improvement, related research is often combined with other quantum signature. However, this type of quantum signature has one thing in common, that is, the generation and verification of signature depend heavily on the shared classical secret key. In order to increase the reliability of signature, the homomorphic aggregation technique is applied to quantum multi-signature, and then we propose a quantum homomorphic multi-signature protocol. Unlike previous quantum multi-signature protocols, this protocol utilizes homomorphic properties to complete signature generation and verification. In the signature generation phase, entanglement swapping is introduced, so that the individual signatures of multiple users are aggregated into a new multi-signature. The original quantum state is signed by the shared secret key to realize the verification of the signature in the verification phase. The signature process satisfies the homomorphic property, which can improve the reliability of the signature.
Abstract 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.
According to the principle of quantum entanglement swapping of GHZ states, this paper put forward a blind signature scheme based on quantum entanglement. Without performing any unitary operation, all participants just need to do Bell measurements on new entangled particles emerging from entanglement swapping of GHZ states to complete blind signature and verification. It is not difficult to prove that the proposed scheme processes the features of nonforgeability, non-disavowal and blindness. Furthermore, compared to some other blind signature schemes on entangled states, our scheme is more efficient because except a few decoy particles, only 2 GHZ states are required for signing each 3 bits in the message.
In this paper, we propose a new quantum signature protocol with identity-based threshold multiple verifiers. In this protocol, first, the signature process combines the HMAC hash function with the participant identity to realize the compression encryption of the signature message, at the same time, the signature particles are encoded and generated by selecting the 3-particle GHZ state of the [Formula: see text] spatially localizable distinguished (LOCC), which avoids the complex entanglement operation and effectively improves the signature efficiency; second, it takes at least t verifying members of the set of valid verifications specified by the signer to verify the validity of the final signature, which increases the utility of the signature protocol in multi-verification scenarios; finally, the security analysis shows that the proposed threshold multiparty verifiable quantum signature protocol scheme can resist entanglement measurement attacks, intercept retransmission attacks, and at the same time be unforgeable, nonrepudiable, and traceable. Most importantly, the protocol does not require Quantum One-Way Function (QOWF), Quantum State Swap Test (SWAP), and has no complex entanglement operations. Therefore, the proposed scheme is more efficient than similar multiparty signature protocols.