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Modern Physics Letters A

A novel quantum ring signature based on secret sharing

Xingjia Wei, Dianjun Lu, Shuangshuang Luo, Zhihui Li

Published Dec 28, 2023• 5 citations
Publisher

Abstract

Quantum signature has become a hot topic in the current research of digital signature schemes due to its unconditional security. As a special kind of digital signature, ring signatures are frequently employed in practical situations because of their superior anonymity. In this work, we propose a quantum ring signature scheme based on secret sharing that does not use entanglement states. To guarantee the complete security of the participants’ secret keys, the idea of secret sharing is incorporated into the quantum key distribution process during the key distribution stage. Each ring member contributes his private key share to the final verification formula through a recursive relationship throughout the signing and verification phases, and the verifier can utilize his private key share along with the user’s public key to confirm the ring members’ authenticity; The [Formula: see text]-AS2U hash function is used to encrypt the ring signer’s identity during the entire signature process, which assures the signer’s identity’s complete anonymity, effectively protects the signer’s privacy, and is more in line with practical requirements.

DOI
10.1142/s0217732323501754

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Quantum signature has become a hot topic in the current research of digital signature schemes due to its unconditional security. As a special kind of digital signature, ring signatures are frequently employed in practical situations because of their superior anonymity. In this work, we propose a quantum ring signature scheme based on secret sharing that does not use entanglement states. To guarantee the complete security of the participants’ secret keys, the idea of secret sharing is incorporated into the quantum key distribution process during the key distribution stage. Each ring member contributes his private key share to the final verification formula through a recursive relationship throughout the signing and verification phases, and the verifier can utilize his private key share along with the user’s public key to confirm the ring members’ authenticity; The [Formula: see text]-AS2U hash function is used to encrypt the ring signer’s identity during the entire signature process, which assures the signer’s identity’s complete anonymity, effectively protects the signer’s privacy, and is more in line with practical requirements.
In quantum cryptography research area, quantum digital signature is an important research field. To provide a better privacy for users in constructing quantum digital signature, the stronger anonymity of quantum digital signatures is required. Quantum ring signature scheme focuses on anonymity in certain scenarios. Using quantum ring signature scheme, the quantum message signer hides his identity into a group. At the same time, there is no need for any centralized organization when the user uses the quantum ring signature scheme. The group used to hide the signer identity can be immediately selected by the signer himself, and no collaboration between users.Since the quantum finite automaton signature scheme is very efficient quantum digital signature scheme, based on it, we propose a new quantum ring signature scheme. We also showed that the new scheme we proposed is of feasibility, correctness, anonymity, and unforgeability. And furthermore, the new scheme can be implemented only by logical operations, so it is easy to implement.
Quantum digital signatures (QDSs), generating correlated bit strings among three remote parties for signatures through quantum law, can guarantee nonrepudiation, authenticity, and integrity of messages. Recently, a one-time universal-hashing QDS framework, exploiting the quantum asymmetric encryption and universal hash functions, has been proposed to significantly improve the signature rate and ensure unconditional security by directly signing the hash value of long messages. However, similar to quantum key distribution, this framework utilizes keys with perfect secrecy by performing privacy amplification that introduces cumbersome matrix operations, thereby consuming large computational resources, causing delays, and increasing failure probability. Here, we prove that, different from private communication, imperfect quantum keys with partial information leakage can be used for digital signatures and authentication without compromising the security while having eight orders of magnitude improvement on signature rate for signing a megabit message compared with conventional single-bit schemes. This study significantly reduces the delay for data postprocessing and is compatible with any quantum key generation protocols. In our simulation, taking two-photon twin-field key generation protocol as an example, QDS can be practically implemented over a fiber distance of 650 km between the signer and receiver. For the first time, this study offers a cryptographic application of quantum keys with imperfect secrecy and paves a way for the practical and agile implementation of digital signatures in a future quantum network.
In cryptography, a ring signature is anonymous as it hides the signer’s identity among other users. When generating the signature, the users are arranged as a ring. Compared with group signatures, a ring signature scheme needs no group manager or special setup and supports flexibility of group choice. However, the anonymity provided by ring signatures can be used to conceal a malicious signer and put other ring members under suspicion. At the other extreme, it does not allow the actual signer to prove their identity and gain recognition for their actions. A deniable ring signature is designed to overcome these disadvantages. It can initially protect the signer, but if necessary, it enables other ring members to deny their involvement, and allows the real signer to prove who made the signed action. Many real-world applications can benefit from such signatures. Inspired by the requirement for them to remain viable in the post-quantum age, this work proposes a new non-interactive deniable ring signature scheme based on lattice assumptions. Our scheme is proved to be anonymous, traceable and non-frameable under quantum attacks.
Recently, Yang et al. proposed a kind of quantum cryptographic schemes based on secret sharing. The main idea is drawn from the case, where any n participants who share a secret K can co-operate as K does. This process can be applied to encryption, authentication, signature and so on. Unfortunately, since there is no identity authentication of the share’s holder, these schemes inherit the limitation of secret sharing in practice. If some participants do not follow the protocol, the protocol would be a failure at last. Moreover, these schemes encounter another serious attack. Any two participants can co-operate to defeat the schemes by sending different shares to the parties unknown to the distributor of the secret K, such that these parties can execute the protocol as well. The attack proves that it is not enough for quantum cryptographic schemes that only the secret key is secure.
In the most arbitrated quantum signatures (AQSs), the signers and verifiers need to perform the quantum key distribution protocols or some other protocols to share secret keys before signing a signature. In some schemes, the entangle states, which are not easily implemented, have to be prepared and distributed among the partners. Based on single photon and one-way functions, a new AQS scheme without entangled states is proposed. In our scheme, the signer generates a quantum signature on the classical message with his/her private key and the one-way function. The arbitrator communicates with the signer through a classical unencrypted channel. The signer and verifier need not perform the key distribution protocol before signing a message. On the other hand, without entangled states, our scheme can reduce the complexity of implementation. Then, our scheme is more efficient than the similar schemes. At the same time, our scheme is secure against forgery attack and disavowal attack.
operators, a new quantum signature scheme is proposed. In our scheme, the signer's private key is generated by a trusted private key generator (PKG), while the identity information of the signer is used as the corresponding public key. Both of the private key and public key of the signer are classical bit strings, which can be easily stored and reused. Given a quantum signature, anyone can verify the validity of the quantum signature with the signer's identity. Therefore, our scheme is a public-key quantum signature without a digital certificate, which has the merits of an identity-based cryptosystem and can simplify the key management of the quantum signature system. On the other hand, our scheme need not use any quantum swap test during the signature verification phase. Furthermore, by the signature proof, our scheme can arbitrate the potential disputation of losing quantum signature, which cannot be arbitrated in most of the quantum signature schemes. So our scheme has the property of strong non-repudiation. It also has the security properties of information-theoretic security, unforgeability, etc. Our scheme can achieve a high efficiency of 70%. Therefore, our quantum signature scheme is more secure, practicable, and efficient than the similar schemes.