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Zhongguo kexue. Wulixue Lixue Tianwenxue

Arbitrated quantum (t,n) threshold group signature scheme based on multi-coin quantum walk

SHANG Tao, HOU PengLin, LIU YuChen, XIONG KeYu, LIU JianWei

Published Nov 7, 2023• 2 citations
Publisher

Abstract

The quantum group signature is a variant of the arbitrated quantum signature with special properties. Most existing teleportation-based quantum group signature schemes do not possess threshold properties, and extending them to quantum threshold group signatures is difficult. Therefore, to realize the extension from ordinary quantum signature to quantum (t, n) threshold group signature and solve the problem of low efficiency of quantum signature based on joint Bell state measurement, this paper proposes a quantum (t, n) threshold group signature scheme based on generalized teleportation implemented by multi-coin quantum walk. In the proposed scheme, n signers form a group, and only t signers can generate a valid signature on behalf of the group using the quantum walking system. In addition, a verifier checks the validity of the signature through the quantum one-time pad and quantum comparison algorithm using a trusted arbiter. The security analysis shows that the proposed scheme meets the requirements of unforgeability, nonrepudiation, threshold security, signer identity traceability, and signer anonymity. In terms of efficiency, the proposed scheme uses teleportation based on multi-coin quantum walk to transmit the quantum message without the need to prepare entangled quantum states in advance. It then replaces the joint Bell measurement of quantum teleportation with a more efficient projection measurement. Moreover, the proposed scheme uses random numbers and public boards, which can avoid the repudiation of signatures and guarantee their integrity.

DOI
10.1360/sspma-2023-0361

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The quantum group signature is a variant of the arbitrated quantum signature with special properties. Most existing teleportation-based quantum group signature schemes do not possess threshold properties, and extending them to quantum threshold group signatures is difficult. Therefore, to realize the extension from ordinary quantum signature to quantum (t, n) threshold group signature and solve the problem of low efficiency of quantum signature based on joint Bell state measurement, this paper proposes a quantum (t, n) threshold group signature scheme based on generalized teleportation implemented by multi-coin quantum walk. In the proposed scheme, n signers form a group, and only t signers can generate a valid signature on behalf of the group using the quantum walking system. In addition, a verifier checks the validity of the signature through the quantum one-time pad and quantum comparison algorithm using a trusted arbiter. The security analysis shows that the proposed scheme meets the requirements of unforgeability, nonrepudiation, threshold security, signer identity traceability, and signer anonymity. In terms of efficiency, the proposed scheme uses teleportation based on multi-coin quantum walk to transmit the quantum message without the need to prepare entangled quantum states in advance. It then replaces the joint Bell measurement of quantum teleportation with a more efficient projection measurement. Moreover, the proposed scheme uses random numbers and public boards, which can avoid the repudiation of signatures and guarantee their integrity.
In this paper, a group signature scheme based on quantum walk for quantum messages is proposed. Our scheme uses long step quantum walk-based teleportation and modified quantum one-time pad to authenticate the quantum messages respectively. In our scheme, the signer in a group signs the quantum messages by quantum walk-based teleportation and modified quantum one-time pad. The verifier can verify the signature via quantum walk-based teleportation while the group manager verifies the signature and identifies the signer via modified quantum one-time pad. The security analysis shows that the scheme can reach the properties of group signature. Compared to the teleportation via EPR pairs or Bell-like states, quantum walks are more flexible and use less measurement resources. Quantum teleportation via long-step quantum walk is more secure than that via one-step quantum walk in previous related works. The scheme can apply to arbitrary finite dimensional quantum systems and can also be possible to realize in practice.
Quantum signature is quantum counterpart of classical digital signature, which has been widely applied to modern communication, such as electronic payment, electronic voting and electronic medical, owing to its great implication in ensuring the authenticity and the integrity of the message and the non-repudiation. Arbitrated quantum signature (AQS) is an important and practical type of quantum signature. The AQS algorithm is a symmetric key cryptography-based quantum signature algorithm, and its implementation requires the trusted arbitrator to be directly involved. In this paper, employing the key-controlled chained CNOT (KCCC) operation as the appropriate encryption (decryption) algorithm, we suggest an AQS scheme based on teleportation of quantum walks with two coins on a four-vertex cycle, which is used to transfer the message copy from the sender to the receiver. In light of the model of teleportation of quantum walks, the sender encodes the message to be signed into her or his coin state, and the necessary entangled states can be created as a result of the conditional shift between the coin state and the position state. The measurements performed on the generated entangled states are the bases of signature production and message recovery. Then according to the classical measurement results from the sender, the receiver performs the appropriate local unitary operations (i.e., Pauli operations) on his own coin state to recover the original message and further verifies the validity of the completed signature by using the appropriate verification algorithms under the aid of the trustworthy arbitrator. The suggested AQS scheme makes the following contributions: 1) the necessary entangled states for quantum teleportation of message copy do not need preparing in advance, and they can be produced automatically by the first step of quantum walks; 2) the scheme satisfies the features of non-repudiation, un-forgeability and non-disavowal due to the use of the KCCC operation; 3) the scheme may be achieved by linear optical elements such as beam splitters, wave plates, etc., because quantum walks have proven to be realizable in different physical systems and experiments. Analysis and discussion show that the proposed AQS scheme possesses the impossibility of disavowals by the signer and the receiver and impossibility of forgeries by anyone. Comparisons reveal that the designed AQS protocol is favorable. Furthermore, it provides an idea by employing the quantum computing model into quantum communication protocols with a possible improvement with respect to its favorable properties, for example, the automatic generation of entangled states via the first step of quantum walks on different models. In the near future, we will further investigate the production of entanglement by quantum walks and its applications with some improvements in designing the quantum communication protocols.
Group signature scheme is a method of allowing a member of a group to sign a message anonymously on behalf of the group. The group administrator is in charge of adding group members and has the ability to reveal the original signer in the event of disputes. Based on controlled quantum teleportation with three-particle entangled W states, we propose a new quantum group signature scheme with designated receiver. Security analysis proves that the proposed scheme possesses the characteristics of group signature and resists the usual attacks. Compared with previous proposed schemes, this scheme follows security definition of group signature fully and meets its basic requirements.
In this paper, based on multi-arbitrators and the product states, a new quantum signature scheme (QSS) is proposed. In our scheme, two arbitrators are used to share private keys with the signer. The signer encodes the bit message into orthogonal product states, which are locally indistinguishable. Then, to produce the signature, the signer signs the product states with the key-controlled Hadamard operator and Y operator. Our scheme has the good virtues as follows. First, our signature not only has the security property of unforgeability, but also has the property of strong non-repudiation. Second, when signing a message and verifying a signature, the partners do not need to prepare or transmit any entangled particle. Third, the partners do not need to perform the state comparison algorithm. Fourth, the signer does not need to share any private key with the signature verifier. For our scheme, the signer only shares two private keys with the arbitrators. At last, in our scheme, the repudiation can be flexibly solved. Compared with the other schemes with semi-trusted arbitrator, ours has better performances in security, practicability and efficiency.
The quantum proxy signature is one of the most significant formalisms in quantum signatures. We put forward a quantum proxy signature scheme using quantum walk-based teleportation and quantum one-time pad CNOT (QOTP-CNOT) operation, which includes four phases, i.e., initializing phase, authorizing phase, signing phase and verifying phase. The QOTP-CNOT is achieved by attaching the CNOT operation upon the QOTP and it is applied to produce the proxy signature state. The quantum walk-based teleportation is employed to transfer the encrypted message copy derived from the binary random sequence from the proxy signer to the verifier, in which the required entangled states do not need to be prepared ahead and they can be automatically generated during quantum walks. Security analysis demonstrates that the presented proxy signature scheme has impossibility of denial from the proxy and original signers, impossibility of forgery from the original signatory and the verifier, and impossibility of repudiation from the verifier. Notably, the discussion shows the complexity of the presented algorithm and that the scheme can be applied in many real scenarios, such as electronic payment and electronic commerce.