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Applied Sciences

Quantum Proxy Signature Scheme with Discrete Time Quantum Walks and Quantum One-Time Pad CNOT Operation

Yanyan Feng, Qian Zhang, Jinjing Shi, Shuhui Chen, Ronghua Shi

Published Aug 20, 2020• 7 citations
Publisher

Abstract

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.

DOI
10.3390/app10175770

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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.
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.
Proxy signature is a special signature which provided the signer can delegate his signing capability to others.The proxy signature provides that the original signer can delegate his signing permission to a proxy signer, and the proxy signer can replace the original signer to sign the message.In this paper, we propose a proxy signature scheme based on ideas from classical proxy signature schemes and quantum cryptography.The scheme is implemented by Bell states and a symmetrical quantum key cryptosystem.Compile with classical proxy signature schemes, the new scheme can guarantee the security by using quantum key distribution and one-time pads.And it also can prove that the scheme have the characteristics of non-counterfeit, non-disavowal and traceability.Furthermore, the new scheme uses a special quantum encryption to ensure the receiver cannot forge the signature.The validity of the new scheme can be verified, and it is a secure proxy signature scheme.
Abstract For signing quantum messages, the arbitrated quantum signature (AQS) has been widely investigated to date. However, most of the existing AQS protocols are susceptible to different aspects of disavowal and forgery attacks due to the use of quantum one time pad (QOTP) encryption featuring the encryption manner with qubit by qubit and the commutative property of Pauli operations. We develop an AQS protocol with boson sampling-based random unitary encryption. The unique encryption is used to encrypt the message copy (ciphertext) to produce the signature, which can circumvent the drawbacks of the QOTP encryption and stand against the signer Alice’s disavowal and the verifier Bob’s forgery attacks including existential forgery under known message attacks. The employment of a random array via the public board can prevent Bob’s repudiation attacks on the receipt and the integrality of the signature. The quantum walk-based teleportation is applied to teleport the message copy from Alice to Bob, which can avoid preparing the essential entanglement resource beforehand. Security analyses and discussions show that our AQS protocol is with impossibility of disavowal from Alice and Bob and impossibility of forgery from anyone.
With the development of science and technology and the appearance of various special conditions that cause signers to be unable to sign, proxy signature is gradually becoming a hot spot in cryptography research. This paper combines proxy signature, quantum teleportation, and multi-party verification and proposes a multi-party verifiable quantum proxy signature scheme based on quantum teleportation. This scheme has the following characteristics: The authentication method based on the Hash function can effectively solve the problem of identity identification among members; in order for the proxy signer to be able to verify the correctness of the proxy authorization, a form of proxy signature authorization that concatenates the identity information of the original signer is used. The security analysis shows that our scheme is unforgeable and undeniable and can resist intercept-resend attacks and cheating attacks.
This paper presented a quantum proxy signature scheme which allowed users to obtain the signature and verify of a quantum bit sequence by using the entanglement characteristic of the EPR state and the way of classical encode.In this new scheme,the original signer could delegate his or her signing rights to proxy signer.Guaranteed the unconditionally security of this scheme by quantum key distribution and one time pad.Results show that this new scheme satisfy non-counterfeit,non-disavowal and traceability.