In this research work, we offer a quantum public key encryption protocol scheme that is constructed via lackadaisical quantum walks (LQWs) on cycle graphs. Our proposed protocol scheme involves the laziness parameter or loop-weight (l) at each vertex and coin phase (θ) as tunable variables, which effectively increases the performance of the cryptographic model. The sender encrypts the message using LQW evolution which is governed by shift operator and 3 dimensional coin operator. The receiver, given final quantum state as public key and correct parameters as secrete key, is able to decrypt the message with high fidelity. Any differences in the parameters shows a drastic drop in fidelity due to the sensitive behavior of quantum walk dynamics dependent on secret key variables. We also study the correctness, security and efficiency of the proposed protocol scheme. The findings show promising efficiency and protection against eavesdropping. The method proposed in the work introduces a novel method for QPKE, leveraging the robust mathematical framework of quantum walks.
In this research work, we offer a quantum public key encryption protocol scheme that is constructed via lackadaisical quantum walks (LQWs) on cycle graphs. Our proposed protocol scheme involves the laziness parameter or loop-weight (l) at each vertex and coin phase (θ) as tunable variables, which effectively increases the performance of the cryptographic model. The sender encrypts the message using LQW evolution which is governed by shift operator and 3 dimensional coin operator. The receiver, given final quantum state as public key and correct parameters as secrete key, is able to decrypt the message with high fidelity. Any differences in the parameters shows a drastic drop in fidelity due to the sensitive behavior of quantum walk dynamics dependent on secret key variables. We also study the correctness, security and efficiency of the proposed protocol scheme. The findings show promising efficiency and protection against eavesdropping. The method proposed in the work introduces a novel method for QPKE, leveraging the robust mathematical framework of quantum walks.
Quantum Cryptography is a rapidly developing field of research that benefits from the properties of Quantum Mechanics in performing cryptographic tasks. Quantum walks are a powerful model for quantum computation and very promising for quantum information processing. In this paper, we present a quantum public-key cryptographic system based on quantum walks. In particular, in the proposed protocol the public-key is given by a quantum state generated by performing a quantum walk. We show that the protocol is secure and analyze the complexity of public key generation and encryption/decryption procedures.
A verifiable quantum secret sharing protocol using quantum walks on a lattice is proposed in this paper. The protocol utilizes generalized Bell states as the initial quantum resource, integrating the quantum walk evolution operator U with the global shift operator Gab to facilitate joint encrypted transmission among multiple participants. A bidirectional identity authentication mechanism based on hash functions is introduced to ensure the legitimacy of all communication parties, which effectively resists impersonation attacks. Random decoy particles are randomly prepared in either the Zd or Xd basis and inserted into the transmission sequence, enabling real-time eavesdropping detection on the quantum channel. In the secret reconstruction phase, a public verification mechanism is designed to allow participants to verify the correctness of the recovered secret and identify internal dishonest behaviors. Security analysis demonstrates that the protocol achieves information-theoretic security, resisting typical external attacks such as intercept-resend, measure-resend, and entangle-measure attacks, as well as collusion attacks from dishonest internal participants. Compared with existing quantum-walk-based secret sharing schemes, the proposed protocol maintains high qubit efficiency while supporting both identity authentication and public verifiability, thus possessing stronger practicality and security.
Compatibility with noisy intermediate-scale quantum (NISQ) devices is crucial for the realistic implementation of quantum cryptographic protocols. We investigate a cryptographic scheme based on discrete-time quantum walks (DTQWs) on cyclic graphs that exploits Parrondo dynamics, wherein periodic evolution emerges from a deterministic sequence of individually chaotic coin operators. We construct an explicit quantum circuit realization tailored to NISQ architectures and analyze its performance through numerical simulations in Qiskit under both ideal and noisy conditions. Protocol performance is quantified using probability distributions, Hellinger fidelity, and total variation distance. To assess security at the circuit level, we model intercept-resend and man-in-the- middle attacks and evaluate the resulting quantum bit error rate. In the absence of adversarial intervention, the protocol enables reliable message recovery, whereas eavesdropping induces characteristic disturbances that disrupt the periodic reconstruction mechanism. We further examine hardware feasibility on contemporary NISQ processors, specifically ibm_torino, incorporating qubit connectivity and state-transfer constraints into the circuit design. Our analysis demonstrates that communication between spatially separated logical modules increases circuit depth via SWAP operations, leading to cumulative noise effects. By exploring hybrid state-transfer strategies, we show that qubit selection and connectivity play a decisive role in determining fidelity and overall protocol performance, highlighting hardware-dependent trade-offs in NISQ implementations.
Public-key cryptosystems for quantum messages are considered from two aspects: public-key encryption and public-key authentication. Firstly, we propose a general construction of quantum public-key encryption scheme, and then construct an information-theoretic secure instance. Then, we propose a quantum public-key authentication scheme, which can protect the integrity of quantum messages. This scheme can both encrypt and authenticate quantum messages. It is information-theoretic secure with regard to encryption, and the success probability of tampering decreases exponentially with the security parameter with regard to authentication. Compared with classical public-key cryptosystems, one private-key in our schemes corresponds to an exponential number of public-keys, and every quantum public-key used by the sender is an unknown quantum state to the sender.
Information security is the cornerstone and lifeblood of national security in the information society, and anonymous quantum communication is one of the important ways to protect information security. Using quantum walk randomness to effectively solve sensitive problems such as leakage of identity information. In this paper, an anonymous communication scheme based on quantum walks on the Cayley graph is proposed. First, both parties in the communication hide their identity information, and the sender Alice anonymously selects the receiver Bob through logic or operation. Secondly, the trusted third party and the communicating parties use the BB84 protocol to generate and distribute the security key. Alice encrypts the information sequence according to the security key to obtain the blind information; Bob uses the joint Bell state measurement and security key to sign and the trusted third party verifies the signature information. Third, the trusted third party calculates the position probability distribution function of Bob’s quantum walk via the Fourier transform, converts the position information corresponding to the maximum probability into a confirmation frame and sends it to Alice; Alice uses the quantum compression algorithm by decreasing dimensions to reduce the number of transmitted information bits(the length of the information bit can be reduced by up to 37.5%) and uses the security key to complete the information encryption and then transmit the information to the location indicated by the confirmation frame. Bob uses quantum walks to search the location node to obtain the transmission information and complete the anonymous quantum communication. Finally, the security analysis of the scheme is carried out, and the numerical simulation results of the Cayley graph of 200 nodes are given. At the 10-step walk, the maximal probability of the 6th node is 45.31%. According to the simulation results, the probability that Bob is eavesdropped on the specific location at his 10-step walk during the communication of this scheme is approximately 6 × 10–7%, so the receiver can avoid the identity information from the eavesdropping with a high probability, and the quantum network anonymity protocol is not broken.
Lackadaisical quantum walks (LQW) extend discrete-time quantum walks (DTQW) by introducing weighted self-loops, enabling improved spatial-search performance through controlled localization of the walker. Despite substantial theoretical progress, practical gate-level implementations suitable for quantum hardware remain largely unexplored, limiting evaluation under realistic architectural constraints, noise, and resource requirements. In this work, we present a gate-level implementation framework for lackadaisical quantum walk search. The proposed construction encodes the position and coin spaces into qubit registers, and realizes the walk dynamics through oracle, coin, and flip-flop shift operations. We validate the circuit by reproducing the expected search behavior for single and multiple marked vertices and by analyzing the effect of the self-loop weight on the success probability. We further evaluate the implementation under realistic noisy settings using superconducting hardware's noise models. Logical resource analysis shows that, for grids ranging from 8×8 to 64×64, the transpiled gate count increases from 3.63×105 to 4.38×106 and the circuit depth from 2.13×105 to 2.56×106. Finally, fault-tolerant resource estimates based on a surface-code model using the Microsoft Quantum Resource Estimator demonstrate the substantial space-time trade-off associated with magic-state production. The results establish a practical circuit-level pathway for implementing the LQW search and provide a basis for evaluating its performance.