Research On Quantum Cryptography Protocols Based On Grover’s Search Algorithm

Quantum cryptography is the development of the combination of quantum mechanics and classical cryptography.In contrast with classical cryptography,which relies on computational complexity to achieve computational security,quantum cryptography can achieve theoretical unconditional security by exploiting the fundamental principles of quantum mechanics,including the no-cloning theorem.As a result,a wide range of researchers have taken a keen interest in it and have made significant theoretical and experimental breakthroughs.Nowadays,several research branches have been derived from the field of quantum cryptography,such as quantum secret sharing,quantum private query,quantum secure multi-party summation,quantum key agreement,and so on.Grover’s search algorithm,as one of the most famous algorithms in the field of quantum information,has an extremely wide application prospect due to its superior computing power.With the intensive research of researchers,many quantum machine learning algorithms based on the Grover’s search algorithm have emerged,such as quantum K-means clustering algorithm and quantum support vector machine algorithm.Of course,the application of Grover’s search algorithm is not only limited to quantum algorithms,but also can be applied to the design of quantum cryptographic protocols.In this paper,we study and analyze two quantum cryptographic protocols based on the Grover’s search algorithm.The details are as follows.1、A quantum secure multi-party summation based on Grover’s search algorithm is proposed.In this protocol,a semi-trusted third party is introduced for assisting the participants in the task of collaborative computation.Specifically,the participants encode their private information using the unitary operation in Grover’s algorithm.And the security of the communication is guaranteed according to the linear correlation of the quantum states after different numbers of encoding operations.The protocol analysis shows that the protocol can achieve the purpose of multi-party summation and can resist some common attacks.In addition,only single qubits need to be prepared and measured in the protocol,which makes the proposed protocol feasible using current technology.2、An authenticable quantum key agreement protocol is designed using Grover’s search algorithm.By analyzing different types of quantum key agreement protocols,we found that although the circle-type quantum key agreement protocols are more efficient in terms of execution efficiency,they have some security vulnerabilities.Therefore,using the nature of Grover’s search algorithm,we design a quantum key agreement protocol with authentication.In this protocol,a semi-trusted third party is employed to assist the participants in the authentication and key negotiation.In which,each participant prepares two-qubit states and transmits these sequences between participants in a circletype.The protocol still encodes the private key of the participant using the unitary operation of Grover’s search algorithm.Moreover,we design identity encoding operations that conforms to the characteristics of the algorithm,and combine the classical hash function to authenticate the participants’ identities.The security analysis of the protocol shows that the protocol can successfully resist not only some common external attacks and participant attacks,but also impersonation attacks.