Efficient model detection method for eavesdropping attack of quantum key distribution protocol

Abstract

The invention provides an efficient model detection method for an eavesdropping attack of a quantum key distribution protocol, and the method comprises the steps: 10, carrying out the modeling of an interaction process of the quantum key distribution protocol based on a superoperator value Markov chain, and obtaining a quantum key distribution protocol model; step 20, integrating attack behaviors of an eavesdropper in the quantum key distribution protocol model to obtain a quantum key distribution protocol eavesdropping attack model; step 30, implementing mutual simulation equivalent reduction on the quantum key distribution protocol eavesdropping attack model to obtain a mutual simulation quotient model; step 40, based on the mutual simulation quotient model, formally defining the correctness attribute of the eavesdropping attack of the quantum key distribution protocol by adopting quantum computing tree logic; and step 50, verifying whether the mutual simulation quotient model meets the correctness attribute or not. According to the efficient model detection method for the eavesdropping attack of the quantum key distribution protocol, the eavesdropping attack is considered in the protocol modeling process, meanwhile, the state space is simplified, and the model detection efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of analysis and verification of quantum cryptographic protocols, and in particular to an efficient model detection method for eavesdropping attacks on quantum key distribution protocols. Background Art

[0002] The analysis and verification of quantum cryptographic protocols is a complex system engineering. Since the behavior of quantum systems often does not conform to people's intuition, design flaws are inevitably introduced in the process of manually designing protocols, making it difficult for the protocols to achieve the expected security; or, the protocols are considered to be very secure in the early stages, but are still proven to have defects and loopholes during actual operation. Therefore, it is necessary to conduct formal analysis and verification of the security of quantum cryptographic protocols. At the same time, due to the high complexity of the analysis and verification process of the protocol, static testing and manual verification methods can no longer achieve the purpose of detecting the defects of the protocol itself and potential attacks. Therefore, the protocol automation verification technology has received more and more attention.

[0003] At present, the most widely used technology in the verification of security protocols is model checking. Model checking refers to using an abstract method to obtain a model for a given system, and using an exhaustive method to automatically check whether the model is consistent with the given paradigm. However, model checking is generally used for classical systems with finite or countably infinite state spaces, while the state space of quantum systems is essentially continuous, so how to apply model checking technology to quantum cryptographic protocols is a challenging problem. The paper "Qmc: A model checker for quantum systems" provides an ingenious solution, restricting the state space to a set of states that can be described finitely, called stable substates, and restricting quantum operations to Clifford groups. It uses a completely classical algorithm, but can only model systems that can be expressed in the form of quantum stable substates. The paper "QPMC: A model checker for quantum programs and protocols" breaks through the constraints of stable substates and is more suitable for general quantum protocols, in which quantum effects are completely encoded by superoperator label transfers, while position information remains classical. However, this method does not take into account the threat of eavesdropping attacks that may be suffered by the protocol in practical applications. At the same time, as the number of quantum bits increases, the problem of state space explosion also needs to be solved urgently. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide an efficient model detection method for eavesdropping attacks on quantum key distribution protocols, taking into account the threat of eavesdropping attacks in the protocol modeling process, and introducing the mutual simulation equivalence theory to construct a streamlined state space to improve the efficiency of model detection.

[0005] In order to solve the above technical problems, the present invention provides an efficient model detection method for quantum key distribution protocol eavesdropping attack, comprising the following steps: Step 10, modeling the interaction process of the quantum key distribution protocol based on the super operator value Markov chain to obtain a quantum key distribution protocol model; Step 20, integrating the attack behavior of the eavesdropper into the quantum key distribution protocol model to obtain the quantum key distribution protocol eavesdropping attack model; the attack behavior includes interception operation, retransmission operation and basis vector guessing operation; Step 30, performing mutual simulation equivalence reduction on the quantum key distribution protocol eavesdropping attack model to obtain a mutual simulation quotient model; Step 40, based on the bisimulation quotient model, the correctness property of the quantum key distribution protocol eavesdropping attack is formally defined using the quantum computing tree logic; Step 50, verify whether the bisimulation quotient model satisfies the correctness property.

[0006] Further, the step 20 specifically includes: The attack probability of the eavesdropper is determined. The eavesdropper's strategy is to randomly select basis vectors and re-prepare the quantum state according to the measured results and the selected basis vectors. The eavesdropper's attack behavior is integrated into the quantum key distribution protocol model to obtain the quantum key distribution protocol eavesdropping attack model.

[0007] Further, the step 30 specifically includes: Step 301, in the quantum key distribution protocol eavesdropping attack model, find all state pairs that simultaneously satisfy equations (2), (3) and (4) to form a set of equivalent state pairs: Formula (2) Formula (3) Formula (4) In the formula, represents the label function, represents the successor function, represents bisimulation, Indicates a state. Indicates another state, express A successor state of express a successor state of Step 302, converting the set of equivalent state pairs into a set of equivalence classes; Step 303, obtaining the quotient space of the state space under the equivalence relation according to the equivalence class set; Step 304, obtaining a mutual simulation quotient model according to the transfer system and quotient space of the quantum key distribution protocol eavesdropping attack model.

[0008] Furthermore, in step 302, the set of equivalent state pairs is converted into a set of equivalent classes using formula (5): Formula (5) In the formula, represents an equivalence class, Represents a state set, Indicates a state. express An equivalent state.

[0009] Furthermore, in step 303, according to the equivalence class set, the quotient space of the state space under the equivalence relation is obtained using formula (6): Formula (6) In the formula, Represents the quotient space.

[0010] Furthermore, in step 304, according to the quantum key distribution protocol eavesdropping attack model and the quotient space, the mutual simulation quotient model is obtained using equation (7): Formula (7) In the formula, represents the bisimulation quotient model, represents the quantum key distribution protocol eavesdropping attack model, Indicates any action. represents a set of atomic propositions, Represents a label function.

[0011] Further, the step 40 specifically includes: Based on the bisimulation quotient model, a logical formula for verifying the correctness properties of the model is designed according to the quantum computing tree logical grammar (8): Formula (8) In the formula, represents an atomic proposition, ; , represents a super operator, ; Indicates the number of steps, ; Represents the state formula, Represents a path formula.

[0012] Further, the step 50 specifically includes: For a given state of the key distribution protocol eavesdropping attack model and a state formula , by calculating the state Does it satisfy the set Implement the model validation process; The recursive definition rules that satisfy the set are (9)-(12): Formula (9) Formula (10) Formula (11) Formula (12) Among them, equations (9) to (11) are solved directly through set operations; equation (12) is solved according to the path formula The grammatical structure of is recursively expanded into equation (13)-(15): Formula (13) Formula (14) Formula (15); The simulation verification environment is built using the MATLAB platform, and the bisimulation quotient model is verified to meet the correctness properties according to equations (9) to (15).

[0013] The efficient model detection method for quantum key distribution protocol eavesdropping attack provided by the present invention integrates the interception, retransmission and basis vector guessing operations of the eavesdropper into the key distribution protocol model to fully simulate the eavesdropping attack scenario; introduces the mutual simulation equivalence theory, starts from the symmetric structure of the quantum protocol, identifies and merges the redundant states with consistent behaviors, and constructs a streamlined protocol behavior model; based on the mutual simulation quotient of the model, the correctness properties of the protocol are formally defined using the quantum computing tree logic; finally, it is verified whether the mutual simulation quotient model satisfies the defined correctness properties. The method of the present invention not only effectively solves the state space explosion problem and improves the detection efficiency, but also provides efficient correctness verification in the protocol design stage, helps discover and repair potential security vulnerabilities, and has important theoretical significance and practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 A flow chart of an efficient model detection method for quantum key distribution protocol eavesdropping attacks provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0015] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0016] An efficient model detection method for eavesdropping attacks on quantum key distribution protocols, such as Figure 1 As shown, the following steps are included: Step 10, modeling the interaction process of the quantum key distribution protocol based on the superoperator valued Markov chain to obtain a key distribution protocol model.

[0017] Step 20, integrating the attack behavior of the eavesdropper into the key distribution protocol model to obtain the key distribution protocol eavesdropping attack model, wherein the attack behavior includes interception operation, retransmission operation and basis vector guessing operation.

[0018] Step 30, performing mutual simulation equivalence reduction on the key distribution protocol eavesdropping attack model to obtain a mutual simulation quotient model.

[0019] Step 40, based on the mutual simulation quotient model, the correctness property of the quantum key distribution protocol eavesdropping attack is formally defined using the quantum computing tree logic.

[0020] Step 50, verify whether the bisimulation quotient model satisfies the correctness property.

[0021] Specifically, in step 10, the interaction process of the quantum key distribution protocol is first analyzed, and a quantum key distribution protocol model is constructed based on the superoperator valued Markov chain to formally describe the quantum state preparation, transmission and measurement behaviors of the legitimate communication parties.

[0022] The construction process specifically includes: defining the state space set of the quantum key distribution protocol model, defining the transfer super operator matrix of the quantum key distribution protocol model, defining the atomic proposition set of the quantum key distribution protocol model, defining the label function of the quantum key distribution protocol model, and obtaining the quantum key distribution protocol model shown in formula (1): Formula (1) In the formula, Represents the quantum key distribution protocol model; Represents a state set; represents the transfer super operator matrix, , represents a finite-dimensional Hilbert space; for any , , express The unit super operator on ; represents a set of atomic propositions, Represents the label function, from arrive 's mapping.

[0023] In step 20, the eavesdropper's attack behavior is integrated into the quantum key distribution protocol model. The attack behavior includes interception operation, retransmission operation and basis vector guessing operation, which affects the protocol behavior by interfering with the quantum state transfer and measurement process.

[0024] As a preferred example, step 20 specifically includes: Determine the attack probability of an eavesdropper The strategy of the eavesdropper is to randomly select basis vectors and re-prepare quantum states according to the measured results and the selected basis vectors. The attack behavior of the eavesdropper is integrated into the quantum key distribution protocol model to obtain the quantum key distribution protocol eavesdropping attack model.

[0025] As a preferred example, step 30 specifically includes: Step 301, in the quantum key distribution protocol eavesdropping attack model, find all state pairs that simultaneously satisfy equations (2), (3) and (4) to form a set of equivalent state pairs: Formula (2) Formula (3) Formula (4) In the formula, represents the label function, represents the successor function, represents bisimulation, Indicates a state. Indicates another state, express A successor state of express A successor state. , recorded as .

[0026] Step 303, using formula (5) to convert the set of equivalent state pairs into a set of equivalent classes: Formula (5) In the formula, represents an equivalence class, Represents a state set, Indicates a state. express An equivalent state of . ,if , then .

[0027] Step 303, according to the equivalence class set, use formula (6) to obtain the quotient space of the state space under the equivalence relation: Formula (6) In the formula, Represents the quotient space.

[0028] Step 304, according to the quantum key distribution protocol eavesdropping attack model and quotient space, use formula (7) to obtain the mutual simulation quotient model: Formula (7) In the formula, Represents the bisimulation quotient model. Represents the eavesdropping attack model of quantum key distribution protocol. represents any action. Since the action transfer super operator is ignored, Replace all transfer super operators. Represents a set of atomic propositions. represents the label function, .

[0029] As a preferred example, step 40 specifically includes: Based on the bisimulation quotient model, the logical formula for verifying the correctness properties of the model is designed according to the quantum computing tree logic QCTL syntax (8): Formula (8) In the formula, represents an atomic proposition, ; , represents a super operator, ; Indicates the number of steps, ; Represents the state formula, Represents a path formula.

[0030] As a preferred example, step 50 specifically includes: For a given state of the key distribution protocol eavesdropping attack model and a state formula , by calculating the state Does it satisfy the set Implement the model validation process; The recursive definition rules that satisfy the set are (9)-(12): Formula (9) Formula (10) Formula (11) Formula (12) Among them, equations (9) to (11) are solved directly through set operations; equation (12) is solved according to the path formula The grammatical structure of is recursively expanded into equation (13)-(15): Formula (13) Formula (14) Formula (15); The simulation verification environment is built using the MATLAB platform, and the bisimulation quotient model is verified to meet the correctness properties according to equations (9) to (15).

[0031] The following takes the BB84 protocol as an example and uses the method of the present invention to perform detection.

[0032] Step 10: Analyze the interaction process of the BB84 protocol as follows: Step 1: The sender randomly creates two bit strings and , the size of each bit string is n; Step 2: The sender prepares a string of qubits , of size n, such that The i-th qubit of , where x and y are and , and , , , ; Step 3: The sender sends the quantum bit string Send to the recipient; Step 4: The receiver randomly generates a bit string of size n ; In step 5, the receiver measures each qubit received from the sender based on the measurement basis determined by the bits it generated: if The i-th position of is k, then he uses { , }Measurement The i-th quantum bit of , where k = 0 or 1; let the measurement result be , which is also a bit string of size n; Step 6: The receiver sends the measurement basis he chooses The sender sends the information back to the sender, who then sends her measurement Send to the recipient; Step 7: The sender and receiver determine where the bit string is located. and equal; they discard those corresponding to and The bits are not equal and bits in .

[0033] The state space set of the BB84 protocol model is defined as: ; The transfer super operator matrix of the BB84 protocol model is: The sender prepares the quantum state: , , , , , ; The receiver randomly selects the basis vector: and ,in, ; Receiver measurement: , , , and ; termination: ; Among them, X and Z are Pauli-X and Pauli-Z superoperators respectively. , , ; The set of atomic propositions of the BB84 protocol model is ; The label function of the BB84 protocol model is , .

[0034] Step 20, integrating attacker behaviors based on the BB84 protocol model obtained in step 10, including interception operations, retransmission operations, and basis vector guessing operations.

[0035] The state space set of the BB84 protocol eavesdropping attack model is: ; The transfer super operator matrix of the BB84 protocol eavesdropping attack model is: The sender prepares the quantum state: , , , , , ; Eavesdropper has The probability of eavesdropping is: and ,in, ; If the eavesdropper is not eavesdropping, the receiver randomly selects the measurement basis: and ,in, =7,9,11,13; Receiver measurement: , , , and ; If an eavesdropper eavesdrops, the eavesdropper randomly selects a basis vector: and ,in, =8,10,12,14; the eavesdropper re-prepares the quantum state based on the measurement results: , , , , , , , , , , , ; The receiver randomly selects the measurement basis: and ,in, ; Receiver measurement: , , , , ; termination: ; The atomic proposition set of the BB84 protocol eavesdropping attack model is ; The label function of the BB84 protocol eavesdropping attack model is , .

[0036] Step 30, in the BB84 protocol eavesdropping attack model obtained in step 20, find all state pairs that simultaneously satisfy equations (2), (3) and (4). , we get the set of all state pairs belonging to the equivalence relation in the BB84 protocol eavesdropping attack model: .

[0037] Convert all equivalence relations into equivalence classes, and get the set of all equivalence classes in the BB84 protocol eavesdropping attack model as follows: .

[0038] Get the quotient space in the BB84 protocol eavesdropping attack model for: .

[0039] Get the bisimulation quotient model.

[0040] Step 40, assuming that the probability of the eavesdropper eavesdropping is , then the total probability of the eavesdropper successfully eavesdropping is , the total probability of successful key distribution is .

[0041] Based on the bisimulation quotient model obtained in step 30, the logical formula for testing the correctness of the model is designed according to the grammar formula (8) of QCTL: ,

[0042] in, .

[0043] The simulation verification environment is built using the MATLAB platform. According to equations (9) to (15), it is verified whether the bisimulation quotient model satisfies the correctness properties described by the above formula.

[0044] The efficient model detection method for quantum key distribution protocol eavesdropping attacks in this embodiment constructs a protocol model for the quantum key distribution protocol and integrates attacker behavior based on the protocol model. It can model different types of quantum key distribution protocols and has universality. The mutual simulation equivalence theory is introduced, starting from the symmetric structure of the quantum protocol, redundant states with consistent behaviors are identified and merged, and a streamlined protocol behavior model is constructed to alleviate the common state explosion problem in model verification, reduce the state space and state migration required for verification, and thus reflect the efficiency of the model.

[0045] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above specific embodiments. The above specific embodiments and the description in the specification are only for further illustrating the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of the present invention to be protected is defined by the claims and their equivalents.

Claims

1. An efficient model detection method for quantum key distribution protocol eavesdropping attacks, characterized in that: The following steps are involved: Step 10, modeling the interaction process of the quantum key distribution protocol based on the super operator value Markov chain to obtain a quantum key distribution protocol model; Step 20, integrating the attack behavior of the eavesdropper into the quantum key distribution protocol model to obtain the quantum key distribution protocol eavesdropping attack model; the attack behavior includes interception operation, retransmission operation and basis vector guessing operation; Step 30, performing mutual simulation equivalence reduction on the quantum key distribution protocol eavesdropping attack model to obtain a mutual simulation quotient model; Step 40, based on the bisimulation quotient model, the correctness property of the quantum key distribution protocol eavesdropping attack is formally defined using the quantum computing tree logic; Step 50, verify whether the bisimulation quotient model satisfies the correctness property.

2. The efficient model detection method for quantum key distribution protocol eavesdropping attack according to claim 1 is characterized in that: The step 20 specifically includes: The attack probability of the eavesdropper is determined. The eavesdropper's strategy is to randomly select basis vectors and re-prepare the quantum state according to the measured results and the selected basis vectors. The eavesdropper's attack behavior is integrated into the quantum key distribution protocol model to obtain the quantum key distribution protocol eavesdropping attack model.

3. The efficient model detection method for quantum key distribution protocol eavesdropping attack according to claim 1 is characterized in that: The step 30 specifically includes: Step 301, in the quantum key distribution protocol eavesdropping attack model, find all state pairs that simultaneously satisfy equations (2), (3) and (4) to form a set of equivalent state pairs: Formula (2) Formula (3) Formula (4) In the formula, represents the label function, represents the successor function, represents bisimulation, Indicates a state. Indicates another state, express A successor state of express a successor state of Step 302, converting the set of equivalent state pairs into a set of equivalence classes; Step 303, obtaining the quotient space of the state space under the equivalence relation according to the equivalence class set; Step 304, obtaining a mutual simulation quotient model according to the transfer system and quotient space of the quantum key distribution protocol eavesdropping attack model.

4. The efficient model detection method for quantum key distribution protocol eavesdropping attack according to claim 3, characterized in that: In step 302, the set of equivalent state pairs is converted into a set of equivalent classes using equation (5): Formula (5) In the formula, represents an equivalence class, Represents a state set, Indicates a state. express An equivalent state.

5. The efficient model detection method for quantum key distribution protocol eavesdropping attack according to claim 3, characterized in that: In step 303, according to the equivalence class set, the quotient space of the state space under the equivalence relation is obtained using formula (6): Formula (6) In the formula, Represents the quotient space.

6. The efficient model detection method for quantum key distribution protocol eavesdropping attack according to claim 3, characterized in that: In step 304, according to the quantum key distribution protocol eavesdropping attack model and quotient space, the mutual simulation quotient model is obtained using equation (7): Formula (7) In the formula, represents the bisimulation quotient model, represents the quantum key distribution protocol eavesdropping attack model, Indicates any action. represents a set of atomic propositions, Represents a label function.

7. The efficient model detection method for quantum key distribution protocol eavesdropping attack according to claim 1 is characterized in that: The step 40 specifically includes: Based on the bisimulation quotient model, a logical formula for verifying the correctness properties of the model is designed according to the quantum computing tree logical grammar (8): Formula (8) In the formula, represents an atomic proposition, ; , represents a super operator, ; Indicates the number of steps, ; Represents the state formula, Represents a path formula.

8. The efficient model detection method for quantum key distribution protocol eavesdropping attack according to claim 1 is characterized in that: The step 50 specifically includes: For a given state of the key distribution protocol eavesdropping attack model and a state formula , by calculating the state Does it satisfy the set Implement the model validation process; The recursive definition rules that satisfy the set are (9)-(12): Formula (9) Formula (10) Formula (11) Formula (12) Among them, equations (9) to (11) are solved directly through set operations; equation (12) is solved according to the path formula The grammatical structure of is recursively expanded into equation (13)-(15): Formula (13) Formula (14) Formula (15); The simulation verification environment is built using the MATLAB platform, and the bisimulation quotient model is verified to meet the correctness properties according to equations (9) to (15).

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