A zero-knowledge proof quantum identity authentication method and system

Abstract

The application discloses a zero-knowledge proof quantum identity authentication method and system, and the authentication method comprises the following steps: setting a proving party as Alice and a verifying party as Bob in communication, setting a judgment function for Alice, and providing the corresponding input and output of the judgment function for Bob; Bob prepares 2K groups of superposition states, and sends one group to Alice; Alice performs a phase inversion operation on the received superposition state in combination with the input and output mapping of the judgment function; Bob performs a phase inversion operation on the function output of the superposition state in hand; Bob measures the results inverted by Alice and Bob respectively through a swap test quantum circuit diagram; Bob sends the remaining K-1 groups of superposition state copies to Alice in turn, and Alice and Bob repeat the inversion calculation and measurement steps; and according to the measurement results, the authenticity of the quantum identity information of Alice is judged; the application guarantees that the two parties can complete identity authentication without leaking other information of themselves, and improves the shortcomings of the traditional quantum identity authentication.

Description

TECHNICAL FIELD

[0001] The application relates to a zero-knowledge proof quantum identity authentication method and system, in particular to a zero-knowledge proof quantum identity authentication method and system based on swap test and phase encoding. BACKGROUND

[0002] With the increasing progress of communication informationization and Internet of Things technology, human life has entered the big data era. While we enjoy the convenience of informationization, various security problems such as privacy leakage and illegal data transmission frequently occur, so how to protect information security has been widely concerned by people from all walks of life. In response to the needs of the times, cryptography technology has developed rapidly, and its application field is also expanding. As an important branch of quantum cryptography, quantum authentication has received more and more attention. Quantum authentication is divided into the following aspects: quantum identity authentication, quantum entity authentication and quantum message authentication. Quantum identity authentication is the premise of secure communication between transaction parties and the first line of defense for network security. Existing identity authentication technologies usually need the help of a third party or need to disclose part of their own privacy information, which may be attacked by the third party; the confidentiality of useful information is relatively low, and high-security information exchange and data transmission cannot be achieved. SUMMARY

[0003] The purpose of the application is to provide a zero-knowledge proof quantum identity authentication method and system based on swap test and phase encoding to solve the problem of possible information leakage in the identity authentication process and further improve the security and performance of identity authentication.

[0004] Technical scheme: The zero-knowledge proof quantum identity authentication method comprises the following steps:

[0005] (1) Set the proving party as Alice and the verifying party as Bob, set a decision function for Alice, and provide the corresponding input and output of the decision function for Bob;

[0006] (2) Bob prepares 2K sets of superposition states and sends one set to Alice;

[0007] (3) Alice performs a phase flip operation on the received superposition states combined with the input and output mapping of the decision function;

[0008] (4) Bob performs a phase flip operation on the function output of the superposition states in his hand;

[0009] (5) Bob measures the results of Alice and Bob after the flip through the swap test quantum circuit diagram;

[0010] (6) Bob sends the remaining K-1 copies of superposition states to Alice one by one, and repeats steps (3) to (5), and judges the authenticity of Alice's quantum identity information according to the measurement results.

[0011] In step (1), a decision function C(x) is given, where C: {0,1} n →{0,1}, n is the number of quantum bits, C(0) = 0; Alice is the owner of the function c(x), and Bob has the input S = {S1, S2,..., S N} and the output T = {T1, T2,..., T N} corresponding to the function C(x), C(S i ) = T i , T i ∈{0,1}, i = 1, 2,..., N; Bob does not have any other function-related information except the input and output corresponding to the function.

[0012] In step (2), before authentication, Bob prepares 2K groups of the same superposition state Keep 2K-1 groups, and send one group to Alice, where K is a large constant.

[0013] In step (3), Alice receives the superposition state sent by Bob Then perform a phase flip operation U A , where The subscript A indicates that the operator is Alice; let the output obtained by Alice after performing decision function C(x) calculation on the input {S1, S2,..., S N} be {T'1, T'2,..., T' N}, T' i ∈{0,1}, i = 1, 2,..., N; let the result obtained by Alice after phase flip be It is concluded that:

[0014] U A

[0015] In step (4), Bob performs a phase flip operation U B on one of the superposition states in his hand ; for the given state |x>, The subscript B indicates that the operator is Bob; let the result obtained by Bob after phase flip be |ψ>, and it is concluded that:

[0016]

[0017] In step (5), Bob designs a swap test quantum circuit diagram, Alice and Bob put the flipped results into the circuit in turn, and the quantum identity information provided by Alice is measured to verify the legitimacy of Alice; the circuit input state is After passing through the first Hadamard gate, the result is After passing through the controlled swap gate, the result is After passing through the last Hadamard gate, | Phi > is obtained, and The first quantum bit of the output state | Phi > is measured using the measurement basis {| 0 >, | 1 >}.

[0018] In step (6), the higher the probability of measuring the first quantum state as | 0 >, the closer the two quantum states and | Psi > are, and if The quantum identity information of Alice is true, and the authentication is successful; the higher the probability of measuring the first quantum state as | 1 >, the farther the two quantum states and | Psi > are.

[0019] The application also provides a zero-knowledge proof quantum identity authentication system, comprising:

[0020] A setting module is configured to set a proving party as Alice and a verifying party as Bob, set a decision function for Alice, and provide the corresponding input and output of the decision function for Bob;

[0021] A preparation module is configured to prepare 2K sets of superposition states by Bob, and send one set to Alice;

[0022] A proving party processing module is configured to perform a phase flip operation on the received superposition state combined with the input and output mapping of the decision function by Alice;

[0023] A verifying party processing module is configured to perform a phase flip operation on the function output of the superposition state in hand by Bob;

[0024] A measurement module is configured to measure the flipped results of Alice and Bob by Bob through the swap test quantum circuit diagram;

[0025] A verification module is configured to send the remaining K-1 sets of superposition state copies to Alice in turn by Bob, and judge the authenticity of the quantum identity information of Alice according to the repeated running results of the proving party processing module, the verifying party processing module and the measurement module.

[0026] In the setting module, a decision function C (x) is given, wherein C: {0, 1} n→{0, 1}, where n is the number of qubits, C(0) = 0; Alice is the owner of the function C(x), and Bob has N sets of inputs S = {S1, S2, ..., S...} corresponding to the function C(x). N} and output T = {T1, T2, ..., T N}, C(S i ) = T i T i ∈{0,1}, i=1,2,...,N; Bob has no other function-related information except for the function's corresponding input and output;

[0027] In the preparation module, prior to authentication, Bob prepares 2K identical superposition states. Keep 2K-1 of them and send the other group to Alice, where K is a large constant;

[0028] In the proof-processing module, Alice receives the superposition state sent by Bob. Then perform a phase flip operation U A ,in The subscript A indicates that the operator is Alice; let Alice operate on input {S1, S2, ..., S...} N The output obtained after calculating the decision function C(x) is {T′1, T′2, ..., T′}. N}, T′ i ∈{0,1}, i=1,2,...,N; Let Alice obtain the phase-flipped result as Conclusion:

[0029] U A

[0030] In the verification processing module, Bob holds a set of superposition states in his hand. Perform phase flip operation U B For a given state |x>, The subscript B indicates that the operator is Bob; let the phase flipped result obtained by Bob be |ψ>, then we get:

[0031]

[0032] In the measurement module, Bob designed a swap test quantum circuit diagram. Alice and Bob respectively input the flipped results into the circuit to perform quantum measurements on the quantum identity information provided by Alice, verifying the legitimacy of Alice's identity; the circuit input state is... The result after passing through the first Hadamard gate is: The result after the controlled swap gate is After passing through a Hadamard gate, | Phi > is obtained, and The first qubit of the output state | Phi > is measured using the measurement basis set { | 0 >, | 1 >} ;

[0033] In the checking module, if the probability of measuring the first quantum state as | 0 > is higher, the two quantum states and | Psi > are closer, and if the quantum identity information of Alice is true, and the authentication is successful; if the probability of measuring the first quantum state as | 1 > is higher, the two quantum states and | Psi > are farther apart.

[0034] Advantages: Compared with the prior art, the present application has the following remarkable advantages: 1. The identity authentication of both parties can be completed without revealing other information of themselves, and the deficiencies of the traditional quantum identity authentication are improved; 2. The function input bit string is prepared into a superposition state for transmission, and the communication efficiency is improved. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 The flowchart of the embodiment of the present application is shown in the figure;

[0036] Figure 2 The quantum circuit schematic diagram of the swap test of the present application is shown in the figure;

[0037] Figure 3 The quantum identity authentication schematic diagram of the zero-knowledge proof of the present application is shown in the figure. DETAILED DESCRIPTION

[0038] The technical solutions of the present application will be further described below in combination with the drawings and embodiments.

[0039] As shown in the drawings, the present application provides a zero-knowledge proof quantum identity authentication method and system based on swap test and phase encoding, and the specific process steps are as follows:

[0040] Step 1, assuming that there are two communicating parties Alice and Bob, Alice is the party who proves her own identity, and is the prover in the zero-knowledge proof, Bob is the party who verifies the identity of Alice, and is the verifier in the zero-knowledge proof, Alice is the owner of the judgment function C(x), wherein C: { 0, 1} n → { 0, 1}, n is the number of quantum bits, C(0) = 0. The information owned by Bob is N groups of input S = { S1, S2,..., S N} and output T = { T1, T2,..., T N} corresponding to the function C(x), C(S i ) = T i , T i∈{0,1}, i = 1, 2, ..., N. Alice needs to prove that she owns C(x) without revealing any information about the function (except for T and S owned by Bob). For example, if n = 4, Alice has a key K, and the function E... K (a) is an encryption algorithm that uses the key K, where C(x) = C(b||a) is E K (a) The b-th bit. Let N be 3, S = {00||11, 01||11, 00||01}, T = {0, 1, 1}.

[0041] Step 2, Bob prepares 2K identical superposition states. Keep 2K-1 of these groups and send the other group to Alice, where K is a large constant. For example, if K = 10, the superposition state is...

[0042] Step 3, Alice processes the received superposition state Perform phase flip operation U A ,in The phase flip result is:

[0043] U A :

[0044] Let the result be for but

[0045] Step 4, Bob examines the superposition of states he has. Perform phase flip operation U B For a given state |x>,

[0046] U B :

[0047] The result obtained by flipping Bob's phase If |ψ>, then

[0048] Step 5: Bob designs a swap test quantum circuit diagram. Alice and Bob each input the flipped result sequentially into the circuit to perform quantum measurements on the quantum identity information provided by Alice, verifying the legitimacy of Alice's identity. The circuit input state is... The result after passing through the first Hadamard gate is: The result after the controlled swap gate is Finally, after passing through a Hadamard gate, we obtain |Φ>. The first qubit of the output state |Φ> is measured using the {|0>, |1>} measurement basis.

[0049] In step 6, Bob sends the remaining K-1 sets of superposition state copies to Alice one by one. Bob and Alice perform phase flips on the superposition states one by one, obtaining K-1 output states. The first qubit of the K output states |Φ> is measured using the {|0>, |1>} measurement basis.

[0050] According to the calculation, the probability of measuring |0> is If |ψ> and are two identical quantum states, the probability of measuring |0> is 1, that is, Alice's identity authentication is successful.

Claims

1. A zero-knowledge proof quantum identity authentication method, characterized in that, Includes the following steps: (1) Set Alice as the provider and Bob as the verifier in the communication process. Set a decision function for Alice and provide Bob with the corresponding input and output of the decision function. include: Given a decision function ,in, , It is the number of qubits. Alice is a function The owner, Bob owns group functions Corresponding input and output , Bob possesses no other information related to functions besides their corresponding inputs and outputs. (2) Bob prepares 2K sets of superposition states and sends one set to Alice; including: Bob prepared prior to certification. Group of superposition states Keep it in The group sends another group to Alice, in which It is a constant; (3) Alice performs a phase-flipping operation on the input-output mapping of the received superposition state combined with the decision function; including: Alice received the superposition state sent by Bob. Then perform a phase flip operation. ,in The subscript A indicates that the operator is Alice; let Alice respond to the input... Perform a decision function The output obtained after calculation is { } The result obtained by Alice after phase reversal is: Therefore, we can conclude that: ； (4) Bob performs a phase-flipping operation on the function output of a set of superposition states in his hand; including: Bob has a set of superposition states in his hand Perform phase flip operation For a given state , The subscript B indicates that the operator is Bob; the result of flipping the phase obtained by Bob is... Therefore, we can conclude that: ； (5) Bob uses the swap test quantum circuit diagram to measure the results of Alice and Bob's respective flips; including: Bob designs a swap test quantum circuit diagram. Alice and Bob each input the flipped result into the circuit sequentially to perform quantum measurements on the quantum identity information provided by Alice, verifying Alice's legitimacy. The circuit input state is... The result after passing through the first Hadamard door is The result after passing through the controlled swap gate is Finally, after passing through a Hadamard door, you will get... ,but ,use , Measurement basis output state The first quantum bit is measured; (6) Bob sends the remaining K-1 sets of superposition state copies to Alice sequentially, repeating steps (3) to (5), and determines the authenticity of Alice's quantum identity information based on the measurement results; including: If the first quantum state is measured to be The higher the probability, the better the two quantum states. and The closer, if If Alice's quantum identity information is true, the authentication is successful; if the first quantum state is measured as... The higher the probability, the better the two quantum states. and The more distant they become.

2. A zero-knowledge proof quantum identity authentication system, characterized in that, include: The configuration module is used to configure Alice as the provider and Bob as the verifier in the communication process, to define a decision function for Alice, and to provide Bob with the corresponding inputs and outputs of the decision function; including: providing a decision function. ,in, , It is the number of qubits. Alice is a function The owner, Bob owns group functions Corresponding input and output , Bob possesses no other information related to functions besides their corresponding inputs and outputs. The preparation module is used by Bob to prepare 2K sets of superposition states and send one set to Alice; it includes: Bob preparing... Group of superposition states Keep it in The group sends another group to Alice, in which It is a constant; The proof processing module is used by Alice to perform a phase-flipping operation on the input-output mapping of the received superposition state combined with the decision function; including: Alice receiving the superposition state sent by Bob. Then perform a phase flip operation. ,in The subscript A indicates that the operator is Alice; let Alice respond to the input... Perform a decision function The output obtained after calculation is { } The result obtained by Alice after phase reversal is: Therefore, we can conclude that: ； The verification processing module is used by Bob to perform a phase-flipping operation on the function output of a set of superposition states in his hand; it includes: a set of superposition states in Bob's hand. Perform phase flip operation For a given state , The subscript B indicates that the operator is Bob; the result of flipping the phase obtained by Bob is... Therefore, we can conclude that: ； The measurement module is used by Bob to test a quantum circuit diagram via swap, measuring the results of Alice and Bob's respective flips. It includes: Bob designing a swap test quantum circuit diagram; Alice and Bob sequentially input their flipped results into the circuit to perform quantum measurements on the quantum identity information provided by Alice, verifying the legitimacy of Alice's identity; the circuit input state is... The result after passing through the first Hadamard door is The result after passing through the controlled swap gate is Finally, after passing through a Hadamard door, you will get... ,but ,use , Measurement basis output state The first quantum bit is measured; The verification module is used by Bob to sequentially send the remaining K-1 sets of superposition state copies to Alice, and to determine the authenticity of Alice's quantum identity information based on the repeated runs of the proof processing module, the verification processing module, and the measurement module; including: if the first quantum state is measured as... The higher the probability, the better the two quantum states. and The closer, if If Alice's quantum identity information is true, the authentication is successful; if the first quantum state is measured as... The higher the probability, the better the two quantum states. and The more distant they become.

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