Quantum secure direct communication method based on one-time pad mode

Abstract

The invention discloses a quantum secure direct communication method based on a one-time pad mode, which belongs to the technical field of quantum communication, and comprises the following steps: Bob prepares a batch of coherent states and sends the coherent states to Alice through a quantum channel, the Alice divides the received coherent states into two groups, performs homodyne detection on one group and sends a detection result to Bob, and the Bob sends the detection result to the Alice; the Bob performs security detection according to the first effective information amount; the Alice encodes the coherent states according to the secret information and sends the encoded coherent states to the Bob, the Bob randomly selects one coherent state to execute homodyne detection and sends a result to the Alice, and the Alice performs security detection according to the second effective information amount; bob performs homodyne detection on other coherent states, calculates a threshold value, and demodulates the threshold value to obtain secret information; the continuous variable quantum state is adopted, generation and detection are easy, loss is small in the transmission process, safety is high, and compatibility with the standard telecommunication technology can be achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of quantum communication, and in particular relates to a quantum secure direct communication method based on a one-time pad mode. Background Art

[0002] In classical secure communication, the one-time pad is the only classical encryption method that is theoretically absolutely secure so far. In the classical one-time pad, since the keys used by both parties for encryption and decryption are completely random to the eavesdropper, and the keys are only used once, the ciphertext transmitted in the channel, that is, the file obtained by encrypting the confidential information with the key, is completely random to the eavesdropper; that is, the confidential information that the eavesdropper can obtain from the ciphertext is the same as the confidential information he can directly guess, so the absolute security of the classical one-time pad is actually based on the completely random result of the key.

[0003] Quantum secure direct communication is a new branch of quantum communication. Unlike quantum key distribution, which establishes a random key between the communicating parties, in quantum secure direct communication, the sender's secret message is directly transmitted to the receiver without sharing the private key in advance. In other words, quantum secure direct communication has no ciphertext, no key, and even no key management. Only protocols that meet the following two requirements can be called quantum secure direct communication: on the one hand, after the quantum bit is transmitted, the receiver should directly read out the secret information without the need for additional classical information; on the other hand, even if there is an eavesdropper present, the encoded quantum state should not be leaked, that is, the eavesdropper cannot obtain any useful information in the quantum state.

[0004] At present, most quantum secure direct communication protocols are based on the discrete variable state of single photons for communication. However, single photons are difficult to be compatible with standard telecommunications technology, and are not easy to generate and detect. They are prone to large losses during transmission, resulting in low communication efficiency. Summary of the invention

[0005] The purpose of the present invention is to provide a quantum secure direct communication method based on a one-time pad mode to solve the problem of low communication efficiency of existing quantum secure direct communication.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is a quantum secure direct communication method based on a one-time pad mode, comprising the following steps:

[0007] S1. The sender prepares a set of coherent states A and sends it to the receiver through a quantum channel;

[0008] S2. The receiver randomly divides the received coherent state A into coherent state S and coherent state B, performs homodyne detection on each coherent state in the coherent state S, and sends the orthogonal position, orthogonal momentum and homodyne detection result of the coherent state S to the sender. The sender performs a security check based on the first effective information amount. If the first effective information amount is greater than the security threshold, the next step is performed. If the first effective information amount is less than the security threshold, the communication is abandoned.

[0009] S3. The receiver encodes the coherent state B according to the secret information. If the secret information sent is 0, the unitary operation D(α1) is used for encoding. If the secret message sent is 1, the unitary operation D(α2) is selected for encoding, and the encoded coherent state B is sent to the sender.

[0010] S4, the sender randomly selects a coherent state from the received coherent state B to perform homodyne detection, and sends the orthogonal position, orthogonal momentum and homodyne detection result of the coherent state to the receiver, and the receiver performs a security check based on the second effective information amount. If the second effective information amount is greater than the security threshold, the next step is performed. If the second effective information amount is less than the security threshold, the communication is abandoned;

[0011] S5. The sender performs homodyne detection on the remaining coherent states B and calculates the threshold. If the homodyne detection result is less than the threshold, the sender believes that the receiver is performing the unitary operation D(α1) and demodulates to obtain the secret information 0. If the homodyne detection result is greater than the threshold, the sender believes that the receiver is performing the unitary operation D(α2) and demodulates to obtain the secret information 1.

[0012] S6. After demodulation is completed, the sender calculates the quantum bit error rate of the secret information 0 and 1, and determines whether the quantum channel is secure based on the quantum bit error rate.

[0013] Furthermore, in step S1, the coherent state A received by the receiver is represented by |X A +iP A >, where:

[0014]

[0015] In the formula, X A is the orthogonal position of the coherent state received by the receiver, P A is the orthogonal momentum of the coherent state received by the receiver, X B is the orthogonal position of the coherent state sent by the sender, P B is the orthogonal momentum of the coherent state sent by the sender, i is the imaginary unit, δX ex Represents X A The channel noise, δP ex Indicates P A The channel noise, δX vRepresents X A The shot noise, δP v Indicates P A The shot noise, ∈ is the excess noise in the transmission process, T is the transmission efficiency, T = 10 -0.02L , L is the transmission distance, V B is the modulation variance of the sender.

[0016] Furthermore, in step S2, the receiver performs homodyne detection and the result is represented as |X' A +iP' A >, where:

[0017]

[0018] Where X' A is the orthogonal position obtained by homodyne detection, P' A is the orthogonal momentum obtained by homodyne detection, i is the imaginary unit, X B is the orthogonal position of the coherent state sent by the sender, P B is the orthogonal momentum of the coherent state sent by the sender, η represents the homodyne detection efficiency, T is the transmission efficiency, δX ex Represents X' A The channel noise, δP ex P' A The channel noise, δX v Represents X' A The shot noise, δP v P' A The shot noise, δX el Represents X' A The electrical noise, δP el P' A The electrical noise, v el is the numerical value of electrical noise.

[0019] Further, in step S2, the first effective information amount is expressed as:

[0020] ΔI1=βI AB -x AE

[0021] In the formula, ΔI1 is the first effective information amount, β is the negotiation efficiency, I AB is the Shannon mutual information between the receiver and the sender, χ AE is the Hoogland bound of the mutual information between the receiver and a possible eavesdropper, and the security threshold is greater than zero.

[0022] Furthermore, in step S3, the unitary operation D(α1) is expressed as:

[0023]

[0024] In the formula, α1 is an intermediate parameter with no practical significance. is the change in the mean value of the quantum state caused by the unitary operation D(α1), i is the imaginary unit, X A is the orthogonal position of the coherent state received by the receiver, P A is the orthogonal momentum of the coherent state received by the receiver, X u Represents X A The first Gaussian variable, P u Indicates P A The first Gaussian variable, X u , P u Satisfies Gaussian distribution The intermediate parameters have no practical meaning. V is the variance, χ line To detect the additional noise, χ line =1 / T+∈-1, T is the transmission efficiency, ∈ is the excess noise in the transmission process;

[0025] The unitary operation D(α2) is expressed as:

[0026]

[0027]

[0028] In the formula, α2 is an intermediate parameter with no practical significance. is the change in the mean value of the quantum state caused by the unitary operation D(α2), X v Represents X A The second Gaussian variable, P v Indicates P A The second Gaussian variable.

[0029] Further, in step S4, the second effective information amount is expressed as:

[0030] ΔI2=βI AB -x BE

[0031] In the formula, ΔI2 is the second effective information amount, β is the negotiation efficiency, I AB is the Shannon mutual information between the receiver and the sender, χ BE is the Hoogland bound of the mutual information between the sender and the possible eavesdropper, and the security threshold is greater than zero.

[0032] Further, in step S5, the threshold is expressed as:

[0033]

[0034] In the formula, is the threshold value, is the change in the mean value of the quantum state caused by the unitary operation D(α1), is the change in the mean of the quantum state caused by the unitary operation D(α2).

[0035] Further, in step S6, the quantum bit error rate is calculated as:

[0036]

[0037] Where P 0err is the quantum bit error rate of secret information 0, P 1err is the quantum bit error rate of secret information 1, is the threshold value, is the change in the mean value of the quantum state caused by the unitary operation D(α1), is the change in the mean value of the quantum state caused by the unitary operation D(α2), σ u It is an intermediate parameter with no practical meaning, and x is the integral variable.

[0038] The beneficial effects of the present invention are:

[0039] The present invention uses unitary operations to express secret information, including two stages: security detection and information transmission. In the security detection stage, Bob and Alice randomly select part of the coherent state to calculate the effective information amount, and judge the security of the channel by comparing the effective information amount and the security threshold. This stage can avoid eavesdropping by EVE and increase communication security; in the information transmission stage, Alice encodes the coherent state of the secret message through two different unitary operations, and then sends it back to Bob. The unitary operation can maintain the normalization and coherence of the quantum state and ensure the integrity of the information.

[0040] The present invention uses the quantum state of continuous variables for direct communication, continuing the advantage of compatibility with standard telecommunication technology, and the coherent state has good noise resistance during transmission, which is suitable for long-distance communication. If the communicating parties Alice and Bob need to share a batch of quantum states, then Alice can load secret information on the quantum state and publish it on the standard telecommunication channel. This process is completely random for Eve, and has the same security as the classical encryption method of one-time pad, that is, absolutely safe. The present invention uses the quantum state of continuous variables, which is easy to generate and detect, has low loss during transmission, high security, and is compatible with standard telecommunication technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0042] Figure 1 This is a flow chart of a quantum secure direct communication method based on a one-time pad mode according to the present invention;

[0043] Figure 2 This is a schematic diagram of a function of quantum bit error rate in Example 1 of the present invention;

[0044] Figure 3 It is a schematic diagram of a function of the first effective information amount in Embodiment 2 of the present invention. DETAILED DESCRIPTION

[0045] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] A quantum secure direct communication method based on a one-time pad mode comprises the following steps:

[0047] S1. The sender Bob prepares a set of coherent states A and sends them to the receiver Alice through a quantum channel. Each coherent state is represented by |X B +iP B >, where X B is the orthogonal position of the coherent state sent by Bob, P B is the orthogonal momentum of the coherent state sent by Bob, i is the imaginary unit, X B and P B Obey Gaussian distribution V B is the modulation variance of Bob. The coherent state A is affected by the quantum channel noise during the transmission process, so the coherent state received by Alice is expressed as |X A +iP A >, where:

[0048]

[0049] In the formula, X A is the orthogonal position of the coherent state received by Alice, P Ais the orthogonal momentum of the coherent state received by Alice, i is an imaginary unit, δX ex Represents X A The channel noise, δP ex Indicates P A The channel noise, δX v Represents X A The shot noise, δP v Indicates P A The shot noise, ∈ is the excess noise in the transmission process, T is the transmission efficiency, T = 10 -0.02L , L is the transmission distance.

[0050] S2. Alice randomly divides the received coherent state A into coherent state S and coherent state B, and performs homodyne detection on each coherent state in coherent state S. The detection result is expressed as |X' A +iP' A >, where:

[0051]

[0052] Where X' A is the orthogonal position obtained by homodyne detection, P' A is the orthogonal momentum obtained by homodyne detection, η represents the homodyne detection efficiency, δX el Represents X' A The electrical noise, δP el P' A The electrical noise, v el Indicates the specific numerical value of electrical noise.

[0053] After the detection is completed, Alice sends the orthogonal position, orthogonal momentum and homodyne detection results of the coherent state S to Bob, who performs security detection based on the first effective information amount, which is expressed as:

[0054] ΔI1=βI AB -x AE

[0055]

[0056] In the formula, ΔI1 is the first effective information amount, β is the negotiation efficiency, I AB is the Shannon mutual information between Alice and Bob, χ AE is the (Holevo) bound of the mutual information between Alice and the possible eavesdropper Eve, V is the variance, χ tot is the total noise of the channel input, χ tot = x line +χ hom / T,χ homis the oscillator homomorphic noise, χ line To detect the additional noise, χ line =1 / T+∈-1, S is the von Neumann entropy, is the first quantum state, is the second quantum state.

[0057] Considering the Gaussian state G(x) in the first effective information derivation, it can be further simplified as:

[0058]

[0059] where G(x) = (x+1)log2(x+1)-xlog2x, λ i is the symplectic eigenvalue.

[0060] The first quantum state The covariance matrix of for:

[0061]

[0062] Among them is The identity matrix, is the Pauli matrix, diag is the matrix constructor;

[0063] satisfy:

[0064]

[0065] In the formula, λ 1,2 is the covariance matrix The corresponding symplectic eigenvalues, A and B are intermediate parameters with no practical significance, where:

[0066] A=V 2 +T 2 (V+χ line ) 2 -2T(V 2 -1)

[0067] B=T 2 (x line +1) 2

[0068] Similarly, the second quantum state The covariance matrix of λ 3,4,5 is the covariance matrix The corresponding symplectic eigenvalues ​​satisfy:

[0069]

[0070] In the formula, C is an intermediate parameter with no practical significance, among which:

[0071]

[0072] The security threshold is set to be greater than zero. If the first amount of valid information is greater than the security threshold, proceed to the next step. If the first amount of valid information is less than the security threshold, it indicates that an attack exists and communication is abandoned.

[0073] S3. Alice encodes the coherent state B according to the secret information. If the secret message sent is 0, the unitary operation D(α1) is selected for encoding, which is:

[0074]

[0075] In the formula, α1 is an intermediate parameter with no practical significance. is the change in the mean value of the quantum state caused by the unitary operation D(α1), X u Represents X A The first Gaussian variable, P u Indicates P A The first Gaussian variable satisfies the Gaussian distribution σ u The intermediate parameters have no practical meaning. T is the transmission efficiency;

[0076] If the secret message sent is 1, the unitary operation D(α2) is selected for encoding, which is:

[0077]

[0078] In the formula, α2 is an intermediate parameter with no practical significance. is the change in the mean value of the quantum state caused by the unitary operation D(α2), X v Represents X A The second Gaussian variable, P v Indicates P A The second Gaussian variable.

[0079] Alice sends the encoded coherent state B to Bob through a standard telecommunication channel.

[0080] S4. Bob randomly selects a coherent state from the received coherent state B to perform homodyne detection. After the detection is completed, Bob sends the orthogonal position, orthogonal momentum and homodyne detection result of the coherent state to Alice. Alice performs security detection based on the second effective information amount. The second effective information amount is expressed as:

[0081] ΔI2=βI AB -x BE

[0082] In the formula, ΔI2 is the second effective information amount, β is the negotiation efficiency, I AB is the Shannon mutual information between Alice and Bob, χ BE is the Hoogley bound for the mutual information between Bob and the possible eavesdropper Eve;

[0083] A security threshold is set, the security threshold is greater than zero, if the second effective information amount is greater than the security threshold, proceed to the next step, if the second effective information amount is less than the security threshold, the communication is abandoned.

[0084] S5. Bob performs homodyne detection on the remaining coherent state B and calculates the threshold, which is expressed as:

[0085]

[0086] In the formula, is the threshold value;

[0087] If the homodyne detection result is less than the threshold, Bob believes that Alice is performing the unitary operation D(α1) and demodulates to obtain the secret information 0. If the homodyne detection result is greater than the threshold, Bob believes that Alice is performing the unitary operation D(α2) and demodulates to obtain the secret information 1.

[0088] S6. After demodulation is completed, Bob calculates the quantum bit error rate of the secret information 0 and 1, and judges whether the quantum channel is secure based on the quantum bit error rate. The quantum bit error rate is:

[0089]

[0090] Where P 0err is the quantum bit error rate of secret information 0, P 1err is the quantum bit error rate of secret information 1, σ u It is an intermediate parameter with no practical meaning, and x is the integral variable.

[0091] like Figure 1 As shown, it is a schematic diagram of the flow of the quantum secure direct communication method based on the one-time pad mode of the present invention.

[0092] Example 1

[0093] A quantum secure direct communication method based on a one-time pad mode provided by the present invention is used for quantum communication, and ∈=0.01 is set. set up The quantum bit error rates are 1, 4, and 7, respectively. The results are as follows Figure 2 As shown, it can be seen that the added parameters The value of can reduce the quantum bit error rate, that is, setting two unitary operations D(α1) and D(α2) with large differences can obtain better performance. In addition, choosing a smaller modulation variance over a shorter transmission distance can further reduce the quantum bit error rate.

[0094] Example 2

[0095] A quantum secure direct communication method based on a one-time pad mode provided by the present invention is used for quantum communication, and ∈=0.05, β=0.95, v el =0.01, η=0.6, detection modulation variance V B The influence of transmission distance on the first effective information volume, such as Figure 3 As shown, it can be seen that the first effective information amount slowly decreases as the modulation variance increases in the transmission distance. In the figure, 80% ΔImax(U) and 80% ΔImax(L) represent the upper and lower dividing lines of 80% of the optimal value of the first effective information amount. It can be seen that the optimal value of the first effective information amount can be obtained by selecting the corresponding modulation variance according to the transmission distance.

[0096] Each embodiment in this specification is described in a related manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0097] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A quantum secure direct communication method based on a one-time pad mode, characterized in that: The following steps are involved: S1. The sender prepares a set of coherent states A and sends it to the receiver through a quantum channel; S2. The receiver randomly divides the received coherent state A into coherent state S and coherent state B, performs homodyne detection on each coherent state in the coherent state S, and sends the orthogonal position, orthogonal momentum and homodyne detection result of the coherent state S to the sender. The sender performs a security check based on the first effective information amount. If the first effective information amount is greater than the security threshold, the next step is performed. If the first effective information amount is less than the security threshold, the communication is abandoned. S3. The receiver encodes the coherent state B according to the secret information. If the secret information sent is 0, the unitary operation D(α1) is used for encoding. If the secret message sent is 1, the unitary operation d(α2) is selected for encoding, and the encoded coherent state B is sent to the sender. S4, the sender randomly selects a coherent state from the received coherent state B to perform homodyne detection, and sends the orthogonal position, orthogonal momentum and homodyne detection result of the coherent state to the receiver, and the receiver performs a security check based on the second effective information amount. If the second effective information amount is greater than the security threshold, the next step is performed. If the second effective information amount is less than the security threshold, the communication is abandoned; S5. The sender performs homodyne detection on the remaining coherent states B and calculates the threshold. If the homodyne detection result is less than the threshold, the sender believes that the receiver is performing the unitary operation D(α1) and demodulates to obtain the secret information 0. If the homodyne detection result is greater than the threshold, the sender believes that the receiver is performing the unitary operation D(α2) and demodulates to obtain the secret information 1. S6. After demodulation is completed, the sender calculates the quantum bit error rate of the secret information 0 and 1, and determines whether the quantum channel is secure based on the quantum bit error rate.

2. A quantum secure direct communication method based on a one-time pad mode according to claim 1, characterized in that: In step S1, the coherent state A received by the receiver is represented by |X A +iP A >, where: Where, X A is the orthogonal position of the coherent state received by the receiver, P A is the orthogonal momentum of the coherent state received by the receiver, X B is the orthogonal position of the coherent state sent by the sender, P B is the orthogonal momentum of the coherent state sent by the sender, i is the imaginary unit, δX ex Represents X A The channel noise, δP ex Indicates P A The channel noise, δX v Represents X A The shot noise, δP v Indicates P A The shot noise, ∈ is the excess noise in the transmission process, T is the transmission efficiency, T = 10 -0.02L , L is the transmission distance, V B is the modulation variance of the sender.

3. A quantum secure direct communication method based on a one-time pad mode according to claim 1, characterized in that: In step S2, the receiver performs homodyne detection and the result is represented as |X' A +iP' A >, where: Where X' A is the orthogonal position obtained by homodyne detection, P' A is the orthogonal momentum obtained by homodyne detection, i is the imaginary unit, X B is the orthogonal position of the coherent state sent by the sender, P B is the orthogonal momentum of the coherent state sent by the sender, η represents the homodyne detection efficiency, T is the transmission efficiency, δX ex Represents X' A The channel noise, δP ex P' A The channel noise, δX v Represents X' A The shot noise, δP v P' A The shot noise, δX el Represents X' A The electrical noise, δP el P' A The electrical noise, v el is the numerical value of electrical noise.

4. According to claim 1, a quantum secure direct communication method based on a one-time pad mode is characterized in that: In step S2, the first effective information amount is expressed as: ΔI1=βI AB -x AE In the formula, ΔI1 is the first effective information amount, β is the negotiation efficiency, I AB is the Shannon mutual information between the receiver and the sender, χ AE The Hoogler bound for the mutual information between the receiver and possible eavesdroppers; The safety threshold is greater than zero.

5. The quantum secure direct communication method based on the one-time pad mode according to claim 1, characterized in that: In step S3, the unitary operation D(α1) is expressed as: In the formula, α1 is an intermediate parameter with no practical significance, Q is the change in the mean value of the quantum state caused by the unitary operation D(α1), i is an imaginary unit, and X A is the orthogonal position of the coherent state received by the receiver, P A is the orthogonal momentum of the coherent state received by the receiver, X u Represents X A The first Gaussian variable, P u Indicates P A The first Gaussian variable, X u , P u Satisfies Gaussian distribution The intermediate parameters have no practical meaning. V is the variance, χ line To detect the additional noise, χ line =1 / T+∈-1, T is the transmission efficiency, ∈ is the excess noise in the transmission process; The unitary operation D(α2) is expressed as: In the formula, α2 is an intermediate parameter with no practical significance. is the change in the mean value of the quantum state caused by the unitary operation D(α2), X v Represents X A The second Gaussian variable, P v Indicates P A The second Gaussian variable.

6. A quantum secure direct communication method based on a one-time pad mode according to claim 1, characterized in that: In step S4, the second effective information amount is expressed as: ΔI2=βI AB -x BE In the formula, ΔI2 is the second effective information amount, β is the negotiation efficiency, I AB is the Shannon mutual information between the receiver and the sender, χ BE The Hoogler bound for the mutual information between the sender and possible eavesdroppers; The safety threshold is greater than zero.

7. A quantum secure direct communication method based on a one-time pad mode according to claim 1, characterized in that: In step S5, the threshold is expressed as: In the formula, is the threshold value, is the change in the mean value of the quantum state caused by the unitary operation D(α1), is the change in the mean of the quantum state caused by the unitary operation D(α2).

8. The method for quantum secure direct communication based on a one-time pad mode according to claim 1, characterized in that: In step S6, the quantum bit error rate is calculated as: Where P 0err is the quantum bit error rate of secret information 0, P 1err is the quantum bit error rate of secret information 1, is the threshold value, is the change in the mean value of the quantum state caused by the unitary operation D(α1), is the change in the mean value of the quantum state caused by the unitary operation D(α2), σ u It is an intermediate parameter with no practical meaning, and x is the integral variable.

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