Efficient data negotiation method and device suitable for CV-QKD

Abstract

The invention provides an efficient data negotiation method and device suitable for CV-QKD. The method comprises the following steps: inputting data x and data y; setting a dimension d of data negotiation; constructing a d-dimensional random orthogonal matrix B (d); calculating a specular reflection matrix S according to the data x; calculating a mapping relation according to the mirror reflection matrix S and the orthogonal matrix B (d); calculating mapped data v according to the mapping relation and the data y; and calculating negotiated data R according to the mapped data v. According to the data negotiation scheme based on the Butterfly random orthogonal matrix, the corresponding optimal negotiation dimension can be selected for data negotiation according to the signal-to-noise ratio of the negotiated data, and the loss of the signal-to-noise ratio after negotiation is controlled within an acceptable range, so that efficient data negotiation is realized, and finally, the security code rate of the CV-QKD system is effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of continuous variable quantum key distribution (CV-QKD), and in particular to an efficient data negotiation method and device suitable for CV-QKD. Background Art

[0002] With the development of quantum physics and quantum information theory, quantum cryptography, based on the principles of quantum mechanics, has been proven to possess unconditional security in the information-theoretic sense. The most representative technology is quantum key distribution (QKD). QKD primarily encompasses two technical approaches: discrete variable and continuous variable. Continuous variable quantum key distribution (CV-QKD) uses the orthogonal components of the quantum light field as the information carrier. It offers advantages such as high security code rates over short and medium transmission distances and compatibility with most components in traditional optical communications. It represents a key development direction for quantum key distribution technology.

[0003] The CV-QKD system includes the preparation, transmission, detection and classical data post-processing of quantum states. The overall block diagram is as follows: Figure 1 The data post-processing process significantly affects the overall security of the system and the key generation rate. After the data post-processing on the classical channel, Alice (sender) and Bob (receiver) obtain a set of completely consistent security keys. The data post-processing flow chart is shown in Figure 2 As shown in the figure, data negotiation, as a key step in the CV-QKD system, directly affects the processing rate, security code rate and maximum transmission distance of the actual data post-processing system.

[0004] Since information in CV-QKD systems is carried on continuous variables, legitimate communicating parties obtain continuous variables rather than binary bits after data filtering. Therefore, a data negotiation algorithm is typically required to convert continuous variables into discrete form. The bit strings of both communicating parties are then agreed upon by exchanging negotiation information in this discrete form. This strategy reduces complexity while minimizing the final key rate. Currently, there are three main negotiation algorithms for CV-QKD: symbol negotiation, slice negotiation, and multidimensional negotiation. Symbol negotiation places high demands on the quantum channel and offers lower performance. Specific parameters for slice negotiation, such as the quantization interval, estimation function, and binary error correction code, must be selected based on the actual modulation scheme, making optimization complex. The bit error rate caused by hard quantization decisions is very high at low signal-to-noise ratios, resulting in low coordination efficiency for slice negotiation at low signal-to-noise ratios. Multidimensional negotiation directly utilizes continuous variables, mapping the original Gaussian-distributed continuous variables into uniformly distributed discrete variables through rotation operations. Since the rotation maps the continuous variables to binary bits, a maximum of one bit of information can be represented. For long-distance CV-QKD systems, the amount of data that can be extracted from each pulse is far less than 1 bit, and there is almost no information loss after rotation. Therefore, multidimensional negotiation is well-suited for systems with extremely low signal-to-noise ratios. However, when the transmission distance is short and the signal-to-noise ratio of the CV-QKD system is high, current multidimensional negotiation schemes suffer from significant information loss, and the signal-to-noise ratio of the negotiated data will be severely reduced. Mapping continuous variables into discrete variables uniformly distributed on a higher-dimensional sphere through higher-dimensional mapping relationships can reduce negotiation losses. However, current multidimensional negotiation schemes can only achieve data negotiation in 8 dimensions at most, which is not conducive to efficient data negotiation when the system signal-to-noise ratio is high. Summary of the Invention

[0005] In view of the problem that the current multi-dimensional negotiation scheme can only realize multi-dimensional negotiation with a maximum dimension of 8 and cannot reduce the negotiation loss through a higher-dimensional mapping relationship when the signal-to-noise ratio of the CV-QKD system is large, the present invention provides an efficient data negotiation method and device suitable for CV-QKD, which constructs an arbitrary dimension d=2 based on a random orthogonal matrix. n (n=1,2,3,…) mapping relationship, realizes efficient data negotiation of CV-QKD system under any signal-to-noise ratio, and controls negotiation loss within an acceptable range. In addition, the computational complexity of generating a random orthogonal matrix of dimension d by matrix decomposition is O(d 3 ), when high-dimensional data negotiation is used, the computational complexity of constructing a high-dimensional random orthogonal matrix is ​​extremely large, which seriously affects the data negotiation rate. Therefore, the present invention also reduces the computational complexity to O(d 2 logd), which can effectively reduce the complexity of data negotiation and improve the data negotiation rate during high-dimensional data negotiation.

[0006] The present invention provides an efficient data negotiation method applicable to CV-QKD, comprising the following steps:

[0007] Input data x and data y;

[0008] Set the dimension d of data negotiation;

[0009] Construct a d-dimensional random orthogonal matrix B(d);

[0010] Calculate the mirror reflection matrix F according to the data x;

[0011] Calculate the mapping relationship based on the mirror reflection matrix F and the orthogonal matrix B(d);

[0012] Calculate the mapped data v according to the mapping relationship and data y;

[0013] Calculate the negotiated data R based on the mapped data v.

[0014] Furthermore, the calculation formula for constructing the d-dimensional random orthogonal matrix B(d) is:

[0015]

[0016] When d=2, Randomly select values ​​in the interval [0,2π], B1(1)=B2(1)=1, I d / 2 is a unit matrix of dimension d / 2; executing the B(d) calculation formula twice can obtain two different B(2) matrices; substituting B(2) into the calculation formula can calculate B(4), and repeatedly executing the B(d) calculation formula can obtain the Butterfly random orthogonal matrix of the required dimension.

[0017] Furthermore, the mirror reflection matrix F is:

[0018] F=I d -2W*W T

[0019] Among them, I d is a unit matrix of dimension d, and the vector W is obtained by normalizing the vector W0=X0-C. X0 is the coordinate of the normalized data x under the random orthogonal matrix B(d). r is a set of random numbers.

[0020] Furthermore, the mapping relationship is:

[0021] M(x,u)=F*B(d)

[0022] Wherein, u represents the data obtained after mapping the data x.

[0023] Furthermore, the mapped data v is:

[0024] v=M(x,u)y

[0025] Furthermore, the negotiated data R is:

[0026]

[0027] Among them, ||x|| represents the modulus length of the subsequence of data x with a sequence length of d; ||y|| represents the modulus length of the subsequence of data y with a sequence length of d.

[0028] The present invention also provides an efficient data negotiation device suitable for CV-QKD, comprising:

[0029] Input module, used to input data x and data y;

[0030] Dimension setting module, used to set the dimension d of data negotiation;

[0031] Random orthogonal matrix generation module, used to construct a d-dimensional random orthogonal matrix B(d);

[0032] A mirror reflection matrix calculation module is used to calculate the mirror reflection matrix F according to the data x;

[0033] A mapping relationship calculation module, used to calculate the mapping relationship based on the mirror reflection matrix F and the orthogonal matrix B(d);

[0034] A data mapping module is used to calculate the mapped data v based on the mapping relationship and the data y;

[0035] The negotiated data calculation module is used to calculate the negotiated data R based on the mapped data v.

[0036] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0037] In a typical CV-QKD system, the input data x and y both follow a Gaussian distribution, and the noise z = yx also follows a Gaussian distribution. Assume the signal-to-noise ratio of the signal x to the noise z is 0.36. Using an existing, commonly used multi-dimensional negotiation scheme, when the negotiation dimension is 8, the calculated signal-to-noise ratio based on the negotiated data is 0.3298, severely degrading the signal-to-noise ratio of the negotiated data.

[0038] For the same data, using the new and efficient data negotiation scheme proposed in the present invention, when the negotiation dimension is set to 8, the signal-to-noise ratio calculated based on the negotiated data is 0.3309, and the signal-to-noise ratio loss is still large. However, the dimension of the mapping relationship of the data negotiation scheme proposed in the present invention is variable. When the data negotiation dimension is set to 16, the signal-to-noise ratio calculated based on the negotiated data is 0.3453, and the signal-to-noise ratio loss is reduced. When higher-dimensional data negotiation is used, the data negotiation scheme proposed in the present invention can further reduce the signal-to-noise ratio loss after negotiation. In short, the data negotiation scheme based on the Butterfly random orthogonal matrix proposed in the present invention can select the corresponding preferred negotiation dimension for data negotiation according to the signal-to-noise ratio of the negotiated data, and control the signal-to-noise ratio loss after negotiation within an acceptable range, thereby achieving efficient data negotiation and ultimately effectively improving the security code rate of the CV-QKD system. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is the flow chart of the CV-QKD system.

[0040] Figure 2 This is the data post-processing flow chart of the CV-QKD system.

[0041] Figure 3 Flowchart of an efficient data negotiation method applicable to CV-QKD in an embodiment of the present invention.

[0042] Figure 4 2 is a schematic diagram of an efficient data negotiation device suitable for CV-QKD in an embodiment of the present invention. DETAILED DESCRIPTION

[0043] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of 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. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0044] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are intended to fall within the scope of protection of the present invention.

[0045] Example

[0046] Assuming that the modulated data at the transmitter of the CV-QKD system is x, and the corresponding detection result obtained after the detection at the receiver is y, the data y and x are grouped, with d data as a group, where d is the mapping relationship dimension used for data negotiation and the mapping relationship is M(x,u). The data u obtained after the data x is mapped satisfies u=M(x,u)x, and the data v obtained after the data y is mapped is M(x,u)y. The data u and v are both uniformly distributed, and the final negotiated data R can be obtained based on the data u and v. The efficient data negotiation method proposed in the present invention is based on constructing a random orthogonal matrix of arbitrary dimension d=2 n (n=1,2,3,…) mapping relationship M(x,u), and finally obtain the negotiated data R.

[0047] Take reverse data negotiation as an example, Figure 3 As shown, this embodiment proposes an efficient data negotiation method suitable for CV-QKD, including the following steps:

[0048] (1) Input data x and data y;

[0049] (2) Setting the dimension d of data negotiation;

[0050] (3) Construct a d-dimensional random orthogonal matrix B(d);

[0051] (4) Calculate the mirror reflection matrix F based on the data x:

[0052] F=I d -2W*W T

[0053] Among them, I d is a unit matrix of dimension d, and the vector W is obtained by normalizing the vector W0=X0-C. X0 is the coordinate of the normalized data x under the random orthogonal matrix B(d). r is a set of random numbers.

[0054] (5) Calculate the mapping relationship based on the mirror reflection matrix F and the orthogonal matrix B(d):

[0055] M(x,u)=F*B(d)

[0056] (6) Calculate the mapped data v based on the mapping relationship M(x,u) and the data y:

[0057] v=M(x,u)y

[0058] (7) Calculate the negotiated data R based on the mapped data v:

[0059]

[0060] Among them, ||x|| represents the modulus length of the subsequence of data x with a sequence length of d; ||y|| represents the modulus length of the subsequence of data y with a sequence length of d.

[0061] In the data negotiation method proposed by the present invention, constructing a random orthogonal matrix with a dimension of d is the key. The traditional method of constructing an orthogonal matrix using matrix decomposition has a computational complexity of O(d 3 ), when high-dimensional data negotiation is used, the computational complexity of constructing a high-dimensional random orthogonal matrix is ​​extremely large, which seriously affects the data negotiation rate. In the present invention, the high-dimensional matrix of the Butterfly random orthogonal matrix can be directly calculated using its low-dimensional matrix, and the computational complexity is O(d 2 logd), which is calculated as follows:

[0062]

[0063] When d=2, B1(1)=B2(1)=1,I d / 2 is the identity matrix of dimension d / 2, Randomly select values ​​in the interval [0, 2π]. Execute the B(d) formula twice to obtain two different B(2) matrices. Substitute B(2) into the formula to calculate B(4). Repeat the B(d) formula to obtain the Butterfly random orthogonal matrix of the desired dimension.

[0064] Taking 8-dimensional data negotiation as an example, the calculation process of an 8-dimensional Butterfly random orthogonal matrix is ​​as follows:

[0065] (1) Parameters Randomly taking the values ​​1.4442 and 5.7330, we get:

[0066]

[0067] (2) Parameters Randomly pick the values ​​5.8594 and 1.3280, substitute them into B1(2) and B2(2), and calculate:

[0068]

[0069] (3) Parameters Randomly pick the value 1.5312 and substitute it into B1(4) and B2(4), and we get:

[0070]

[0071] Corresponding to the above-mentioned efficient data negotiation method, such as Figure 4 As shown, this embodiment also provides an efficient data negotiation device, including:

[0072] Input module, used to input data x and data y;

[0073] Dimension setting module, used to set the dimension d of data negotiation;

[0074] Random orthogonal matrix generation module, used to construct a d-dimensional random orthogonal matrix B(d);

[0075] A mirror reflection matrix calculation module is used to calculate the mirror reflection matrix F according to the data x;

[0076] A mapping relationship calculation module, used to calculate the mapping relationship based on the mirror reflection matrix F and the orthogonal matrix B(d);

[0077] A data mapping module is used to calculate the mapped data v based on the mapping relationship and the data y;

[0078] The negotiated data calculation module is used to calculate the negotiated data R based on the mapped data v.

[0079] The working principle of each functional module in the above-mentioned efficient data negotiation device refers to the above-mentioned efficient data negotiation method, which will not be repeated here.

[0080] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. An efficient data negotiation method for CV-QKD, characterized in that: The steps include: Input data x and data y; Set the dimension d of data negotiation; Construct a d-dimensional random orthogonal matrix B(d); Calculate the specular reflection matrix F based on the data x; Calculate the mapping relationship based on the mirror reflection matrix F and the orthogonal matrix B(d); Calculate the mapped data v according to the mapping relationship and the data y; Calculate the negotiated data R based on the mapped data v.

2. The efficient data negotiation method for CV-QKD according to claim 1, characterized in that: The calculation formula for constructing the d-dimensional random orthogonal matrix B(d) is: When d = 2, Randomly select values ​​in the interval [0,2π], B1(1)=B2(1)=1, I d / 2 is a unit matrix of dimension d / 2. Executing the B(d) calculation formula twice will yield two different B(2) matrices. Substituting B(2) into the calculation formula will yield B(4). Repeating the B(d) calculation formula will yield a Butterfly random orthogonal matrix of the required dimension.

3. The efficient data negotiation method for CV-QKD according to claim 1, characterized in that: The specular reflection matrix F is: F=I d -2W*W T Among them, I d is a unit matrix of dimension d. Vector W is obtained by normalizing vector W0=X0-C. X0 is the coordinate of data x after normalization in random orthogonal matrix B(d). r is a set of random numbers.

4. The efficient data negotiation method for CV-QKD according to claim 1, characterized in that: The mapping relationship is: M(x,u)=F*B(d) Wherein, u represents the data obtained after mapping the data x.

5. The efficient data negotiation method for CV-QKD according to claim 1, characterized in that: The mapped data v=M(x,u)y.

6. The efficient data negotiation method for CV-QKD according to claim 1, characterized in that: The negotiated data R is: Among them, ||x|| represents the subsequence modulus length of the sequence length of data x is d; ||y|| represents the subsequence modulus length of the sequence length of data y is d.

7. An efficient data negotiation device suitable for CV-QKD, characterized in that: include: Input module, used for inputting data x and data y; A dimension setting module, used to set the dimension d of data negotiation; A random orthogonal matrix generation module is used to construct a d-dimensional random orthogonal matrix B(d); A mirror reflection matrix calculation module is used to calculate the mirror reflection matrix F according to the data x; A mapping relationship calculation module, used to calculate the mapping relationship according to the mirror reflection matrix F and the orthogonal matrix B(d); A data mapping module, used for calculating the mapped data v according to the mapping relationship and the data y; The negotiated data calculation module is used to calculate the negotiated data R according to the mapped data v.

8. The efficient data negotiation device for CV-QKD according to claim 7, characterized in that: The calculation formula for constructing the d-dimensional random orthogonal matrix B(d) is: When d = 2, Randomly select values ​​in the interval [0,2π], B1(1)=B2(1)=1, I d / 2 is a unit matrix of dimension d / 2. Executing the B(d) calculation formula twice will yield two different B(2) matrices. Substituting B(2) into the calculation formula will yield B(4). Repeating the B(d) calculation formula will yield a Butterfly random orthogonal matrix of the required dimension.

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