Quantum secret sharing method based on multi-ring discrete modulation coherent state
By using a quantum secret sharing method based on multi-ring discrete modulation coherent states, the problems of signal source complexity and insufficient transmission distance in existing technologies are solved, and long-distance quantum secret sharing with high reliability and security is achieved.
Patent Information
- Application Number
- CN202310297644.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-03-24
- Publication Date
- 2025-11-25
- Estimated Expiration
- 2043-03-24
AI Technical Summary
Existing discrete variable quantum secret sharing technologies are complex and expensive in signal source preparation and measurement, while continuous variable quantum secret sharing has low tolerance for channel loss and noise, and discrete modulated coherent states cannot meet the requirements of long-distance multi-party quantum secure communication in terms of maximum transmission distance.
A quantum secret sharing method using multi-ring discrete modulation coherent states is adopted. By preparing multi-ring discrete modulation coherent states and performing multiple measurements, the channel transmittance and key rate are determined by combining the publicly available data from the classical post-processing stage. Finally, the encrypted key is calculated and used for information sharing.
It improves the reliability and security of quantum secret sharing, extends the transmission distance, and enhances the performance of continuous variable quantum key distribution links.
Smart Images
Figure CN116346337B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of quantum communication, and particularly relates to a quantum secret sharing method based on a multi-ring discrete modulation coherent state. BACKGROUND
[0002] With the development of economy and technology and the improvement of people's living standards, people have higher and higher requirements for the security of communication data. Therefore, quantum key distribution technology has attracted widespread attention due to its excellent data security.
[0003] At present, the traditional quantum key distribution technology is generally used for point-to-point communication. With the development of technology, people need a system that can meet the communication of multiple users, so some researchers have proposed quantum secret sharing technology. Compared with the point-to-point quantum key distribution protocol, the quantum secret sharing protocol involves multiple users, so some of the users may be dishonest. The quantum secret sharing protocol can simultaneously satisfy the communication of multiple users, that is, a legitimate user (called dealer) wants to share a secure key with a group of remote users through an insecure quantum channel, and the dealer knows that some of the users are not trustworthy, so the dealer will divide the key into several parts and send them to different users. A single user cannot decode the encrypted message alone, but only when all users work together can they share the same key with the dealer.
[0004] Generally, quantum secret sharing can be divided into two categories, namely discrete variable quantum secret sharing and continuous variable quantum secret sharing. Discrete variable quantum secret sharing uses the polarization state of single photons to transmit information, while continuous variable quantum secret sharing encodes information through the orthogonal components of the light field. At present, discrete variable quantum secret sharing has been widely studied, and various schemes have been proposed. However, in the process of discrete variable quantum secret sharing, the preparation and measurement of the signal source are relatively complex, and the implementation equipment is expensive. On the contrary, in the process of continuous variable quantum secret sharing, the continuous variable signal source is easier to prepare, and is compatible with the current optical communication network. Therefore, continuous variable quantum secret sharing has a more extensive application prospect.
[0005] Some scholars proposed a continuous variable quantum secret sharing protocol, and proved that the protocol is theoretically unconditionally secure for eavesdroppers and untrusted users; however, the protocol has relatively low tolerance for channel loss and noise. Considering the factors of practical application and performance, some researchers use weak coherent states as signal sources, so that the quantum secret sharing has better performance; however, this method needs to modulate the signal into a Gaussian distribution, which is difficult to realize in practice. Subsequently, because discrete modulation coherent states are easy to prepare and more resistant to noise, some scholars use discrete modulation coherent states for quantum secret sharing protocols, which use traditional optical modulation methods such as quadrature phase shift keying (QPSK) to discretely modulate the quantum signal of quantum secret sharing, thereby eliminating the implementation obstacles of continuous variable quantum secret sharing modulation, and obtaining relatively good results. However, discrete modulation continuous variable quantum secret sharing cannot fully meet the needs of long-distance multi-party quantum secure communication in terms of the key performance indicator of maximum transmission distance. SUMMARY
[0006] The purpose of the present application is to provide a multi-ring discrete modulation coherent state-based quantum secret sharing method with high reliability, good security and long transmission distance.
[0007] The multi-ring discrete modulation coherent state-based quantum secret sharing method provided by the present application comprises the following steps:
[0008] S1. Obtain the data information of the target quantum secret sharing network;
[0009] Quantum phase:
[0010] S2. Each user in the network prepares a multi-ring discrete modulation coherent state and sends it to a legitimate user, and the legitimate user obtains a measurement result according to the received data;
[0011] S3. Repeat step S2 several times to obtain a set amount of original data;
[0012] Classical post-processing phase:
[0013] S4. The legitimate user discloses a first part of the original data, and each user discloses the corresponding data, so as to determine the quantum channel transmittance between each user and the legitimate user;
[0014] S5. The legitimate user discloses a second part of the original data, and each user discloses the corresponding data, so as to determine the key rate of the point-to-point link between the legitimate user and each user;
[0015] S6. The legitimate user calculates the final key according to a third part of the original data, and encrypts the target information to obtain encrypted information;
[0016] S7. The legitimate user sends the encrypted information obtained in step S6 to each user, thereby realizing quantum secret sharing based on discrete modulation coherent states.
[0017] The data information of the target quantum secret sharing network is obtained in step S1, and specifically includes the following steps:
[0018] The target quantum secret sharing network includes n users and a legitimate user dealer; the n users and the legitimate user dealer are connected in series through an optical fiber channel, and the legitimate user dealer is located at the end of the network.
[0019] Each user in the network prepares a multi-ring discrete modulation coherent state and sends it to the legitimate user in step S2, and the legitimate user obtains measurement results according to the received data, specifically including the following steps:
[0020] The jth user prepares a multi-ring discrete modulation coherent state and sends it to the next user in the network; during the preparation process, the jth user adjusts the modulation variance of itself and the transmittance of the beam splitter, thereby introducing a displacement amount (x j ,p j ); wherein x j is the orthogonal component of the coherent state prepared by the jth user in the X direction, and p j is the orthogonal component of the coherent state in the P direction;
[0021] The mixed state received by the legitimate user dealer is represented as where T j is the channel transmittance from the jth user to the legitimate user dealer; the legitimate user dealer measures the received mixed state through a heterodyne detector, thereby obtaining measurement results (x d ,p d ), wherein x d is p d is
[0022] The preparation of a multi-ring discrete modulation coherent state includes the following steps:
[0023] The quantum states in the constellation diagram are dispersed onto R concentric circles, and the modulated coherent state α k is represented as where k is the coherent state number, and takes values of 0, 1,..., N-1, N is the total number of states in the constellation diagram; α r is the radius corresponding to the rth concentric circle, i.e., the amplitude of the coherent state on the rth concentric circle, r takes values of 1, 2,..., R, R is the number of concentric circles; q is the serial number of the coherent state in the rth concentric circle, and takes values of 0, 1,..., N r , Nr is the number of coherent states in the rth concentric circle; θ r is the phase difference between the coherent states in the rth concentric circle,
[0024] In the modulation process, the first concentric circle is the innermost concentric circle and the number of coherent states is 4, the number of coherent states of the first concentric circle is 12, and the number of coherent states of the r'th concentric circle is 2 r +1 .
[0025] The first part of data in the original data is disclosed by the legal user dealer, and the corresponding data is disclosed by each user, so as to determine the quantum channel transmissivity between each user and the legal user dealer, and the specific steps include the following steps:
[0026] The legal user dealer selects a plurality of data as the first part of data in the received original data;
[0027] The legal user dealer discloses the first part of data, and each user also discloses the data corresponding to the first part of data;
[0028] The legal user dealer determines the quantum channel transmissivity between each user and the legal user dealer according to the disclosed data;
[0029] Finally, the legal user dealer and each user discard the data disclosed in this step.
[0030] The second part of data in the original data is disclosed by the legal user dealer, and the corresponding data is disclosed by each user, so as to determine the key rate of the point-to-point link between the legal user dealer and each user, and the specific steps include the following steps:
[0031] A. The legal user dealer selects a plurality of data as the second part of data in the remaining original data;
[0032] B. The legal user dealer discloses the second part of data, and requires other users except the jth user to disclose the corresponding data, j = 1, 2,..., n;
[0033] C. The legal user dealer recalculates the measurement results according to the disclosed data, so as to obtain the corresponding measurement results Wherein, is the orthogonal component of the coherent state sent by the jth user in the X direction calculated by the legal user dealer, is the orthogonal component of the coherent state sent by the jth user in the P direction calculated by the legal user dealer, At this point, the point-to-point continuous variable quantum key distribution link between the j-th user and the legitimate user dealer is established.
[0034] D. Based on the obtained measurement results The key rate R of the point-to-point continuous-variable quantum key distribution link between the j-th user and the legitimate user dealer is calculated. j ;
[0035] E. Repeat steps B through D a total of n times to obtain the key rates R1 to R2 of the point-to-point continuous variable quantum key distribution link between each user and the legitimate user dealer. n ;
[0036] F. To ensure system security, select R1 to R2. n The minimum key rate is taken as the final key rate R of the system; at the same time, the legitimate user dealer and each user discard the data disclosed in step B.
[0037] Step S6 involves the legitimate user calculating the final key based on the third part of the original data and encrypting the target information to obtain encrypted information. This process includes the following steps:
[0038] If the final key R is greater than 0, the legitimate user dealer selects some data from the remaining original data as the third part of the data;
[0039] The third part of the data is used as the key, so that the legitimate user dealer shares an independent key K with each user. j j = 1, 2, ..., n;
[0040] The final key K is calculated as follows: In the formula This is bitwise addition modulo 2;
[0041] The legitimate user (dealer) uses the final key K to encrypt the target information M, resulting in the encrypted information E.
[0042]
[0043] The quantum secret sharing method based on multi-ring discrete modulation coherent state provided by this invention upgrades the performance of each continuous variable quantum key distribution link by extending the modulation scheme to a multi-ring scheme. Therefore, the method of this invention can greatly improve the performance of continuous variable quantum secret sharing protocol, and has high reliability, good security and long transmission distance. Attached Figure Description
[0044] Figure 1 This is a schematic diagram of the method flow of the present invention.
[0045] Figure 2 A result schematic diagram of a target quantum secret sharing network of the present application.
[0046] Figure 3 A schematic diagram of a discrete modulation constellation of the present application.
[0047] Figure 4 A schematic diagram of raw data usage of the present application.
[0048] Figure 5 A schematic diagram of the relationship between key rate and modulation variance of an embodiment of the present application.
[0049] Figure 6 A schematic diagram of the relationship between quantum secret sharing key rate and distance when n = 2 under different modulation schemes of an embodiment of the present application,
[0050] Figure 7 A schematic diagram of the relationship between average photon number and error probability under different modulation schemes of an embodiment of the present application. DETAILED DESCRIPTION
[0051] As Figure 1 shown is a method flow schematic diagram of the present application: the quantum secret sharing method based on the multi-ring discrete modulation coherent state provided by the present application includes the following steps:
[0052] S1. Obtain data information of a target quantum secret sharing network; specifically including the following steps:
[0053] The target quantum secret sharing network includes n users and a legitimate user dealer; the n users and the legitimate user dealer are connected in series through an optical fiber channel, and the legitimate user dealer is located at the end of the network;
[0054] The network topology diagram is as shown in Figure 2 ;
[0055] Quantum phase:
[0056] S2. Each user in the network prepares a multi-ring discrete modulation coherent state and sends it to the legitimate user, and the legitimate user dealer obtains measurement results according to the received data; specifically including the following steps:
[0057] The jth user prepares a multi-ring discrete modulation coherent state and sends it to the next user in the network; in the preparation process, the jth user adjusts the modulation variance of itself and the transmittance of the beam splitter, thereby introducing a displacement (x j ,p j ); wherein x j is the orthogonal component of the coherent state prepared by the jth user in the X direction, and p j is the orthogonal component of the coherent state in the P direction;
[0058] The mixed state received by the legitimate user dealer is represented as where T j is the channel transmissivity from the jth user to the legitimate user dealer; the legitimate user dealer measures the received mixed state through a heterodyne detector, thereby obtaining a measurement result (x d , p d ); where x d is p d is
[0059] In specific implementation, preparing a multi-ring discrete modulated coherent state includes the following steps (as shown in FIG. 1) : Figure 3
[0060] The quantum states in the constellation are dispersed onto R concentric circles, and the modulated coherent state α k is represented as where k is the number of the coherent state, and takes values of 0, 1,..., N-1, N is the total number of states in the constellation; α r is the radius corresponding to the rth concentric circle, that is, the amplitude of the coherent state on the rth concentric circle, r takes values of 1, 2,..., R; q is the serial number of the coherent state in the rth concentric circle, and takes values of 0, 1,..., N r , N r is the number of coherent states in the rth concentric circle; θ r is the phase difference between the coherent states in the rth concentric circle, and
[0061] In the modulation process, the first concentric circle is the innermost concentric circle and the number of coherent states is 4, the number of coherent states of the first concentric circle is 12, and the number of coherent states of the r'th concentric circle is 2 r ' +1 ;
[0062] S3. Repeat step S2 several times to obtain a set number of original data;
[0063] Classical post-processing stage:
[0064] S4. The legitimate user dealer discloses a first part of data in the original data, and each user discloses the corresponding data, so as to determine the quantum channel transmissivity between each user and the legitimate user dealer; specifically including the following steps:
[0065] The legitimate user dealer selects a plurality of data in the received original data as the first part of data;
[0066] The legal user dealer discloses the first part of data, and each user also discloses the corresponding data of the user;
[0067] The legal user dealer determines the quantum channel transmissivity between each user and the legal user dealer according to the disclosed data;
[0068] Finally, the legal user dealer and each user discard the data disclosed in this step;
[0069] S5. The legal user discloses the second part of data in the original data, and each user discloses the corresponding data, so as to determine the key rate of the point-to-point link between the legal user dealer and each user; Specifically, the following steps are included:
[0070] A. The legal user dealer selects a number of data as the second part of data in the remaining original data;
[0071] B. The legal user dealer discloses the second part of data and requires other users except the jth user to disclose the corresponding data, j = 1, 2,..., n;
[0072] C. The legal user dealer re-calculates the measurement results according to the disclosed data, so as to obtain the corresponding measurement results Wherein is the orthogonal component of the coherent state sent by the jth user in the X direction calculated by the legal user dealer, is the orthogonal component of the coherent state sent by the jth user in the P direction calculated by the legal user dealer, At this time, the point-to-point continuous variable quantum key distribution link between the jth user and the legal user dealer is established;
[0073] D. According to the obtained measurement results The key rate R of the point-to-point continuous variable quantum key distribution link between the jth user and the legal user dealer is calculated j ;
[0074] E. Repeat steps B to D for n times to obtain the key rates R1 to R n between each user and the legal user dealer;
[0075] F. In order to ensure the security of the system, the key rate with the minimum value among R1 to R n is selected as the final key rate R of the system; at the same time, the legal user dealer and each user discard the data disclosed in this step B;
[0076] S6. The legitimate user dealer calculates the final key according to the third part of data in the original data, and encrypts the target information to obtain encrypted information; specifically including the following steps:
[0077] If the final key rate R is greater than 0, the legitimate user dealer selects some data as the third part of data in the remaining original data (wherein the use of the original data can refer to Figure 4 illustrated); in specific implementation, the third part of data can be all data selected at this time, or part of the data selected at this time;
[0078] The third part of data is used as a key, so that the legitimate user dealer shares an independent key K j with each user, j = 1, 2,..., n;
[0079] The final key K calculated is wherein is a bitwise addition modulo 2;
[0080] The legitimate user dealer encrypts the target information M using the final key K to obtain encrypted information E as
[0081]
[0082] S7. The legitimate user dealer sends the encrypted information obtained in step S6 to each user, and completes the sharing of the target information M among all users. The encrypted information E can be decoded only when all users cooperate, thereby realizing quantum secret sharing based on multi-ring discrete modulation coherent states.
[0083] As Figure 3 illustrated, Figure 3 (a) is an existing modulation method, in which case each coherent state can represent 2 bits of data. In order to further improve its performance, the number of coherent states in the constellation diagram can be further increased, as illustrated in Figure 3 (b). By adjusting in this way, each coherent state can carry 4 bits of data. In theory, the efficiency of quantum secret sharing should be greatly improved as the amount of information carried by each coherent state increases. In fact, although this method can improve performance, its effect is very limited. The main reason is that this adjustment greatly reduces the distance between each coherent state, which greatly increases the error rate of the quantum detector in identifying discrete modulation coherent states. The scheme proposed in the present application considers this problem and introduces amplitude as a variable into discrete modulation. In the scheme of the present application, the coherent state is no longer located on one amplitude ring, but is scattered to different rings (as Figure 3(c) shown, i.e. quantum states are dispersed on multiple concentric circles. By this extension, it is obvious that the distance between adjacent coherent states is increased and the number of quantum states of the present application remains the same as Figure 3 (b). So far, the present application solves the problem of increasing error probability of quantum detectors. And the present application scheme can be further extended, as Figure 3 (d) shown, the present application can be extended to a three-ring 32-state modulation scheme. Therefore, the present application method can effectively improve the performance of quantum secret sharing by increasing the number of coherent states without causing the increase of error probability. In addition, when considering the implementation of discrete modulation continuous variable quantum secret sharing scheme, the traditional single-ring discrete modulation strategy needs a very small modulation variance to ensure the security of its key transmission, and the smaller variance will result in a very low signal-to-noise ratio at the receiving end, increasing the complexity of data negotiation in the system post-processing. While the present application allows a larger modulation variance, as Figure 5 shown, which is beneficial to improve the signal-to-noise ratio, thereby improving the data negotiation efficiency.
[0084] The performance of the present application scheme is shown in Figure 6 . Figure 6 The relationship between the key rate and the farthest distance of the farthest user to the legitimate user dealer under different modulation schemes in the quantum secret sharing system with 2 users is described, and it can be seen from the figure that the performance of the present application method is improved by nearly 50% compared to the original QPSK scheme, and when the number of double-ring states is 16, the safe transmission distance of the entire system can be extended to 100km. Through the increase of the number of rings and the number of states, the key rate can be further improved. Although it can also be seen from the figure that the key rate of the present application scheme still cannot reach the theoretical value of Gaussian modulation, in actual implementation, Gaussian modulation is more difficult to implement, and in actual application, it cannot reach its theoretical maximum value. While discrete modulation is simple to prepare and has strong noise resistance, it is more suitable for practical application, so the problem to be discussed by the present application is how to maximize the performance of discrete modulation quantum secret sharing.
[0085] In Figure 7 , the present application calculates the error rate of quantum detectors when using different modulation schemes, and compared with the single-ring modulation method with the same number of coherent states, the error probability obtained by the present application method is smaller, which fully illustrates the superiority of the present application scheme. When the number of coherent states increases, the error probability will decrease, which is also in line with the actual situation, because when the number of coherent states becomes more and more, the distance between each quantum state will decrease, which will greatly affect the accuracy of the quantum detector.
Claims
1. A quantum secret sharing method based on multi-loop discrete modulation coherent state, comprising the following steps: S1.Obtaining data information of a target quantum secret sharing network; specifically comprising the following steps: The target quantum secret sharing network comprises n users and a legitimate user dealer; the n users and the legitimate user dealer are connected in series through an optical fiber channel, and the legitimate user dealer is located at the end of the network; Quantum phase: S2.Each user in the network prepares a multi-loop discrete modulation coherent state and sends it to the legitimate user, and the legitimate user obtains measurement results according to the received data; specifically comprising the following steps: The jth user prepares a multi-ring discrete modulated coherent state and sends it to the next user in the network; in the preparation process, the jth user adjusts the modulation variance of itself and the transmissivity of the beam splitter, thereby introducing a displacement amount (x j ,p j ); wherein x j is the orthogonal component of the coherent state prepared by the jth user in the X direction, and p j is the orthogonal component of the coherent state in the P direction; The mixed state received by the legitimate user dealer is represented as where T j is the channel transmissivity from the jth user to the legitimate user dealer; A legitimate user dealer measures the received mixed state via the heterodyne detector, thereby obtaining a measurement result (x d ,p d ), where x d is p d is S3.Repeating step S2 for several times to obtain a set number of original data; Classical post-processing phase: S4.The legitimate user discloses a first part of the original data, and each user discloses the corresponding data, so as to determine the quantum channel transmittance between each user and the legitimate user; S5.The legitimate user discloses a second part of the original data, and each user discloses the corresponding data, so as to determine the key rate of the point-to-point link between the legitimate user and each user; S6.The legitimate user calculates the final key according to a third part of the original data, encrypts the target information, and obtains encrypted information; S7.The legitimate user sends the encrypted information obtained in step S6 to each user, so as to realize quantum secret sharing based on discrete modulation coherent state. 2.The quantum secret sharing method based on multi-loop discrete modulation coherent states according to claim 1, wherein The preparation of a multi-loop discrete modulation coherent state comprises the following steps: The quantum states in the constellation are dispersed onto R concentric circles, and the modulated coherent states |α k > are expressed as where k is the number of the coherent state, and takes values 0, 1,..., N-1, N is the total number of states in the constellation; α r is the radius corresponding to the rth concentric circle, r takes values 1, 2,..., R, R is the number of concentric circles; q is the serial number of the coherent state in the rth concentric circle, and takes values 0, 1,..., N r , N r is the number of coherent states in the rth concentric circle; θ r is the phase difference between the coherent states in the rth concentric circle, In the modulation process, the first concentric circle is the innermost concentric circle and the number of coherent states is 4, the number of coherent states of the first concentric circle is 12, and the number of coherent states of the r'th concentric circle is 2 r'+1 . 3.The quantum secret sharing method based on multi-loop discrete modulation coherent states according to claim 2, wherein The legitimate user discloses a first part of the original data, and each user discloses the corresponding data, so as to determine the quantum channel transmittance between each user and the legitimate user, specifically comprising the following steps: The legitimate user dealer selects a plurality of data in the received original data as the first part of data; The legitimate user dealer discloses the first part of data, and each user also discloses the data corresponding to the first part of data; The legitimate user dealer determines the quantum channel transmittance between each user and the legitimate user dealer according to the disclosed data; Finally, the legitimate user dealer and each user discard the data disclosed in this step.
4. The quantum secret sharing method based on multi-ring discrete modulation coherent states according to claim 3, characterized in that The legitimate user discloses a second part of the original data, and each user discloses the corresponding data, so as to determine the key rate of the point-to-point link between the legitimate user and each user, specifically comprising the following steps: A. The legitimate user dealer selects a plurality of data in the remaining original data as the second part of data; B. The legitimate user dealer discloses the second part of data, and requires other users except the jth user to disclose the corresponding data, j = 1, 2,..., n; C. The legal user dealer recalculates the measurement result according to the disclosed data, thereby obtaining the corresponding measurement result wherein, the jth user sends the orthogonal component of the coherent state in the X direction calculated by the legal user dealer, the jth user sends the orthogonal component of the coherent state in the P direction calculated by the legal user dealer, At this time, the point-to-point continuous variable quantum key distribution link between the jth user and the legal user dealer is established. D. Based on the obtained measurement results The key rate R of the point-to-point continuous variable quantum key distribution link between the jth user and the legitimate user dealer is calculated j ; E. Repeat steps B-D n times to obtain the key rates R1-Rn of the point-to-point continuous variable quantum key distribution link between each user and the legitimate user dealer n ; F.To ensure the security of the system, the key rate of R1~R n with the minimum value is selected as the final key rate of the system; meanwhile, the dealer and each user discard the data disclosed in this step B.
5. The quantum secret sharing method based on polycyclic discrete modulation coherent states according to claim 4, characterized in that The legitimate user calculates the final key according to a third part of the original data, encrypts the target information, and obtains encrypted information, specifically comprising the following steps: If the final key R is greater than 0, the legitimate user dealer selects a plurality of data in the remaining original data as the third part of data; The third part of data is used as a key, so that the legal user dealer shares an independent key K with each user j j = 1, 2,..., n; The final key K is computed as where is bitwise addition modulo 2; The legal user dealer encrypts the target information M with the final key K to obtain the encrypted information E as