CN111865581A - Quantum secret sharing method based on tensor network and quantum communication system - Google Patents
Quantum secret sharing method based on tensor network and quantum communication system Download PDFInfo
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- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
- H04L9/0852—Quantum cryptography
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
- H04L9/0852—Quantum cryptography
- H04L9/0858—Details about key distillation or coding, e.g. reconciliation, error correction, privacy amplification, polarisation coding or phase coding
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- H—ELECTRICITY
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- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3236—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using cryptographic hash functions
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
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Abstract
The invention discloses a quantum secret sharing method based on a tensor network and a quantum communication system. Finally, secret reconstruction is realized based on tensor network state theory and (n, n) threshold group recovery protocol. The expandability of secret information, the expandability represented by the matrix product of quantum multi-body states, transfer characteristics and non-uniqueness are the greatest innovation points of the scheme, the safety and the reliability of quantum communication are guaranteed, and the problem that the dynamic construction cannot be realized by the existing quantum state secret sharing is solved. The diversity of matrix product state representation and the simple graphic representation which can correspond to a tensor network enable the scheme to have better application prospect in the fields of quantum state sharing and information security in the quantum network.
Description
Technical Field
The present invention relates to quantum communication technology, and more particularly, to a quantum secret sharing method and a quantum communication system based on a tensor network.
Background
In a quantum communication system, the security of the existing quantum state secret sharing scheme mostly depends on a transmission protocol, and expansion of an initial secret state is not considered, so that the quantum state secret sharing schemes cannot realize a dynamic function, and once a new participant joins and an old participant exits, the initial secret state is discarded.
However, since quantum computing appeared, people paid more and more attention to the theory and application of the tensor network state, which is a state that can be expressed by a mathematical graph and is an entangled state. Whether the tensor network state algorithm can be applied to quantum state secret sharing or not can be achieved, so that the limitation that the existing quantum state secret sharing scheme cannot achieve dynamic functions can be broken through the uniqueness of matrix product states corresponding to the same state. Therefore, the introduction of tensor network states is a breakthrough and trend in the design of quantum state secret sharing schemes. In addition, matrixing the quantum states, i.e., representing a multi-particle entangled state by a matrix product, has the advantage that the matrix product state can be tied to a simple graphical representation.
In view of the above-mentioned innovations and advantages, it is necessary to design a quantum state secret sharing method combining matrix product state algorithm and graph state.
Disclosure of Invention
In view of this, the invention first provides a quantum secret sharing method based on a tensor network, which utilizes tensor network weight to realize scalability of quantum state sharing, and solves the problem that a quantum secret state sharing scheme cannot realize dynamic change.
In order to achieve the purpose, the invention adopts the following specific technical scheme:
a quantum secret sharing method based on a tensor network is characterized by comprising the following steps:
s1: the distributor prepares quantum state secret information to be shared into sub-secret information according to the number of participants and a preset tensor network model, wherein the sub-secret information comprises physical index information | sigma of each node in the tensor network modeli>And key index information
n represents the number of participants;
s2: distributor throughThe quantum channel converts the physical index information of each node into information sigmai>To the corresponding participant PiAnd publish h (-) and h (x) externallyi) (ii) a Where h (-) denotes a predetermined secure hash function, h (x)i) Representing identity information x from individual participantsiIdentity authentication information calculated according to a preset secure hash function;
s3: each participant checks the received physical index information [ sigma ] i>Confirming whether the eavesdropping is carried out or not by entanglement, and if the eavesdropping is not confirmed, feeding back the identity authentication information h '(x') respectively calculated according to a preset secure hash function through a classical channeli) To the distributor; if h (x)i)＝h'(xi) The distributor considers the participant as a legitimate participant and sends the corresponding key index information to it through a classical channel
S4: each participant transmits authentication information h' (x) calculated according to a predetermined secure hash function through a classical channeli) (ii) a If h (x)i)＝h”(xi) If the participant belongs to a legal participant, the received physical index information | σ is transmitted between the legal participantsi>And key index information
S5: any participant finishes collecting the physical index information | sigma corresponding to all legal participantsi>And key index information
Then, the quantum state secret information that the distributor needs to share is restored according to the predetermined tensor network model of step S1.
Alternatively, the tensor network model predetermined in step S1 employs a matrix product state tensor network model, a tree-like tensor network model, a projection entanglement pair state tensor network model, or a multi-scale entanglement rebinning hypothesis tensor network model.
Optionally, the number of participants is at least two.
Alternatively, the distributor prepares the sub-secret information according to the AKLT model from the quantum-state secret information that needs to be shared.
Alternatively, when the predetermined tensor network model in step S1 adopts a matrix product state tensor network model and the number of participants is 3, the AKLT model is:
Optionally, the identity information x of each participantiAnd adopting respective equipment physical address information or identity number information.
The invention also provides a quantum communication system, which is characterized in that: the quantum secret sharing method is adopted to carry out quantum secret sharing and is used for realizing quantum signature, quantum authentication or quantum key distribution.
The invention has the technical effects that:
by adopting the method, the system security and reliability are higher, the expandability of secret information is stronger, the dynamic function of secret sharing is more conveniently realized, the method has better application prospect in the fields of quantum state sharing and information security in a quantum network, can be further applied to quantum cryptographic protocols such as quantum signature, authentication and key distribution, and can provide a scientific theoretical method for the design of safe, various and strong-expandability quantum secure communication protocols.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a diagram of a four-class common tensor network topology;
FIG. 2 is a topological structure diagram of a matrix product state prepared using an AKLT model;
FIG. 3 is a schematic diagram of the transformation of matrix product states into linear equations.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments, it being understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.
In order to better understand the inventive concept, the following briefly introduces the tensor network state theory and its diversity.
Tensor networks are used not only for mathematics, but also for physical, chemical and machine learning. The basic idea is as follows: an M x n matrix M with real entries can represent a linear mapping from Rn → Rm. Such a mapping may be depicted as a node having two edges. One edge represents the input space and the other edge represents the output space. In other words, the matrix is a two-dimensional array, and an n-dimensional array is referred to as an n-order tensor or an n-tensor. For example, a number can be considered as a zero-dimensional array, i.e., a point, and thus, it is a 0-tensor, which can be plotted as a node with zero edges. Likewise, a vector can be considered as a one-dimensional array, and thus a 1-tensor. It is represented by a node having an edge. The matrix is a two-dimensional array and is thus a 2-tensor. It is represented by a node with two edges. The three-dimensional tensor is a three-dimensional array, and thus is a node with three edges. The product of two or more tensors is represented by a group of nodes and edges, wherein the edges with the same index are contracted, then a plurality of tensors (including vectors, matrixes and high-order tensors) are contracted according to a specific rule to form a network, which is called a tensor network, and the nodes in each tensor network can be limited by physical indexes and key indexes.
As shown in fig. 1, four types of tensor networks that are most successful at present are: a Matrix Product State (MPS) network model shown in fig. 1 (a); the Projected Entangled State tensor network model (PEPS) shown in fig. 1 (b); a tree tensor network model (TTN) shown in fig. 1(c) and a multiscale entanglement hypothesis tensor network Model (MERA) shown in fig. 1(d), in which only tensors in the bottom layer have physical indexes.
However, for a quantum-multi-body system with n degrees of freedom, it can be expressed as:
where the coefficients can be written as the product of a number of tensors:
at this time, there are:
therefore, the system is called Matrix Product State (MPS), because the wave function of a quantum multi-body system can be expanded under a certain set of orthogonal bases, and the number of the orthogonal bases is infinite, the matrix product state representation is not unique.
Based on the above principle, the present embodiment applies the matrix product state to the quantum state secret sharing field, so as to provide a quantum secret sharing method based on tensor network, taking 3 participants as an example, and using a matrix product state tensor network model, which specifically includes the following steps:
S1: the distributor prepares quantum state secret information to be shared into the sub-secret information according to the number of participants and a matrix product state tensor network model, wherein the AKLT model is as follows:
wherein | ψ>Representing a quantum multi-body system containing quantum state secret information to be shared, the sub-secret information including physical index information | σ of each node in the tensor network model1>，|σ2>，|σ3>Key and index informationInformation processing device
S2: the distributor transmits the physical index information [ sigma ] of each node through a quantum channel1>，|σ2>，|σ3>To the corresponding participant P1,P2,P3And publish h (-) and h (x) externally1)，h(x2)，h(x3) (ii) a Where h (-) denotes a predetermined secure hash function, h (x)i) Representing identity information x from individual participantsiIdentity authentication information calculated according to a preset secure hash function, wherein in specific implementation, the identity information of each participant can adopt respective equipment physical address information or identity number information;
s3: each participant checks the received physical index information [ sigma ]1>，|σ2>，|σ3>Confirming whether the eavesdropping is carried out or not by entanglement, and if the eavesdropping is not confirmed, feeding back the identity authentication information h '(x') respectively calculated according to a preset secure hash function through a classical channeli) To the distributor; if h (x) i)＝h'(xi) If the distributor considers that the participant belongs to a legal participant, the distributor sends corresponding key index information to the legal participant through a classical channel;
s4: each participant transmits authentication information h' (x) calculated according to a predetermined secure hash function through a classical channeli) (ii) a If h (x)i)＝h”(xi) If the participant belongs to a legal participant, the received physical index information and key index information are mutually transmitted among the legal participants;
s5: any participant finishes collecting the physical index information | sigma corresponding to all legal participants1>，|σ2>，|σ3>And key index information
Then, the quantum state secret information that the distributor needs to share can be recovered according to the matrix product state tensor network model predetermined in step S1.
The embodiment also provides a quantum communication system, which performs quantum secret sharing by using the quantum secret sharing method, and is used for realizing quantum signature, quantum authentication or quantum key distribution.
The structure of AKLT model mentioned in the implementation process is shown in figure 2, which belongs to the classical model in the field of quantum communication, and is a matrix in figure 2
The value of (b) is determined by a secret matrix M, so that the association relationship of each tensor in the matrix product state tensor network model has a relationship with the entanglement characteristics of each entangled state, and the specific contents can be referred to documents: afflex, Ian, TomKennedy, Elliott Lieb, and Hal Tasaki, "Rigorous results on value-bond groups in antiferromagnetres," Physical Review Letters 59, No.7(1987): 799-.
According to the technical scheme provided by the embodiment, the initial secret is set in the quantum multi-body system | ψ>Suppose a dishonest or attacker wants to steal secret information and intercepts two sub-secrets, pass
To solve for secret state | ψ>The process is equivalent to solving 2 3-element linear equations shown in fig. 3, the uncertainty of the information is itself, and therefore, no information amount about the secret is obtained through the obtained information.
The premise of the application of the matrix product state tensor network is to construct a secret matrix M, and the premise condition just enables secret information to be expandable, the secret matrix to be diversified, and the secret matrix becomes an innovative point and an advantage which are not possessed by other quantum secret sharing schemes.
Due to the non-uniqueness of the matrix state, the dynamic function of secret sharing is easily realized. Once there is an update of a participant (i.e. an old participant exits and a new participant joins), we can reconstruct the matrix product state using a different secret matrix M so that the quantum state can continue to be used without affecting the security of the shared state.
In addition, the application of matrix product state not only makes the scheme more favorable for graphical representation, but also more important | Ψ >Is of1>,|σ2>,|σ3>And
make the participants and the quantum multi-volume state | Ψ>The method is independent of the other method, namely when the participant personally measures, the information in the hands of the participant cannot be acquired, because the sub-secret information can be transferred out along with the measurement through the matrix product operation. It is noted that the transfer of secret information does not mean any physical operation or change of state itself, but merely a re-marking of the physical state.
In summary, the quantum secret sharing method and the quantum communication system based on the tensor network provided by the invention utilize the corresponding relation between classical information and quantum information to reconstruct a quantum state, a distributor combines an AKLT model and a matrix product state representation method to realize secret division, and then distributes the sub-secret to participants through a classical authentication channel and a quantum channel. Finally, secret reconstruction is realized based on tensor network state theory and (n, n) threshold group recovery protocol. The expandability of secret information, the expandability represented by the matrix product of quantum multi-body states, transfer characteristics and non-uniqueness are the greatest innovation points of the scheme, the safety and the reliability of quantum communication are guaranteed, and the problem that the dynamic construction cannot be realized by the existing quantum state secret sharing is solved. The diversity of matrix product state representation and the simple graphic representation which can correspond to a tensor network enable the scheme to have better application prospect in the fields of quantum state sharing and information security in the quantum network. More importantly, the theories can be further applied to quantum cryptography protocols such as quantum signature, authentication and key distribution, and a scientific theoretical method can be provided for the design of safe, various and high-expansibility quantum secure communication protocols.
Through the above description of the embodiments, those skilled in the art will clearly understand that the method of the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better implementation manner. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which is stored in a storage medium (such as ROM/RAM, magnetic disk, optical disk) and includes instructions for enabling a terminal (such as a mobile phone, a computer, a server, or a network device) to execute the method according to the embodiments of the present invention.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (7)
1. A quantum secret sharing method based on a tensor network is characterized by comprising the following steps:
s1: the distributor prepares quantum state secret information to be shared into sub-secret information according to the number of participants and a preset tensor network model, wherein the sub-secret information comprises physical index information | sigma of each node in the tensor network modeli>And key index information
n represents the number of participants;
s2: the distributor transmits the physical index information [ sigma ] of each node through a quantum channeli>To the corresponding participant PiAnd publish h (-) and h (x) externallyi) (ii) a Where h (-) denotes a predetermined secure hash function, h (x)i) Representing identity information x from individual participantsiIdentity authentication information calculated according to a preset secure hash function;
s3: each participant checks the received physical index information [ sigma ]i>Confirming whether the eavesdropping is carried out or not by entanglement, and if the eavesdropping is not confirmed, feeding back the identity authentication information h '(x') respectively calculated according to a preset secure hash function through a classical channeli) To the distributor; if h (x)i)＝h'(xi) The distributor considers the participant as a legitimate participant and sends the corresponding key index information to it through a classical channel 
S4: each participant transmits authentication information h' (x) calculated according to a predetermined secure hash function through a classical channeli) (ii) a If h (x)i)＝h”(xi) If the participant belongs to a legal participant, the received physical index information | σ is transmitted between the legal participantsi>And key index information
S5: any participant finishes collecting the physical index information | sigma corresponding to all legal participantsi>And key index information
Then, the quantum state secret information that the distributor needs to share is restored according to the predetermined tensor network model of step S1.
2. The tensor network-based quantum secret sharing method as recited in claim 1, wherein: the predetermined tensor network model in step S1 adopts a matrix product state tensor network model, a tree-like tensor network model, a projection entanglement pair state tensor network model or a multi-scale entanglement recombination hypothesis tensor network model.
3. The tensor network-based quantum secret sharing method as recited in claim 1, wherein: the number of participants is at least two.
4. The tensor network-based quantum secret sharing method as recited in claim 1, wherein: the distributor prepares the sub-secret information according to the AKLT model from the quantum-state secret information required to be shared.
5. The tensor network-based quantum secret sharing method as recited in claim 4, wherein:
when the predetermined tensor network model in step S1 adopts the matrix product state tensor network model and the number of participants is 3, the AKLT model is:
wherein | ψ>Representing a quantum multi-body system containing quantum state secret information that needs to be shared.
6. The tensor network-based quantum secret sharing method as recited in claim 1, wherein: identity information x of the respective participantiAnd adopting respective equipment physical address information or identity number information.
7. A quantum communication system, characterized by: the quantum secret sharing method of any one of claims 1 to 6 is adopted for quantum secret sharing, and is used for realizing quantum signature, quantum authentication or quantum key distribution.
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| CN114021730A (en) * | 2021-11-19 | 2022-02-08 | 中国科学技术大学 | Physical tensor network state data post-processing method, system, equipment and storage medium |
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