CN110336775A - A Quantum Swarm Authentication Method Based on Grover Algorithm - Google Patents

Abstract

The invention belongs to the technical field of quantum computing and quantum authentication, and relates to a quantum group authentication method based on the Grover algorithm. A private share is used as the identity information of the registered user and sent to the registered user through the classic channel, and a group identifier is generated for the network group and sent to the network group through the classic channel; in the authentication stage, each user participating in the authentication according to his own identity information Carry out unitary transformation to the authentication quantum state with the group identifier, and finally the group returns the authentication quantum state after the unitary transformation to the authentication management center for comparison to obtain the authentication result; the present invention uses the Grover operator, and the Grover operator The usage of the system has been extended, and the group user identity and the network group identifier can be authenticated at the same time, and the double authentication improves the security of the authentication method.

Description

A Quantum Swarm Authentication Method Based on Grover Algorithm

technical field

The invention belongs to the technical field of quantum computing and quantum authentication, and relates to a quantum group authentication method based on a Grover algorithm.

Background technique

As we all know, authentication is an effective method to ensure the integrity of transmitted information, and identity authentication technology is often used in specific scenarios such as e-commerce and voting, and has a very wide range of application scenarios in real life. The security of traditional authentication protocols is mostly based on the computational complexity of discrete logarithms, quadratic residues, and factorization of large numbers in classical cryptography. However, with the rapid development of quantum technology in recent years, the powerful computing power of quantum computers poses a huge challenge to the security of these classical protocols. The quantum encryption technology in the contemporary background is based on the basic principles of quantum physics, and its security is based on the Heisenberg uncertainty principle and the quantum non-cloning theorem, especially some quantum key distribution protocols such as BB84, The B92 protocol has been proven to be unconditionally secure. Quantum authentication is an important branch of quantum cryptography. Therefore, quantum authentication technology is the focus of cutting-edge security technology, and its application of quantum voting is also a research hotspot this year.

In the environment of quantum technology, quantum parallel computing has strong computing potential. The Grover algorithm in the quantum search algorithm is a representative of the application of quantum parallel computing, so it has attracted great attention. The rotation operator and projection operator in the algorithm have high research value, and some existing quantum associative memory models and quantum machine learning algorithms use the idea of the Grover algorithm, but the group identity authentication scheme based on the Grover algorithm still has No, especially the characteristics of the Grover operator can actually be combined with the threshold idea as a group identity authentication algorithm.

In recent years, the research on quantum identity authentication schemes proposed by quantum technology has been increasing, but most of the existing quantum authentication schemes consider the identity authentication of both quantum communication parties. If multiple users participate in the authentication, the authentication process needs to be carried out multiple times. Iterative authentication is inefficient, wastes classical resources and quantum resources, and cannot authenticate multiple user identities at the same time.

This authentication method is proposed aiming at the defect and low efficiency that the existing quantum authentication scheme cannot simultaneously authenticate multiple user identities.

Contents of the invention

In view of this, in view of the need to authenticate multiple user identities at the same time, a quantum group authentication method based on the Grover algorithm that can perform dual authentication on user group identities and network identifiers is proposed. The quantum group authentication method of the algorithm, when multiple users in the network group _GM need to authenticate their identities at the same time, the network group _GM initiates an authentication request to the authentication management center. The authentication management center is responsible for authenticating user group identities and network group identities, including the following steps:

S1. The authentication management center prepares the authentication quantum state for the network group. The quantum state is a two-particle state, expressed as |S _w >;

S2. The authentication management center randomly generates n private shares and group authentication codes according to the Shamir(t,n) threshold idea, and distributes the private shares to ordinary users who need to register in the network group, and ordinary users keep their own group authentication codes , the authentication management center generates a group identifier and sends it to the network group;

S3. After the n ordinary users who need to register in the network group get their private shares, the ordinary users calculate their own private authentication codes, and the t people who participate in the identity authentication respectively compare the authentication quantum states according to their own private authentication codes and group identifiers. Execute the corresponding unitary operation, and the network group will send the authentication quantum state back to the authentication management center;

S4. The authentication management center calculates the authentication parameters according to the group identifier, performs unitary operation and measurement on the authentication quantum state according to the group authentication code, and compares the authentication parameters with the measurement results to obtain the authentication result;

Among them, |·> represents the right vector symbol of the Dirac symbol, |a> represents the single-particle quantum state, and two single-particle quantum states represent a two-particle quantum state through the tensor product symbol, namely |aa> represents a two-particle quantum state.

Further, the two-particle quantum state |S _w > in step S1 is defined as:

Preparation of initial authentication quantum states. The initial authentication quantum state is a two-particle state prepared by the authentication management center. The two-particle quantum state |S _w > is defined as:

Among them, w∈{00,01,10,11}, w is the parameter value corresponding to each two-particle quantum state, and the authentication center randomly prepares one of the above four quantum states as the authentication quantum, and passes the authentication quantum state through The secure quantum channel is sent to the network group G _M that needs authentication; α and β are two intermediate parameters, expressed as

Further, step S2 specifically includes:

S21. The authentication management center randomly selects a polynomial of degree t-1, expressed as: f(x)=a ₀ +a ₁ x+a ₂ x ² +...+a _t-1 x ^t-1 ; where a ₀ is a constant term, and a ₁ ~a _t-1 are polynomial coefficients;

S22. Generate n private shares f(x _l ), l=1,2,...,n;

S23. The authentication management center distributes n private shares to n common users P ₁ , P ₂ ,...,P _n who need to register through the secure classic channel;

S24, then the authentication management center sets a 2t-bit group identifier ID _M (i ₁ , i ₂ ,...,i _2t ) for the network group _GM , and sends it to the network group _GM through a secure classic channel;

in, Indicates a set of non-negative integers smaller than d; a ₀ is a group authentication code, reserved by the authentication management center.

Further, step S3 specifically includes:

S31. The n ordinary users who need to register in the network group are expressed as P ₁ , P ₂ ,...,.P _l ,...,P _n , where the private share received by P _l is expressed as: (x _l , f(x _l )), calculate the private authentication code of ordinary users through the private share, and the private authentication code is the identity information;

S32. The t persons who need to participate in identity authentication are expressed as P ₁ , P ₂ ,...,P _i ,...,P _t , and the network group sends the two-particle authentication quantum state |S _w > to the network group, The network group transmits the authentication quantum state to the first authenticator;

S33. After the user P _i who needs to participate in identity authentication confirms the receipt of the authentication quantum state |S _w > _{, perform} a unitary operation;

_S34 . _The user _{P i who needs} to participate in identity authentication _performs the authentication quantum state | _{S w} > Execute a unitary operation;

S35. After the first authentication participant P ₁ completes the operation, it is sent to the next authentication participant until the transmission t-1 times reaches _Pt ; after the execution is completed, the network group G _M sends the authentication quantum state back to the authentication management center;

Wherein, x _l represents the value of user P _l on the x-coordinate axis; f(x _l ) represents a point on x=x _l on the x-coordinate axis in the two-dimensional coordinate system; i _2t represents the 2ith bit value. Further, step S4 specifically includes:

S41. The authentication management center performs a U _θ unitary operation on the authentication quantum state |S _w > according to the group identity authentication code a ₀ ;

S42. The authentication management center executes an authentication quantum state according to the selection of the initial quantum state |S _w > the corresponding parameter value w. unitary operation;

S43. The authentication management center performs an XOR operation on the identifier ID _M (i ₁ , i ₂ ,...,i _2t ) of the group G _M in pairs to calculate the authentication parameter r, that is, the ID _M (i ₁ , i ₂ ,...,i _2t ) two-bit groups are divided into K(k ₁ ,k ₂ ,...,k _i ,...,k _t ), where k _i ∈(00,01,10, 11), that is, k ₁ =i ₁ i ₂ ,k ₂ =i ₃ i ₄ ,...,k _i =i _2i-1 i _2i ,...,k _t =i _2t-1 i _2t , through different Or operation to obtain the authentication parameter r∈{00,01,10,11}, expressed as

S44. The authentication management center measures |S _w >, and compares the measurement result with the authentication parameters for authentication. If the number of participants in the authentication t is an even number, the authentication management center uses the X base to measure the authentication quantum, and obtains according to the authentication parameter r The measurement result is denoted as |± _Sr >, and |± _Sr > is defined as:

S45. If the number of participants in the authentication t is an odd number, the authentication management center uses the Z base to measure the authentication quantum, and the measurement result obtained according to the authentication parameter r is recorded as |±r>, and |±r> is defined as:

S46. If the obtained measurement result and the value of the authentication parameter can satisfy the corresponding relationship in step S44 or S45, then the group identity and group identifier authentication is passed;

Among them, + means positive phase, - means negative phase; α and β are two intermediate parameters, expressed as

The beneficial effects of the present invention are:

1. The authentication algorithm is based on the Grover operator that can authenticate the network identifier. The authentication scenario is similar to the IP multicast scenario in the computer network. The structural model of the IP multicast technology has two parts: one is multiple network groups, and the network group There is a network identifier; the second is the user's personal host, and each user host has an IP address; and the invention introduces the idea of quantum Shamir (t, n) threshold, which can simultaneously authenticate multiple user identities, and has better applicability sex;

2. Compared with similar schemes, the initial quantum preparation in the present invention is less, and the number of quantum transmissions is less, so the efficiency is higher;

3. The present invention guarantees the security of the method based on quantum characteristics such as the quantum non-cloning principle and the Heisenberg uncertainty principle, and the double authentication of the method further improves the security.

Description of drawings

In order to make the purpose, technical method and beneficial effect of the present invention clearer, the present invention provides the following drawings for illustration:

Fig. 1 is a flow chart of the method of the present invention;

Fig. 2 is a schematic diagram of the network structure of the quantum group authentication method.

Figure 3 is a schematic diagram of the internal structure of the network group of the quantum group authentication method

Fig. 4 is a quantum circuit diagram of the present invention.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

The invention provides a quantum group authentication method based on the Grover algorithm, comprising the following steps:

S1. The authentication management center prepares the authentication quantum state for the network group. The quantum state is a two-particle state, expressed as |S _w >;

S2. The authentication management center randomly generates n private shares and group authentication codes according to the Shamir(t,n) threshold idea, and distributes the private shares to ordinary users who need to register in the network group, and ordinary users keep their own group authentication codes , the authentication management center generates a group identifier and sends it to the network group;

S3. After the n ordinary users who need to register in the network group get their private shares, the ordinary users calculate their own private authentication codes, and the t people who participate in the identity authentication respectively compare the authentication quantum states according to their own private authentication codes and group identifiers. Execute the corresponding unitary operation, and the network group will send the authentication quantum state back to the authentication management center;

S4. The authentication management center calculates the authentication parameters according to the group identifier, performs unitary operation and measurement on the authentication quantum state according to the group authentication code, and compares the authentication parameters with the measurement results to obtain the authentication result;

Among them, |·> represents the right vector symbol of the Dirac symbol, |a> represents the single-particle quantum state, and two single-particle quantum states represent a two-particle quantum state through the tensor product symbol, namely |aa> represents a two-particle quantum state.

This example is a quantum group authentication method based on the Grover algorithm and using the shamir(t,n) threshold idea. This example is divided into the following parties according to the IP multicast structure model in the network: authentication management center, N network groups G ₁ , G ₂ ,...,G _N and multiple users P ₁ , P in the network groups ₂ ,...,P _n . Referring to the method flowchart in FIG. 1, the method of the present invention can be divided into an initialization stage and a group identity authentication stage. A secure quantum channel and a secure classical channel can be established between the authentication management center and multiple network groups G ₁ , G ₂ ,..., _GN , and the authentication management center transmits the initial quantum state on the secure quantum channel, Transfer private share and group identifier information over a secure classic channel.

As shown in Figure 1, this embodiment is mainly divided into two parts to realize the above scheme, one is the initialization phase, and the other is the group identity authentication and measurement authentication phase, the specific steps are as follows:

1. Initialization phase:

Assuming that the network group _GM initiates an authentication request to the authentication management center, _GM has a total of n common users, and t of them are ready to participate in identity authentication.

According to Fig. 2 and Fig. 3, at this stage, the authentication management center mainly shares the initial information with the network groups requiring authentication.

Step 1: First, after the authentication management center receives the authentication request from the group _GM , the authentication management center prepares the authentication quantum state | _{S w} > for the group GM, and the quantum state |S _w > is a two-particle state, where | S _w > is defined as follows:

Among them, w∈{00,01,10,11}, w is the parameter value corresponding to each two-particle quantum state, and the authentication center randomly prepares one of the above four quantum states as the authentication quantum, and passes the authentication quantum state through The secure quantum channel is sent to the network group G _M that needs authentication; α and β are two intermediate parameters, expressed as

The authentication management center randomly prepares one of the above quantum states for the group _GM , and distributes the authenticated initial quantum state |S _w > to the network group _GM through a secure quantum channel.

Step 2: Ordinary users P ₁ , P ₂ ,...,P _n in the network group G _M need to register to be authenticated. The authentication management center uses the Shamir(t,n) threshold idea to randomly generate n private shares ( x _i , f( _xi )), (i=1,2,...,n) and group identity authentication code a ₀ , keep a ₀ for yourself and distribute the private share to the group G _M through a secure classical channel Multiple users P ₁ , P ₂ ,...,P _n .

The secret share preparation algorithm is:

S21. The authentication management center randomly selects a polynomial of degree t-1, expressed as: f(x)=a ₀ +a ₁ x+a ₂ x ² +...+a _t-1 x ^t-1 ;

S22. Generate n private shares f(x _l ), l=1,2,...,n;

S23. The authentication management center distributes n private shares to n common users P ₁ , P ₂ ,...,P _n who need to register through the secure classic channel;

S24, then the authentication management center sets a 2t-bit group identifier ID _M (i ₁ , i ₂ ,...,i _2t ) for the network group _GM , and sends it to the network group _GM through a secure classic channel;

in, Indicates a set of non-negative integers smaller than d; a ₀ is a group authentication code, reserved by the authentication management center.

After the above operations, each user P _l , (l=1,2,...,n) has its own private share, expressed as (x _l , f(x _l )).

Step 3: The authentication management center sets a 2t-bit group identifier ID _M (i ₁ , i ₂ ,...,i _2t ) for the group _GM , and sends it to the network group _GM through a secure classical channel.

The scheme of the present invention utilizes two quanta as the authentication carrier, and the initial quantum is prepared by the authentication management center, as shown in Figure 4, the authentication phases P ₁ , P ₂ ... P _t respectively perform authentication unitary operations on the two quanta, and finally the authentication party authentication management center Quantum unitary transformation will also be performed on the quantum system to measure and verify. The overall circuit of the scheme is relatively simple and easy to implement. The whole process uses a total of 2t+2 quantum logic gates. In the measurement phase, the certification management center uses the X base or Z base in the two-dimensional Hilbert space for measurement. And the entire quantum channel only needs to transmit two particles; TC in Figure 4 refers to the certificate management center.

2. Group identity authentication and measurement authentication stage

Step 1: The private share (x _l ,f(x _l )) received by users P ₁ , P ₂ ,...,P _n in G _M , after l=1,2,...,n, each The following values are calculated: s _l is used as the private authentication code and identity information of P _l .

Step 2: t members in the group G _M need to perform group identity authentication through the authentication management center. Assuming that the members participating in the authentication are P ₁ , P ₂ ..., P _t , the network group transmits the authentication quantum state |S _w > prepared by the authentication management center in the initial stage to the first person P ₁ participating in the authentication.

Step 3: After receiving the authenticated quantum state |S _w >, P ₁ performs an authentication on the authenticated quantum state |S _w > according to the private authentication code s ₁ unitary operation, where the rotation operator defined as:

U(θ ₁ )＝cos(θ ₁ )|0><0|-sin(θ ₁ )|0><1|+sin(θ ₁ )|1><0|+cos(θ ₁ )|1><1|

in The d here is the limited field parameter of the t-degree polynomial in the threshold thought, that is, the quantum dimension.

_{Step 4 : P 1 executes a} unitary operation, where The Grover rotation operator is defined as:

Step 5: P ₁ passes the unitary transformed |S _w > to the next member P ₂ , similarly P ₂ executes an authentication quantum state |S _w > according to the private authentication code s _{2 unitary operation , and perform a} unitary operation. This process continues until passing |S _w 〉 to the last authenticating participant P _t .

Step 6: P _t executes an authentication quantum state |S _w 〉 according to the private authentication code s _t unitary operation, and according to the 2t-1 and 2t bit information of the group G _M identifier ID _M (i ₁ ,i ₂ ,...,i _2t ), perform an authentication quantum state |S _w 〉 unitary operation, P _t transmits |S _w 〉 to the authentication management center through a secure quantum channel.

Step 7: The authentication management center prepares a phase rotation operator U _θ to perform a unitary operation on |S _w 〉 according to the member group identity authentication code a ₀ in its own hands, where U _θ is defined as follows:

U(θ)＝cos(θ)|0><0|-sin(θ)|0><1|+sin(θ)|1><0|+cos(θ)|1><1|

in |·><·| represents the outer product of two quantum states.

Step 8: According to the selection of the initial quantum state |S _w > parameter w, the authentication management center executes a Unitary operation:

where U(S _w )U _Sw is The unitary operation rotation operator is also the Grover projection operator, and I is the identity matrix.

Step 9: Finally, the authentication management center authenticates the group G _M group user identity and group identifier, and the authentication management center uses the group G _M identifier ID _M (i ₁ ,i ₂ ,...,i _2t ) to calculate the authentication parameter r by XOR operation in groups of two bits, that is, ID _M (i ₁ ,i ₂ ,...,i _2i ,...,i _2t ) in groups of two bits is divided into K(k ₁ , k ₂ ,..., _ki ,...,k _t ), where _ki ∈(00,01,10,11), namely k ₁ ＝i ₁ i ₂ ,k ₂ ＝i ₃ i ₄ ,. ..,k _i ＝i _2i-1 i _2i ,...,k _t ＝i _2t-1 i _2t , the authentication parameter r∈{00,01,10,11} is obtained through XOR operation, expressed as

Step 10: The authentication management center measures |S _w >, and compares the measurement result with the authentication parameters for authentication. If the number t of participants in the authentication is even, the authentication management center uses the X basis to measure the authentication quantum, and obtains according to the authentication parameter r The measurement result is recorded as |±S _r >, and |±S _r > is defined as:

If the number of participants in the certification t is an odd number, the certification management center uses the Z base to measure the certification quantum, and the measurement result obtained according to the certification parameter r is recorded as |±r>, and |±r> is defined as:

If the measurement result obtained and the value of the authentication parameter can satisfy the corresponding relationship in step S44 or S45, then the group identity and the group identifier are authenticated; The invention can set corresponding parameters according to the actual situation. The specific examples described here are only used to explain the present invention, not to limit the present invention.

Combining with the current technical background, the present invention proposes a group identity authentication method based on the Grover algorithm, aiming at the requirement of multi-user authentication at the same time.

From the perspective of efficiency, the initial quantum preparation of this scheme only needs to prepare two particles, which is less than similar authentication protocols, and referring to the quantum circuit diagram scheme in Figure 3, only two measurements are required, the measurement consumes less resources, and the total number of particles transmitted by the quantum channel It is 2t+2. Generally speaking, this authentication method is more efficient; in terms of security, this method is based on quantum characteristics such as the quantum non-cloning principle and the Heisenberg uncertainty principle to ensure the security of the method, and the method can be double-authenticated The security is further improved; from the applicability point of view, this method can simultaneously authenticate multiple user identities. The authentication method is based on the Shamir threshold idea, which can overcome the special situation of absent users and partial user authentication.

In the present invention, |·> represents the right arrow symbol of the Dirac symbol, <·| represents the left arrow symbol of the Dirac symbol, and |·><·| represents the outer product of two quantum states, all of which are symbols of quantum states.

Although the embodiments of the present invention have been shown and described, those skilled in the art can understand that various changes, modifications and substitutions can be made to these embodiments without departing from the principle and spirit of the present invention. and modifications, the scope of the invention is defined by the appended claims and their equivalents.

Claims (10)

1. A quantum group authentication method based on Grover algorithm, is characterized in that, comprises the following steps: S1. The authentication management center prepares the authentication quantum state for the network group. The quantum state is a two-particle state, expressed as |S _w >; S2. The authentication management center randomly generates n private shares and group authentication codes according to the Shamir(t,n) threshold idea, and distributes the private shares to ordinary users who need to register in the network group, and ordinary users keep their own group authentication codes , the authentication management center generates a group identifier and sends it to the network group; S3. After the n ordinary users who need to register in the network group get their private shares, the ordinary users calculate their own private authentication codes, and the t people who participate in the identity authentication respectively compare the authentication quantum states according to their own private authentication codes and group identifiers. Execute the corresponding unitary operation, and the network group will send the authentication quantum state back to the authentication management center; S4. The authentication management center calculates the authentication parameters according to the group identifier, performs unitary operation and measurement on the authentication quantum state according to the group authentication code, and compares the authentication parameters with the measurement results to obtain the authentication result; Among them, |·> represents the right vector symbol of the Dirac symbol, |a> represents the single-particle quantum state, and two single-particle quantum states represent a two-particle quantum state through the tensor product symbol, namely |aa> represents a two-particle quantum state. 2. A kind of quantum swarm authentication scheme based on Grover algorithm as claimed in claim 1, it is characterized in that, the two-particle quantum state |S _w > of step S1 is defined as: Among them, w∈{00,01,10,11}, w is the parameter value corresponding to each two-particle quantum state, and the authentication center randomly prepares one of the above four quantum states as the authentication quantum, and passes the authentication quantum state through The secure quantum channel is sent to the network group G _M that needs authentication; α and β are two intermediate parameters, expressed as 3. A kind of quantum group authentication scheme based on Grover algorithm as claimed in claim 1, is characterized in that, step S2 specifically comprises: S21. The authentication management center randomly selects a polynomial of degree t-1, expressed as: f(x)=a ₀ +a ₁ x+a ₂ x ² +...+a _t-1 x ^{t -1} ; S22. Generate n private shares f(x _l ), l=1,2,...,n; S23. The authentication management center distributes n private shares to n common users P ₁ , P ₂ ,...,P _n who need to register through the secure classic channel; S24, then the authentication management center sets a 2t-bit group identifier ID _M (i ₁ , i ₂ ,...,i _2t ) for the network group _GM , and sends it to the network group _GM through a secure classic channel; in, Indicates a set of non-negative integers smaller than d; a ₀ is a group authentication code, reserved by the authentication management center. 4. A kind of quantum group authentication scheme based on Grover algorithm as claimed in claim 1, is characterized in that, step S3 specifically comprises: S31. The n ordinary users who need to register in the network group are expressed as P ₁ , P ₂ ,...,.P _l ,...,P _n , where the private share received by P _l is expressed as: (x _l , f(x _l )), calculate the private authentication code of ordinary users through the private share, and the private authentication code is the identity information; S32. The t persons who need to participate in identity authentication are expressed as P ₁ , P ₂ ,...,P _i ,...,P _t , and the network group sends the two-particle authentication quantum state |S _w > to the network group, The network group transmits the authentication quantum state to the first authenticator; S33. After the user P _i who needs to participate in identity authentication confirms the receipt of the authentication quantum state |S _w > _{, perform} a unitary operation; _S34 . _The user _{P i who needs} to participate in identity authentication _performs the authentication quantum state | _{S w} > Execute a unitary operation; S35. After the first authentication participant P ₁ completes the operation, it is sent to the next authentication participant until the transmission t-1 times reaches _Pt ; after the execution is completed, the network group G _M sends the authentication quantum state back to the authentication management center; Wherein, x _l represents the value of user P _l on the x-coordinate axis; f(x _l ) represents a point on x=x _l on the x-coordinate axis in the two-dimensional coordinate system; i _2t represents the 2ith bit value. 5. A kind of quantum group authentication scheme based on Grover's algorithm as claimed in claim 4, it is characterized in that, said calculating the secret authentication code of common user by private share comprises: Among them, s _l represents the private authentication code of the lth ordinary user, x _m represents the value of user P _m on the x-coordinate axis; mod represents the modulo operation, t represents the number of people participating in the authentication; d represents the polynomial of degree t in the threshold idea The limited domain parameter is just the quantum dimension. 6. a kind of quantum group authentication scheme based on Grover algorithm as claimed in claim 4, is characterized in that, in step S33 The unitary operation is expressed as: U(θ _i )＝cos(θ _i )|0><0|-sin(θ _i )|0><1|+sin(θ _i )|1><0|+cos(θ _i )|1><1| in, Represents the tensor product symbol, |> represents the right vector of the Dirac symbol; <| represents the left vector of the Dirac symbol; _si represents the private authentication code; d represents the limited field parameter of the t-degree polynomial in the threshold idea, which is the quantum dimension; U(θ _i ) means Rotation operator for unitary operation. 7. A kind of quantum group authentication scheme based on Grover algorithm as claimed in claim 1, is characterized in that, in step S34 The unitary operation is expressed as: U(w _i )＝I-2|i _2i-1 i _2i ><i _2i-1 i _2i | Among them, I represents the identity matrix; i _2i represents the 2ith bit value; Indicates the tensor product symbol; |i _2i-1 , i _2i ><i _2i-1 , i _2i | indicates the outer product of two two-particle quantum states; <| indicates the Dirac symbol left vector. 8. A kind of quantum group authentication scheme based on Grover algorithm as claimed in claim 1, is characterized in that, step S4 specifically comprises: S41. The authentication management center performs a U _θ unitary operation on the authentication quantum state |S _w > according to the group identity authentication code a ₀ ; S42. The authentication management center executes an authentication quantum state according to the selection of the initial quantum state |S _w > the corresponding parameter value w. unitary operation; S43. The authentication management center performs an XOR operation on the identifier ID _M (i ₁ , i ₂ ,...,i _2t ) of the group G _M in pairs to calculate the authentication parameter r, that is, the ID _M (i ₁ , i ₂ ,...,i _2i ,...,i _2t ) two-bit pairs are divided into K(k ₁ ,k ₂ ,...,k _i ,...,k _t ), where k _i ∈ (00,01,10,11), namely k ₁ =i ₁ i ₂ , k ₂ =i ₃ i ₄ ,...,k _i =i _2i-1 i _2i ,...,k _t =i _{2t -1} i _2t , the authentication parameter r∈{00,01,10,11} is obtained through XOR operation, expressed as S44. The authentication management center measures |S _w >, and compares the measurement result with the authentication parameters for authentication. If the number of participants in the authentication t is an even number, the authentication management center uses the X base to measure the authentication quantum, and obtains according to the authentication parameter r The measurement result is denoted as |± _Sr >, and |± _Sr > is defined as: S45. If the number of participants in the authentication t is an odd number, the authentication management center uses the Z base to measure the authentication quantum, and the measurement result obtained according to the authentication parameter r is recorded as |±r>, and |±r> is defined as: S46. If the obtained measurement result and the value of the authentication parameter can satisfy the corresponding relationship in step S44 or S45, then the group identity and group identifier authentication is passed; Among them, + means positive phase, - means negative phase; α and β are two intermediate parameters, expressed as 9. A kind of quantum group authentication scheme based on Grover's algorithm as claimed in claim 8, is characterized in that, the unitary operation U _θ in the step S41 is expressed as: U(θ)＝cos(θ)|0><0|-sin(θ)|0><1|+sin(θ)|1><0|+cos(θ)|1><1| Among them, θ is the value set by the authentication management center according to a ₀ and d, expressed as a ₀ represents the group authentication code; d represents the limited domain parameter of the t-degree polynomial in the threshold idea, which is the quantum dimension; <·| represents the left vector of the Dirac symbol; |·> represents the right vector of the Dirac symbol. 10. A kind of quantum group authentication scheme based on Grover's algorithm as claimed in claim 8, is characterized in that, the unitary operation in step S41 Expressed as: Among them, U(S _w ) is a unitary operation The rotation operator of , I is the identity matrix; <·| represents the Dirac symbol left vector; |·> represents the Dirac symbol right vector; |·><·| represents the outer product of two quantum states.