CN114640449B - Multi-user high-dimensional quantum privacy block query method - Google Patents

Abstract

The invention belongs to the field of quantum computation and quantum information, and particularly relates to a multi-user high-dimensional quantum privacy block query method, which comprises the following steps: constructing a multi-user quantum privacy block query system, wherein the system comprises a query user, a database holder and a semi-trusted quantum server; respectively distributing quantum keys to a query user and a database holder in the privacy block query system by adopting a quantum key distribution method; the database holder and the inquiring user encrypt the data in the database by adopting the distributed quantum key to obtain a ciphertext database; searching the ciphertext database by a query user by adopting a Grover quantum search algorithm to obtain ciphertext; the inquiring user decrypts the ciphertext according to the quantum key to obtain a plaintext; the invention improves the speed of inquiring the wanted ciphertext by the user by applying the Grover quantum search algorithm.

Description

A multi-user high-dimensional quantum privacy block query method

Technical Field

The present invention belongs to the field of quantum computing and quantum information, and in particular relates to a multi-user high-dimensional quantum privacy block query method.

Background Art

Private information retrieval aims to protect the user's personal privacy. When a user accesses the database, the database does not know which data entry Alice is interested in. Similarly, the database does not want users to obtain more private information. For classic symmetric private information retrieval (SPIR), the protocol can not only protect user privacy, but also ensure that Alice cannot access any information other than the data entry she is interested in.

Giovannetti et al. extended the classical symmetric private information retrieval protocol (SPIR) to the quantum world and proposed the first quantum privacy query protocol (GLM) based on unitary operation. In this protocol, unitary operation is used to encode data information into the retrieval state. Users use two quantum states to access the database, one quantum state is used for information query, and the other quantum state is used to query the database for deception, which is used to ensure the privacy and security of both parties. The GLM protocol uses a deception-sensitive strategy to detect whether the database Bob has stolen the private information of the user Alice.

Jakobi et al. proposed a practical QPQ protocol using the SARG04 quantum key distribution protocol. This protocol has three main steps: first, Alice and Bob negotiate an asymmetric initial key, that is, Alice only knows part of the key and Bob knows all the keys; then, the key is diluted by bitwise addition to reduce the information Alice knows about the key and obtain the final key; finally, the user can query the information he wants through the final key.

In summary, quantum privacy query protocols are mainly divided into two categories: one is a quantum privacy query protocol based on unitary operations, and the other is a quantum privacy query protocol based on quantum key distribution. However, the first protocol is difficult to apply to large databases because high-dimensional unitary operations are difficult to implement in quantum computers. Most of the second protocols only consider the query of single-user and single-bit data information, which is poor in practicality and efficiency.

Summary of the invention

To solve the problems existing in the above prior art, the present invention proposes a multi-user high-dimensional quantum privacy block query method, which comprises: constructing a multi-user quantum privacy block query system, the system comprising query users {Alice ₁ , Alice ₂ , ..., Alice _n }, a database holder Bob and a semi-trusted quantum server Charlie, Alice _n represents the nth query user; using a quantum key distribution method to distribute quantum keys to query users and database holders in the privacy block query system respectively; the database holder and the query user use the distributed quantum keys to encrypt data in the database to obtain a ciphertext database; the query user uses the Grover quantum search algorithm to search the ciphertext database to obtain a ciphertext; the query user decrypts the ciphertext according to the quantum key to obtain a plaintext.

Preferably, the process of distributing quantum keys to query users and database holders using a quantum key distribution method includes:

S1: Initialize the system and build key encoding rules;

S2: The semi-trusted quantum server Charlie constructs a d-dimensional single-photon product state sequence S, the length of which is N=n+q+χ+δ, where n represents the database size, q represents the number of single-photon product states required for the interaction between Bob and Charlie, χ represents the number of single-photon product states required for the interaction between the query user and Charlie, and δ represents the number of single-photon product states required for the interaction between Bob and the query user; construct subsequences _S1 and _S2 based on the d-dimensional single-photon product state sequence S, where the length of subsequence _S1 is n+q+δ, and the length of subsequence _S2 is χ; select the i-th column in subsequence _S2 in turn, and use the selected i-th column as the subsequence Charlie sends subsequence S ₁ to the database owner Bob, Send to the corresponding query user;

S3: Querying a Subsequence of User Records The initial position of the sequence and the measurement basis corresponding to the sequence, and the subsequence Rearrange and obtain a new sequence S _CA ; the query user sends the measurement basis and the sequence S _CA to Charlie;

S4: Charlie measures the sequence S _CA according to the measurement basis and feeds back the measurement result to Alice _i ;

S5: Alice _i according to the subsequence The measurement results are restored from the initial position; Charlie and Alice _i perform the first safety check through the particles in the sequence S _CA ;

S6: Bob records the initial position of subsequence S ₁ and the measurement basis corresponding to the sequence, and rearranges subsequence S ₁ ; randomly selects particles from q sequences in the rearranged subsequence to form a safety detection sequence S _BC , and the other particles form a sequence S _BA ;

S7: Bob sends S _BC and the measuring machine to Charlie. Charlie measures the particles in the sequence S _BC according to the measurement basis and feeds back the measurement results to Bob.

S8: Bob recovers the measurement result according to the initial position of subsequence S ₁ ; Bob and Alice _i perform a second security check using particles in sequence S _BC ;

S9: Bob extracts n particles from the sequence S _BA to form the sequence Get the measurement basis of the particles at δ positions in the sequence S _BA , and replace the measurement basis of the particles at δ positions with the sequence Sent to the query user; the query user has a query on the sequence Rearrange the qudit in to get the sequence And the sequence Convert to single-photon product state S′ _BA sequence; the query user sends δ particles and measurement basis in S′ _BA to Charlie; where qudit represents a high-dimensional quantum state;

S10: Charlie measures the particles in S′ _BA according to the measurement basis and returns the measurement results to the querying user; the querying user and Bob perform a third safety check on the δ particles in S′ _BA ;

S11: Sort the remaining n particles in S _BA to form a sequence S″ _BA ; Charlie measures the particles in S″ _BA and feeds the measurement results back to Alice _i ; Alice _i restores the position of the measurement results to obtain the restored sequence in, Indicates the measurement result, which is a decimal value;

S12: Bob converts the non-orthogonal qudit pair Published to the system, where |q> is the qudit in Bob's hand, |q> and are all non-orthogonal quantum states, represents the quantum state symbol after quantum Fourier transformation, | > represents the Dirac symbol in quantum;

S13: Alice _i uses the non-orthogonal qudit pair published by Bob to and the recovery sequence S _M uses the key encoding rule to guess the key;

S14: Distribute the inferred key.

Preferably, the key encoding rule includes: Bob and n query users Alice _i (i=1, 2, ..., n) negotiate the corresponding key encoding rule, and the encoding rule includes:

Among them, |0> represents the quantum state 0, represents the quantum state obtained by performing a quantum Fourier transform on quantum state 0, where quantum Fourier transform refers to the operation of quantum states in the quantum field. It represents the quantum state after performing quantum Fourier transform on quantum state d-1, where d represents the dimension.

Preferably, the measurement basis includes Z _d and X _d ; the expression of Z _d is:

The expression of _Xd is:

Among them, Z _d represents the measurement basis in d dimensions, d represents the dimension, |j> represents the quantum state j, j represents a decimal value, X _d represents the measurement basis after quantum Fourier transformation, It represents the quantum state obtained by quantum Fourier transformation of quantum state j, and k is a decimal value.

Preferably, the process of Charlie measuring the sequence according to the measurement basis includes:

Charlie obtains the state of the quantum system |q> and constructs the measurement operator {M _m } = {M ₀ ,M ₁ ,...,M _d-1 };

The probability that the measurement result is m=ν is calculated according to the measurement operator. The expression for probability calculation is:

Among them, M _d-1 represents the measurement operator, where d represents the dimension; m is a decimal value, v is a decimal value, and p(v) represents the probability that the measurement result is m=v. represents the conjugate transpose of M _v , M _v represents the measurement operator, <q| represents the quantum state q, |q> represents the quantum state q;

After measurement, the state of the quantum system is:

in, Represents the quantum state after measurement

Preferably, the process of performing safety detection includes: setting an error threshold τ, taking Charlie and Alice _i as entities A and B respectively; obtaining the number l of particles in the sequence to be safely detected; entity B compares the measurement result sent by entity A based on the initial particle information, and calculates the error rate of the sequence based on the number l of particles in the sequence to be safely detected; if the error rate is higher than the set error threshold, the detection is terminated, otherwise the detection continues until all particle detections are completed.

Preferably, the process of performing key inference includes: obtaining Bob's quantum state |q> and sending the quantum state to Alice _i ; Alice _i randomly selects a measurement basis and sends the measurement basis and the received quantum state to Charlie; Charlie measures the quantum state according to the measurement basis to obtain a measurement result And return the measurement result to Alice _i ; from Randomly select one Will and |q> form a cloth qudit pair Bob publishes qudit in represents the quantum state of the quantum Fourier transform of |κ> Alice _i uses the selected measurement basis to measure |q> and We measure and obtain |q> and The measurement result of Bob is used to determine the quantum state |q> of Bob. The encoding conversion rule is used to convert |q> into decimal to obtain q, which is the key obtained by Alice _i .

Preferably, the process of distributing the inferred key includes: the query user and Bob share a set of asymmetric keys K ^r ={k ₀ ,k ₁ ,...,k _n-1 }, where k _i represents the i-th key in K ^r ; Bob knows all asymmetric keys in the asymmetric key, and the query user knows his corresponding key; Bob calculates for each k _i in, Where _Qi is a decimal value and ι is a decimal value; calculate _Qi ′= _Qi modd according to _Qi , where mod is the remainder symbol; collect all _Q′i to obtain Bob’s final key ^Kf ={ _Q′0 , _Q′1 , ..., Q′n _-1 }; the query user performs the same operation as Bob to determine the number of keys in the query user. If the number of keys is less than 1, recalculate the key in the query user, otherwise the query user obtains the key in a different position. 0≤i ₀ ,i ₁ ,...,i _n-1 ≤n-1, where the subscripts i ₀ ,i ₁ ,...,i _n-1 represent positions.

Preferably, the process of encrypting data in a database using a quantum key includes: Alice _i obtains the key at the i ₀ th , i _{1 th} , ..., i _n-1 th position in K ^f and retrieve the j ₀ ,j ₁ ,...,j _n-1 items Where 0<=j ₀ ,j ₁ ,...,j _n-1 <=n-1; Alice _i calculates the shift numbers s ₀ ,s ₁ ,...s _n-1 respectively, where s _λ =j _λ -i _λ , where λ is a decimal value in the range of {0,1,...,n-1}; sends the calculated shift numbers s ₀ ,s ₁ ,...s _n-1 to Bob, who shifts the key K ^f by s ₀ ,s ₁ ,...s _n-1 respectively to form n Use n Encrypt the data in the database respectively to form a ciphertext database ED ⁰ , ED ¹ ,..., ED ^n-1 , where Represents the n-1th ciphertext in the i-th ciphertext database.

Preferably, the process of the query user using the Grover quantum search algorithm to search for ciphertext includes:

Step 1: Get the number of elements in the ciphertext database;

Step 2: Calculate the initial quantum state |υ>. The calculation formula for the initial quantum state is:

Among them, H represents the quantum gate, represents the tensor product of σ H gates, σ represents the number of bits, represents the tensor product symbol in quantum, |x> represents the quantum state x, and n represents the number of elements in the ciphertext database;

Step 3: Perform k G iterations on the initial quantum state |υ> to obtain the current database state; the calculation formula is:

Among them, G represents a unitary operator in Grover's algorithm, k represents the number of iterations, θ represents the angle, |j ₀ > represents the quantum state j ₀ , and j ₀ is the index subscript that the query user wants to find;

Step 4: Get the index subscript j ₀ of the query user according to the database status;

Step 5: Get the ciphertext to be queried by the querying user according to the index subscript.

Beneficial effects of the present invention:

1) The present invention only requires the user and database to have nearly classical quantum capabilities (quantum rearrangement, access to quantum channels), and the third-party quantum server Charlie provides full quantum capabilities. The semi-quantum technology greatly reduces the quantum costs of the user and database;

2) The present invention improves the speed of users querying the desired ciphertext by applying the Grover quantum search algorithm. The query time complexity is Greatly improve the efficiency of the entire method;

3) The present invention can support multiple users to access a whole block of information at different locations in the database, making the method more practical and efficient.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a multi-user quantum privacy block query method of the present invention;

FIG. 2 is a structural diagram of a single-photon product state sequence in the present invention.

DETAILED DESCRIPTION

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

A specific implementation method of a multi-user high-dimensional quantum privacy block query method, the method is specifically as follows: construct a multi-user quantum privacy block query system, the system includes query users {Alice ₁ , Alice ₂ , ..., Alice _n }, database holder Bob and semi-trusted quantum server Charlie, Alice _n represents the nth query user; a quantum key distribution method is used to distribute quantum keys to query users and database holders in the privacy block query system respectively; the database holder and the query user use the distributed quantum keys to encrypt data in the database to obtain a ciphertext database; the query user uses the Grover quantum search algorithm to search the ciphertext database to obtain a ciphertext; the query user decrypts the ciphertext according to the quantum key to obtain a plaintext.

The multi-user quantum privacy block query system in the present invention mainly includes three types of entities, namely, n query users {Alice ₁ , Alice ₂ , ..., Alice _n }, Bob, the holder of database D, and semi-trusted quantum server Charlie. In database D, n plaintexts {D ₀ , D ₁ , ..., D _n-1 } are stored, where _Di (i = 0, 1, ..., n-1) is a binary bit string, and the bit string length l of _Di (i = 0, 1, ..., n-1) depends on the dimension d, that is, in, represents rounding up; {Alice ₁ , Alice ₂ , ..., Alice _n } and Bob only have the ability to access the quantum channel and rearrange the quantum state.

Charlie has full quantum capabilities, which are used for quantum preparation and quantum measurement. The quantum state prepared by Charlie is a d-dimensional single-photon state set M ₁ and M ₂ ; its expression is:

Where d represents the dimension, |j> represents the quantum state j, and j is a decimal value. It represents the quantum state obtained by quantum Fourier transformation of quantum state j, and k is a decimal value.

Each element in the d-dimensional single-photon state sets _M1 and _M2 is orthogonal to each other. The measurement basis used by Charlie to perform the measurement operation is:

Among them, Z _d represents the measurement basis in d dimensions, and X _d represents the measurement basis after quantum Fourier transform.

The process of distributing quantum keys to query users and database holders using the quantum key distribution method includes:

S1: Initialize the system and build key encoding rules;

S2: The semi-trusted quantum server Charlie constructs a d-dimensional single-photon product state sequence S, the length of which is N=n+q+χ+δ, where n represents the database size, q represents the number of single-photon product states required for the interaction between Bob and Charlie, χ represents the number of single-photon product states required for the interaction between the query user and Charlie, and δ represents the number of single-photon product states required for the interaction between Bob and the query user; construct subsequences _S1 and _S2 based on the d-dimensional single-photon product state sequence S, where the length of subsequence _S1 is n+q+δ, and the length of subsequence _S2 is χ; select the i-th column in subsequence _S2 in turn, and use the selected i-th column as the subsequence Charlie sends subsequence S ₁ to the database owner Bob, Send to the corresponding query user;

S3: Querying a Subsequence of User Records The initial position of the sequence and the measurement basis corresponding to the sequence, and the subsequence Rearrange and obtain a new sequence S _CA ; the query user sends the measurement basis and the sequence S _CA to Charlie;

S4: Charlie measures the sequence S _CA according to the measurement basis and feeds back the measurement result to Alice _i ;

S5: Alice _i according to the subsequence The measurement results are restored from the initial position; Charlie and Alice _i perform the first safety check through the particles in the sequence S _CA ;

S6: Bob records the initial position of subsequence S ₁ and the measurement basis corresponding to the sequence, and rearranges subsequence S ₁ ; randomly selects particles from q sequences in the rearranged subsequence to form a safety detection sequence S _BC , and the other particles form a sequence S _BA ;

S7: Bob sends S _BC and the measuring machine to Charlie. Charlie measures the particles in the sequence S _BC according to the measurement basis and feeds back the measurement results to Bob.

S8: Bob recovers the measurement result according to the initial position of subsequence S ₁ ; Bob and Alice _i perform a second security check using particles in sequence S _BC ;

S9: Bob extracts n particles from the sequence S _BA to form the sequence Get the measurement basis of the particles at δ positions in the sequence S _BA , and replace the measurement basis of the particles at δ positions with the sequence Sent to the query user; the query user has a query on the sequence Rearrange the qudit in to get the sequence And the sequence Convert to single-photon product state S′ _BA sequence; the query user sends δ particles and measurement basis in S′ _BA to Charlie; where qudit represents a high-dimensional quantum state;

S10: Charlie measures the particles in S′ _BA according to the measurement basis and returns the measurement results to the querying user; the querying user and Bob perform a third safety check on the δ particles in S′ _BA ;

S11: Sort the remaining n particles in S _BA to form a sequence S″ _BA ; Charlie measures the particles in S″ _BA and feeds the measurement results back to Alice _i ; Alice _i restores the position of the measurement results to obtain the restored sequence in, Indicates the measurement result, which is a decimal value;

S12: Bob converts the non-orthogonal qudit pair Published to the system, where |q> is the qudit in Bob's hand, |q> and are all non-orthogonal quantum states, represents the quantum state symbol after quantum Fourier transformation, |> represents the Dirac symbol in quantum;

S13: Alice _i uses the non-orthogonal qudit pair published by Bob to and the recovery sequence S _M uses the key encoding rule to guess the key;

S14: Distribute the inferred key.

A specific implementation method of a multi-user high-dimensional quantum privacy block query method, the method is as described in Figure 1, in which (1.1)-(8.1) correspond to the sequence numbers in the protocol process one by one, where the solid line represents the quantum channel, the dotted line represents the classical channel, and G represents the Grover algorithm.

Step 1: System Initialization

(1.1) Negotiated encoding rules

During the system initialization process, the database holder Bob, n query users Alice _i (i＝1,2,...,n) and the quantum server Charlie negotiate the transmission error rate τ. Bob and the n query users Alice _i (i＝1,2,...,n) initially negotiate the corresponding key encoding rules:

Among them, |0> represents the quantum state 0, represents the quantum state obtained by performing a quantum Fourier transform on quantum state 0, where quantum Fourier transform refers to the operation on quantum states in the quantum field; It represents the quantum state after performing quantum Fourier transform on quantum state d-1, where d represents the dimension.

(1.2) Send sequences S ₁ and S ₂

Charlie prepares a d-dimensional single-photon product state sequence S of length N = n + q + x + δ, where n + q + δ single-photon product states are prepared according to Bob's requirements, x single-photon product states are prepared according to {Alice ₁ , Alice ₂ , ..., Alice _n }, and the single-photon product states are prepared from Randomly select from ;. Where n represents the size of the database; χ represents the number of single-photon product states required for the interaction between {Alice ₁ , Alice ₂ , ..., Alice _n } and Charlie in the first safety check; q represents the number of single-photon product states required for the interaction between Bob and Charlie in the second safety check; δ represents the number of single-photon product states required for the interaction between Bob and {Alice ₁ , Alice ₂ , ..., Alice _n } in the third safety check.

As shown in Fig. 2.a, the n+q+δ single-photon product states in sequence S form sequence S ₁ ; as shown in Fig. 2.b, the x single-photon product states form sequence S ₂ , and the i-th (i＝1,2,...,n) column is selected from S ₂ in sequence to generate a subsequence Charlie sends the sequence S ₁ to Bob, and the subsequence Send them to Alice _i (i＝1,2,...,n) respectively.

Step 2: Particle rearrangement and sending

(2.1) Send the rearranged sequences S _CA , S _BC and S _BA

For each subsequence in sequence _S2 that successfully reaches Alice _i (i＝1,2,...,n) Alice _i (i＝1,2,...,n) first records its corresponding initial position and selects the corresponding measurement basis, and then each Alice _i (i＝1,2,...,n) jointly selects a random number to rearrange the particle qudit in the sequence S _CA . S _CA and the measurement basis are sent to Charlie. Charlie measures the particles in S _CA according to the measurement basis informed by Alice _i (i＝1,2,...,n), and feeds back the measurement results to Alice _i (i＝1,2,...,n). Alice _i (i＝1,2,...,n) restores the measurement results to the position before the rearrangement. Charlie and Alice _i (i＝1,2,...,n) perform the first security check on the particles in the sequence S _CA and call the security check process.

For each single-photon product state in sequence _S1 that successfully reaches Bob, Bob also records its corresponding initial position and selects the corresponding measurement basis, and then performs quantum rearrangement on the received n+q+δ single-photon product states. Secondly, Bob randomly selects q from the n+q+δ single-photon product states to form a safety detection sequence S _BC , and sends S _BC and the measurement basis to Charlie. Charlie measures the particles in S BC according to the measurement basis informed by Bob, and feeds the measurement results back to Bob. Bob restores the measurement results to the position before the rearrangement. At this time, Charlie and Bob perform a second safety detection through the particles in _{the sequence S BC ,} calling the safety detection process.

Bob forms the remaining n+δ single-photon product states into a sequence S _BA , and forms a subsequence of the measurement basis corresponding to the single-photon product states at the δ positions and the 1st, 2nd, ..., nth columns of S _BA The sequence is sent to Alice _i (i＝1,2,...,n) in sequence. Each user Alice _i (i＝1,2,...,n) receives the sequence sent by Bob. (i＝1,2,...,n) and the measurement basis at δ positions, each user Alice _i (i＝1,2,...,n) jointly selects a random number ζ to rearrange the sequence Each user will rearrange the sequence A single-photon product state S′ _BA sequence is formed. Alice _i (i＝1,2,...,n) first sends the single-photon product states and measurement basis at δ positions in S′ _BA to Charlie. Then Charlie measures the received particles according to the measurement basis, returns the measurement results to Alice _i (i＝1,2,...,n) and restores them to the original positions. Alice _i (i＝1,2,...,n) and Bob perform the third safety check through δ single-photon product states in the S′ _BA sequence, calling the safety check process. At this point, only n single-photon product states are left, forming the sequence S″ _BA .

The process of performing safety detection includes: setting the error threshold τ, taking Charlie and Alice _i as entities A and B respectively; obtaining the number of particles l in the sequence to be detected; entity B compares the measurement results sent by entity A based on the initial particle information, and calculates the error rate of the sequence based on the number of particles l in the sequence to be detected; if the error rate is higher than the set error threshold, the detection is terminated, otherwise the detection continues until all particles are detected. That is:

Step 3: Particle transport and measurement

(3.1) Charlie measures the particle in S″ _BA

After the third security check is completed, Alice _i (i＝1,2,...,n) randomly selects the Z _d or X _d basis for the particles in S″ _BA , and then sends the n single-photon product states in S″ _BA and the selected measurement basis to Charlie. Then, Charlie performs the corresponding measurement operation and feeds back the corresponding measurement results to Alice _i (i＝1,2,...,n). Finally, Alice _i (i＝1,2,...,n) restores the position of the measurement results to the position before the rearrangement, and the restored measurement result sequence is The length of the sequence is n.

A specific implementation method for measuring a sequence according to a measurement basis, the method comprises: d=4, the measurement basis The measurement operator is expressed as {M _m } = {M ₀ ,M ₁ ,M ₂ ,M ₃ }; before the measurement, the state of the quantum system is |2>, then the probability of the result m = 2 is:

Among them, p represents the probability, represents the conjugate transpose of the measurement operator _M2 , where _M2 represents the measurement operator ω represents Phase; The expression is:

The status after measurement is:

Step 4: Key guessing

(4.1) Alice _i (i＝1,2,...,n) performs key estimation

Each user Alice _i (i＝1,2,...,n) has n measurement result sequences. Bob will publish non-orthogonal qudit Where |q> is the qudit in Bob's hand, |q> is Non-orthogonal quantum states. Alice _i (i＝1,2,...,n) according to Bob's published and your own measurement result sequence As shown in Table 1, the table lists the specific key guessing rules of Alice _i in the dimension d=4.

Assume d = 4 dimensions, and assume that Bob's quantum state is |2>. At this time, Bob will send the quantum state to Alice _i , but Alice _i does not know the specific state of the quantum state, so she will ask Charlie to measure the quantum state. At this time, Alice _i will randomly choose Z ₄ or X ₄ for Charlie to measure. Assuming Alice _i chooses X ₄ measurement basis and gives it to Charlie for measurement, the result of Charlie's measurement may be At this time, Bob will announce qudit Where |2> is what Bob knows, Bob gets from Random Selection and |2> are not orthogonal. Alice _i uses her own measurement results and Bob's We can make a guess, since |2> can be measured through the X ₄ basis. but Through X ₄ basis measurement, we can only get It is impossible to conclude Therefore, Alice _i can know for sure that Bob's quantum state is |2>, which is eventually converted into the decimal key 2.

Table 1 Alice _i key guessing in d=4 dimensions

Step 5: Key post-processing and ciphertext sending

(5.1) Key post-processing

After Step 4, according to the key encoding rule, all users Alice _i (i＝1,2,...,n) share a set of asymmetric keys K ^r with Bob, where each key in K ^r is a decimal. K ^r is completely known to Bob, and each user Alice _i (i＝1,2,...,n) only knows part of the key. ^{K r} consists of k ₀ ,k ₁ ,...,k _n-1 , and k _i (i＝0,1,...,n-1) represents the i-th key of K ^r . First, Bob calculates for each k _i in i＝0,1,...,n-1, where the value of ι can control the number of keys obtained by the user, and then calculate Q′ _i ＝Q _i mod d, and finally generate the final key K ^f , K ^f is composed of Q′ ₀ ,Q′ ₁ ,...,Q′ _n-1 , and Bob obtains all the keys in K ^f . Alice _i (i＝1,2,...,n) performs the same operation as Bob. If the number of keys obtained by Alice _i (i＝1,2,...,n) is less than 1, the protocol restarts; otherwise, Alice _i (i＝1,2,...,n) will obtain a key in a different position. The subscripts i ₀ , i ₁ , ..., _in-1 represent positions, and 0＜＝i ₀ , i ₁ , ..., in _-1 <＝n-1.

Step 6: Encryption

(6.1) Generate ciphertext

Alice _i (i＝1,2,...,n) knows the key of the i ₀ th ,i _{1 th} ,...,i _n-1 th position in K ^f and tries to retrieve the j ₀ , j ₁ , ..., j _n-1 items Where 0＜＝j ₀ ,j ₁ ,...,j _n-1 ＜＝n-1. Alice _i (i＝1,2,...,n) calculates the shift numbers s ₀ ,s ₁ ,...s _n-1 , where s _λ ＝j _λ -i _λ (λ＝0,1,...,n-1) and sends s ₀ ,s ₁ ,...s _n-1 to Bob. Bob shifts the key K ^f by s ₀ ,s ₁ ,...s _n-1 to form n shifted keys. They are used to encrypt database D to form ciphertext databases ED ⁰ , ED ¹ ,..., ED ^n-1 , where

Step 7: Quantum Search

(7.1) Application of Grover's algorithm

Alice _i (i＝1,2,...,n) performs Grover search on the ciphertext database ED ⁱ (i＝0,1,...,n-1). If user Alice ₁ uses the classic algorithm to search for the ciphertext data with index j ₀ in the ED ⁰ database Where 0 <= j ₀ <= n-1, then the time complexity of the search is O(n), which leads to poor search efficiency. User Alice ₁ searches for ciphertext using the Grover quantum search algorithm This will greatly improve the search efficiency. The specific process of Alice ₁ using the Grover algorithm is as follows:

Step 1: Get the number of elements in the ciphertext database;

Step 2: Calculate the initial quantum state |υ>. The calculation formula for the initial quantum state is:

Among them, H represents the quantum gate, represents the tensor product of σ H gates, σ represents the number of bits, represents the tensor product symbol in quantum, |x> represents the quantum state x, and n represents the number of elements in the ciphertext database;

Step 3: Perform k G iterations on the initial quantum state |υ> to obtain the current database state; the calculation formula is:

Among them, G represents a unitary operator in Grover's algorithm, k represents the number of iterations, θ represents the angle, |j ₀ > represents the quantum state j ₀ , and j ₀ is the index subscript that the query user wants to find;

Step 4: Get the index subscript j ₀ of the query user according to the database status;

Step 5: Get the ciphertext to be queried by the querying user according to the index subscript.

After running operator G k times, the probability of detecting the quantum state to be tested is

Step 8: Decryption

(8.1) Decryption to obtain the required plaintext

Alice _i (i＝1,2,...,n) passes Key pair ciphertext Decrypt and obtain the corresponding plaintext

The above embodiments further illustrate the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above embodiments are only preferred implementation modes of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made to the present invention within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims (3)

1. A multi-user high-dimensional quantum privacy block query method, characterized by comprising: constructing a multi-user quantum privacy block query system, the system comprising query users {Alice ₁ , Alice ₂ , ..., Alice _n }, a database holder Bob and a semi-trusted quantum server Charlie, Alice _n represents the nth query user; A quantum key distribution method is used to distribute quantum keys to query users and database holders in the privacy block query system respectively; specifically, the method includes: S1: Initialize the system and construct the key encoding rules; the key encoding rules include: Bob and n query users Alice _i (i＝1,2,...,n) negotiate the corresponding key encoding rules, the encoding rules include: ...... Among them, |0> represents the quantum state 0, represents the quantum state obtained after performing quantum Fourier transform on quantum state 0, It represents the quantum state after performing quantum Fourier transform on quantum state d-1, where d represents the dimension; S2: The semi-trusted quantum server Charlie constructs a d-dimensional single-photon product state sequence S, the length of which is N=n+q+χ+δ, where n represents the database size, q represents the number of single-photon product states required for the interaction between Bob and Charlie, χ represents the number of single-photon product states required for the interaction between the query user and Charlie, and δ represents the number of single-photon product states required for the interaction between Bob and the query user; construct subsequences _S1 and _S2 based on the d-dimensional single-photon product state sequence S, where the length of subsequence _S1 is n+q+δ, and the length of subsequence _S2 is χ; select the i-th column in subsequence _S2 in turn, and use the selected i-th column as the subsequence Charlie sends subsequence S ₁ to the database owner Bob, Send to the corresponding query user; S3: Querying a Subsequence of User Records The initial position of the sequence and the measurement basis corresponding to the sequence are obtained, and the subsequence S ₂ i is rearranged to obtain a new sequence S _CA ; the query user sends the measurement basis and the sequence S _CA to Charlie; the measurement basis includes Z _d and X _d ; the expression of Z _d is: The expression of _Xd is: Among them, Z _d represents the measurement basis in d dimensions, d represents the dimension, |j> represents quantum state j, j is a decimal value, X _d represents the measurement basis after quantum Fourier transformation, represents the quantum state obtained by quantum Fourier transformation of quantum state j, and k is a decimal value; S4: Charlie performs measurement according to the measurement basis sequence S _CA and feeds back the measurement result to Alice _i ; the process of Charlie performing measurement according to the measurement basis sequence includes: Charlie obtains the state of the quantum system |q> and constructs the measurement operator {M _m } = {M ₀ ,M ₁ ,...,M _d-1 }; The probability that the measurement result is m=ν is calculated according to the measurement operator. The expression for probability calculation is: Among them, M _d-1 represents the measurement operator, where d represents the dimension, m and v are both decimal values, and p(v) represents the probability that the measurement result is m=v. represents the conjugate transpose of M _v , M _v represents the measurement operator, and <q| and |q> both represent the quantum state q; After measurement, the state of the quantum system is: in, represents the quantum state q after measurement; S5: Alice _i according to the subsequence The measurement results are restored from the initial position; Charlie and Alice _i perform the first safety check through the particles in the sequence S _CA ; The process of performing safety detection includes: setting the error threshold τ, taking Charlie and Alice _i as entities A and B respectively; obtaining the number of particles in the sequence to be tested for safety Entity B compares the measurement results sent by entity A based on the initial particle information, and calculates the number of particles in the sequence to be safely detected. Calculate the error rate of the sequence; if the error rate is higher than the set error threshold, the detection is terminated, otherwise the detection continues until all particles are detected; S6: Bob records the initial position of the subsequence S ₁ and the measurement basis corresponding to the sequence, and rearranges the subsequence S ₁ ; randomly selects particles from q sequences in the rearranged subsequence to form the safety detection sequence S _BC , and the other particles form the sequence S _BA ; S7: Bob sends S _BC and the measuring machine to Charlie. Charlie measures the particles in the sequence S _BC according to the measurement basis and feeds back the measurement results to Bob. S8: Bob recovers the measurement result according to the initial position of subsequence S ₁ ; Bob and Alice _i perform a second security check using particles in sequence S _BC ; S9: Bob extracts n particles from the sequence S _BA to form the sequence Get the measurement basis of the particles at δ positions in the sequence S _BA , and replace the measurement basis of the particles at δ positions with the sequence Sent to the query user; the query user has a query on the sequence Rearrange the qudit in to get the sequence And the sequence Convert to single-photon product state S′ _BA sequence; the query user sends δ particles and measurement basis in S′ _BA to Charlie; where qudit represents a high-dimensional quantum state; S10: Charlie measures the particles in S′ _BA according to the measurement basis and returns the measurement results to the querying user; the querying user and Bob perform a third safety check on the δ particles in S′ _BA ; S11: Sort the remaining n particles in S _BA to form a sequence S″ _BA ; Charlie measures the particles in S″ _BA and feeds the measurement results back to Alice _i ; Alice _i restores the position of the measurement results to obtain the restored sequence in, Indicates the measurement result, which is a decimal value; S12: Bob converts the non-orthogonal qudit pair Published to the system, where |q> is the qudit in Bob's hand, |q> and are all non-orthogonal quantum states, represents the quantum state symbol after quantum Fourier transformation, |> represents the Dirac symbol in quantum; S13: Alice _i uses the non-orthogonal qudit pair published by Bob to The key encoding rule is used to perform key inference with the recovery sequence S _M. The key inference process includes: obtaining Bob's quantum state |q> and sending the quantum state to Alice _i ; Alice _i randomly selects a measurement basis and sends the measurement basis and the received quantum state to Charlie; Charlie measures the quantum state according to the measurement basis and obtains the measurement result And return the measurement results to Ali _i e; Randomly select one Will and |q> form a cloth qudit pair Bob publishes qudit in represents the quantum state of the quantum Fourier transform of |κ> Alice _i uses the selected measurement basis to measure |q> and We measure and obtain |q> and The measurement result of Bob is used to determine the quantum state |q＞ of Bob. The encoding conversion rule is used to convert |q＞ into decimal to obtain q, which is the key obtained by Alice _i . S14: distributing the inferred key; The database holder and query user use the assigned quantum key to encrypt the data in the database to obtain a ciphertext database; The query user uses the Grover quantum search algorithm to search the ciphertext database to obtain the ciphertext; specifically, it includes: Step 1: Get the number of elements in the ciphertext database; Step 2: Calculate the initial quantum state |υ>. The calculation formula for the initial quantum state is: Among them, H represents the quantum gate, represents the tensor product of σ H gates, σ represents the number of bits, represents the tensor product symbol in quantum, |x> represents the quantum state x, and n represents the number of elements in the ciphertext database; Step 3: Perform k G iterations on the initial quantum state |υ> to obtain the current database state; the calculation formula is: Among them, G represents a unitary operator in Grover's algorithm, k represents the number of iterations, θ represents the angle, |j ₀ > represents the quantum state j ₀ , and j ₀ is the index subscript that the query user wants to find; Step 4: Get the index subscript j ₀ of the query user according to the database status; Step 5: Get the ciphertext to be queried by the querying user according to the index subscript; The querying user decrypts the ciphertext according to the quantum key to obtain the plaintext. 2. A multi-user high-dimensional quantum privacy block query method according to claim 1, characterized in that the process of distributing the inferred key includes: the query user and Bob share a set of asymmetric keys K ^r = {k ₀ , k ₁ , ..., k _n-1 }, where k _i represents the i-th key in K ^r ; Bob knows all the asymmetric keys in the asymmetric keys, and the query user knows his corresponding key; Bob calculates for each k _i in, Where _Qi is a decimal value and ι is a decimal value; calculate _Q′i = _Qi modd according to _Qi , where mod is the remainder symbol; collect all _Q′i to obtain Bob’s final key ^Kf = { _Q′0 , _Q′1 , ..., Q′n _-1 }; the query user performs the same operation as Bob to determine the number of keys in the query user. If the number of keys is less than 1, recalculate the key in the query user, otherwise the query user obtains the key in a different position. 0≤i ₀ ,i ₁ ,...,i _n-1 ≤n-1, where the subscripts i ₀ ,i ₁ ,...,i _n-1 represent positions. 3. A multi-user high-dimensional quantum privacy block query method according to claim 1, characterized in that the process of using quantum keys to encrypt data in a database comprises: Alice _i obtains the key at the i ₀ th , i _{1 th} , ..., i _n-1 th position in K ^f and retrieve the j ₀ ,j ₁ ,...,j _n-1 items Where 0＜＝j ₀ ,j ₁ ,...,j _n-1 ＜＝n-1; Alice _i calculates the shift numbers s ₀ ,s ₁ ,...s _n-1 respectively, where s _λ ＝j _λ -i _λ , where λ is a decimal value in the range of {0,1,...,n-1}; sends the calculated shift numbers s ₀ ,s ₁ ,...s _n-1 to Bob, who shifts the key K ^f through s ₀ ,s ₁ ,..s. _n-1 respectively to form n Use n Encrypt the data in the database respectively to form a ciphertext database ED ⁰ , ED ¹ ,..., ED ^n-1 , where Represents the n-1th ciphertext in the i-th ciphertext database.