CN114640449A - A multi-user high-dimensional quantum privacy block query method - Google Patents

Abstract

The invention belongs to the fields of quantum computing and quantum information, and in particular relates to a multi-user high-dimensional quantum privacy block query method. The method includes: constructing a multi-user quantum privacy block query system, the system including query users, database holders and semi-private blocks. Trusted quantum server; using quantum key distribution method to distribute quantum keys to query users and database holders in the privacy block query system respectively; Encryption to obtain the ciphertext database; the query user uses the Grover quantum search algorithm to search the ciphertext database to obtain the ciphertext; the query user decrypts the ciphertext according to the quantum key to obtain the plaintext; the invention improves the performance by applying the Grover quantum search algorithm. The speed at which the user queries the desired ciphertext.

Description

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

technical field

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

Background technique

The purpose of private information retrieval is to protect the user's personal privacy. When the user accesses the database, the database does not know which data item Alice is interested in. Similarly for databases, databases do not want users to obtain more private information. For classical Symmetrical Private Information Retrieval (SPIR), this protocol can not only protect user privacy, but also ensure that Alice cannot access any other information except the data item she is interested in.

Extending the classical symmetric private information retrieval protocol (SPIR) to the quantum world, Giovannetti et al. propose the first quantum privacy query protocol (GLM) based on unitary operations. In this protocol, data information is encoded into the retrieval state using unitary operations. Users access the database using two quantum states, one quantum state is used for information query, and the other quantum state is used to query the database for fraudulent behavior, 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 user Alice.

Jakobi et al. proposed a practical QPQ protocol using the SARG04 quantum key distribution protocol. There are three main steps in this protocol: 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, aiming at Reduce the information that Alice knows about the key to 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 practicability and efficiency.

SUMMARY OF THE INVENTION

In order to solve the above problems in the prior art, the present invention proposes a multi-user high-dimensional quantum privacy block query method, the method includes: constructing a multi-user quantum privacy block query system, the system includes query users {Alice ₁ , Alice ₂ ,...,Alice _n }, the database holder Bob, and the semi-trusted quantum server Charlie, Alice _n represents the nth query user; the quantum key distribution method is used to query the query user and database in the privacy block query system respectively The holder distributes the quantum key; the database holder and the query user use the distributed quantum key to encrypt the data in the database to obtain the ciphertext database; the query user uses the Grover quantum search algorithm to search the ciphertext database to obtain the encrypted data. The query user decrypts the ciphertext according to the quantum key to obtain the plaintext.

Preferably, 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;

Charlie将子序列S₁发送给数据库持有者Bob，将子序列

发送给对应的查询用户；S2: The semi-trusted quantum server Charlie builds a d-dimensional single-photon product state sequence S, the length of which is N=n+q+χ+δ, where n represents the size of the database, and q represents the single photon required for the interaction between Bob and Charlie. The number of photon product states, 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; according to the d-dimensional single-photon product state _The state sequence S constructs _a subsequence S1 and _a subsequence S2, wherein the length of the subsequence S1 is n+q ₊ δ, and the length of the subsequence S2 is χ _; Select the i-th column as the subsequence

Charlie sends the subsequence S ₁ to the database holder Bob, the subsequence

Send to the corresponding query user;

的初始位置和该序列对应的测量基，并对子序列

进行重新排列，得到新序列S_CA；查询用户将测量基和序列S_CA发送给Charlie；S3: Query user record subsequence

The initial position of the sequence and the corresponding measurement base of the sequence, and the subsequence

Perform rearrangement to obtain a new sequence S _CA ; the query user sends the measurement base and sequence S _CA to Charlie;

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

的初始位置对测量结果进行恢复；Charlie和Alice_i通过序列S_CA中的粒子执行第一次安全检测；S5: Alice _i according to the subsequence

recover the measurement results from the initial position of ; Charlie and Alice _i perform the first safety detection through the particles in the sequence S _CA ;

S6: Bob records the initial position _of the subsequence S1 and the measurement base corresponding to the sequence, and rearranges the subsequence S1 _; randomly selects particles in the q sequences from the rearranged subsequence to form the safety detection sequence S _BC , and 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 base, and feeds back the measurement results to Bob;

S8: Bob recovers the measurement result according to the initial position _of the subsequence S1; Bob and Alice _i perform the second safety check through the particles in the sequence _SBC ;

获取序列S_BA中δ个位置上粒子的测量基，将δ个位置上粒子的测量基和序列

发送给查询用户；查询用户对序列

中的qudit进行重排，得到序列

并将序列

转换为单光子乘积态S′_BA序列；查询用户将S′_BA中δ个粒子和测量基发送给Charlie；其中，qudit表示高维量子态；S9: Bob extracts n particles from the sequence S _BA to form the sequence

Obtain the measurement basis of the particles in the δ positions in the sequence S _BA , and combine the measurement basis of the particles in the δ positions with the sequence

Sent to the querying user; the querying user pairs the sequence

qudit in the rearrangement to get the sequence

and sequence

Convert to single-photon product state S′ _BA sequence; the query user sends the δ particles and measurement basis in S′ _BA to Charlie; where qudit represents high-dimensional quantum state;

S10: Charlie measures the particles in S' _BA according to the measurement base, and returns the measurement results to the querying user; the querying user and Bob perform the third safety inspection on the δ particles in S'_BA;

其中，

表示测量结果，该结果为十进制数值；S11: Sort the remaining n particles in S _BA to form a sequence S"_BA; Charlie measures the particles in S" _BA and feeds back the measurement result to Alice _i ; Alice _i restores the position of the measurement result, get recovery sequence

in,

Indicates the measurement result, which is a decimal value;

公布到系统中，其中|q>为Bob手中的qudit，|q>与

均为非正交的量子态，

表示经过量子傅里叶变换的量子态符号，| >表示量子中的Dirac符号；S12: Bob puts non-orthogonal qudit pairs

Publish to the system, where |q> is the qudit in Bob's hand, and |q> is the same as the

are non-orthogonal quantum states,

represents the quantum state symbol after quantum Fourier transform, | > represents the Dirac symbol in quantum;

和恢复序列S_M采用密钥编码规则进行密钥推测；S13: Alice _i according to the non-orthogonal qudit pair announced by Bob

and recovery sequence S _M using key encoding rules for key guessing;

S14: Distribute the deduced key.

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

表示对量子态0执行量子傅里叶变换后得到的量子态，其中量子傅里叶变换是指量子领域中对量子态的操作，

表示的是对量子态d-1执行量子傅里叶变换后的量子态，d表示维数。where |0> represents quantum state 0,

Represents the quantum state obtained by performing the quantum Fourier transform on quantum state 0, where the quantum Fourier transform refers to the operation of the quantum state in the quantum field,

represents the quantum state after performing the quantum Fourier transform on the quantum state d-1, where d represents the dimension.

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

The expression for _Xd is:

表示量子态j经过量子傅里叶变化得到的量子态，k为十进制数值。Among them, Z _d represents the measurement basis in the d dimension, d represents the dimension, |j> represents the quantum state j, j represents the decimal value, X _d represents the measurement basis after the quantum Fourier transform,

Represents the quantum state obtained by quantum Fourier transformation of quantum state j, and k is a decimal value.

Preferably, the process that Charlie measures the sequence according to the measurement base includes:

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

Calculate the probability that the measurement result is m=ν according to the measurement operator, and the expression for the probability calculation is:

d表示维数；m为十进制数值，v为十进制数值，p(v)表示测量结果为m＝ν的概率，

表示M_v的共轭转置，M_v表示测量算子，<q|表示量子态q，|q>表示量子态q；Among them, M _d-1 represents the measurement operator, where

d is the dimension; m is a decimal value, v is a decimal value, p(v) is the probability that the measurement result is m=ν,

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:

表示测量后的量子态

in,

Represents the quantum state after measurement

Preferably, the process of performing the security detection includes: setting an error threshold τ, and taking Charlie and Alice _i as entities A and B respectively; acquiring the number l of particles in the sequence to be security detection; entity B sending a measurement to entity A according to the initial particle information The results are compared, and the error rate of the sequence is calculated according to 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 particles are detected.

并将测量结果返回给Alice_i；从

中随机选择一个

将

和|q>组成布qudit对

Bob公布qudit对

其中

表示对|κ>执行量子傅里叶变换的量子态

Alice_i采用选取的测量基分别对|q>和

进行测量，分别得到|q>和

的测量结果，根据测量结果确定Bob的量子态|q>，采用编码转换规则将|q>转化为十进制，得到q，该q为Alice_i得到的密钥。Preferably, the process of performing key guessing includes: acquiring Bob's quantum state |q>, and sending the quantum state to Alice _i ; Alice _i randomly selects a measurement basis, and sends the quantum state received by the measurement basis to Charlie; Charlie Measure the quantum state according to the measurement basis to obtain the measurement result

and return the measurement result to Alice _i ; from

randomly choose one

Will

and |q> form a cloth qudit pair

Bob announces qudit pair

in

represents a quantum state that performs a quantum Fourier transform on |κ>

Alice _i uses the selected measurement basis to measure |q> and

Take measurements to get |q> and

According to the measurement result, Bob's quantum state |q> is determined, and |q> is converted into decimal using the coding conversion rule to obtain q, which is the key obtained by Alice _i .

其中，

其中Q_i为十进制数值，ι为十进制数值；根据Q_i计算Q_i′＝Q_imodd，其中，mod为求余符号；将所有的Q′_i进行集合，得到Bob的最终密钥K^f＝{Q′₀,Q′₁,...,Q′_n-1}；查询用户执行和Bob相同的操作，判断查询用户中的密钥数，若密钥数小于1，则重新计算查询用户中的密钥，否则查询用户得到不同位置的密钥

0≤i₀,i₁,...,i_n-1≤n-1，其中下标i₀,i₁,...,i_n-1表示位置。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 ; in the asymmetric key, Bob knows all asymmetric keys, and the query user knows his corresponding key; Bob calculates for each k _i

in,

Wherein Q _i is a decimal value, ι is a decimal value; according to the calculation of Q _i '=Q _{i modd} , where mod is the remainder symbol; all Q' _i are collected to obtain Bob's final key K ^f = {Q′ ₀ ,Q′ ₁ ,...,Q′ _n-1 }; the query user performs the same operation as Bob, and determines the number of keys in the query user. If the number of keys is less than 1, recalculate the query user key in, otherwise query the user to get the key in a different location

0≤i ₀ ,i ₁ ,...,in _-1 ≤n-1, where the subscripts i ₀ ,i ₁ ,...,in _-1 denote positions.

并检索第j₀,j₁,...,j_n-1个项目

其中0<＝j₀,j₁,...,j_n-1<＝n-1；Alice_i分别计算移位数s₀,s₁,...s_n-1，其中s_λ＝j_λ-i_λ，其中λ为十进制数值，范围在{0,1,...,n-1}；把计算出的位移数s₀,s₁,...s_n-1发送给Bob，Bob通过s₀,s₁,...s_n-1分别对密钥K^f进行移位，形成n个

采用n个

分别对数据库中的数据进行加密，形成密文数据库ED⁰,ED¹,...,ED^n-1，其中

表示第i个密文数据库中的第n-1个密文。Preferably, the process of encrypting the data in the database by using the quantum key includes: Alice _i obtains the key at the i ₀ , i ₁ ,..., i _n- 1th 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}; send the calculated displacement numbers s ₀ , s ₁ ,...s _n-1 to Bob, Bob 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 ith ciphertext database.

Preferably, the process that the query user uses the Grover quantum search algorithm to search for ciphertext includes:

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

Step 2: Calculate the initial quantum state |υ>, the calculation formula of the initial quantum state is:

表示σ个H门进行张量积，σ表示比特数，

表示量子中的张量积符号，|x>表示量子态x，n表示密文数据库中的元素个数；Among them, H represents the quantum gate,

represents σ H gates for tensor product, 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 times of G iterations on the initial quantum state |υ> to obtain the current state of the database; the calculation formula is:

Among them, G represents a unitary operator in Grover 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 is looking for;

Step 4: obtain the index subscript j ₀ of the query user according to the state of the database;

Step 5: Obtain the ciphertext to be queried by the query user according to the index subscript.

Beneficial effects of the present invention:

1) The present invention only requires the user side and the database side to have near-classical quantum capabilities (quantum rearrangement, access to quantum channels), and the third-party quantum server Charlie provides full quantum capabilities. The quantum cost of the user side and the database side is greatly reduced through semi-quantum technology;

大大提高整个方法的效率；2) The present invention improves the speed at which the user queries the desired ciphertext by applying the Grover quantum search algorithm, and the query time complexity is:

Greatly improve the efficiency of the whole method;

3) The present invention can support multiple users to access a whole piece of information in different positions of the database, so that the method has better practicability and efficiency.

Description of drawings

1 is a flowchart 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 ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

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

其中，

表示向上取整；{Alice₁,Alice₂,...,Alice_n}和Bob只具备接入量子信道和重排量子态的能力。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 }, the holder of the database D, Bob, and a semi-trusted quantum server. Charlie. There are n plaintexts {D ₀ , D ₁ ,...,D _n-1 } stored in the database D, where D _i (i=0,1,...,n-1) is a binary bit string, D _i The bit string length l of (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 quantum channels and rearrange quantum states.

Charlie has full quantum capability and can be used for quantum preparation and quantum measurement. The quantum states prepared by Charlie are d-dimensional single-photon state sets M ₁ and M ₂ ; its expression is:

表示量子态j经过量子傅里叶变化得到的量子态，k为十进制数值Among them, d represents the dimension, |j> represents the quantum state j, and j represents the decimal value,

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 base used by Charlie to perform the measurement operation is:

Among them, Z _d represents the measurement basis in the d dimension, and X _d represents the measurement basis after the 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;

Charlie将子序列S₁发送给数据库持有者Bob，将子序列

发送给对应的查询用户；S2: The semi-trusted quantum server Charlie builds a d-dimensional single-photon product state sequence S, the length of which is N=n+q+χ+δ, where n represents the size of the database, and q represents the single photon required for the interaction between Bob and Charlie. The number of photon product states, 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; according to the d-dimensional single-photon product state _The state sequence S constructs _a subsequence S1 and _a subsequence S2, wherein the length of the subsequence S1 is n+q ₊ δ, and the length of the subsequence S2 is χ _; Select the i-th column as the subsequence

Charlie sends the subsequence S ₁ to the database holder Bob, the subsequence

Send to the corresponding query user;

的初始位置和该序列对应的测量基，并对子序列

进行重新排列，得到新序列S_CA；查询用户将测量基和序列S_CA发送给Charlie；S3: Query user record subsequence

The initial position of the sequence and the corresponding measurement base of the sequence, and the subsequence

Perform rearrangement to obtain a new sequence S _CA ; the query user sends the measurement base and sequence S _CA to Charlie;

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

的初始位置对测量结果进行恢复；Charlie和Alice_i通过序列S_CA中的粒子执行第一次安全检测；S5: Alice _i according to the subsequence

recover the measurement results from the initial position of ; Charlie and Alice _i perform the first safety detection through the particles in the sequence S _CA ;

S6: Bob records the initial position _of the subsequence S1 and the measurement base corresponding to the sequence, and rearranges the subsequence S1 _; randomly selects particles in the q sequences from the rearranged subsequence to form the safety detection sequence S _BC , and 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 base, and feeds back the measurement results to Bob;

S8: Bob recovers the measurement result according to the initial position _of the subsequence S1; Bob and Alice _i perform the second safety check through the particles in the sequence _SBC ;

获取序列S_BA中δ个位置上粒子的测量基，将δ个位置上粒子的测量基和序列

发送给查询用户；查询用户对序列

中的qudit进行重排，得到序列

并将序列

转换为单光子乘积态S′_BA序列；查询用户将S′_BA中δ个粒子和测量基发送给Charlie；其中，qudit表示高维量子态；S9: Bob extracts n particles from the sequence S _BA to form the sequence

Obtain the measurement basis of the particles in the δ positions in the sequence S _BA , and combine the measurement basis of the particles in the δ positions with the sequence

Sent to the querying user; the querying user pairs the sequence

qudit in the rearrangement to get the sequence

and sequence

Convert to single-photon product state S′ _BA sequence; the query user sends the δ particles and measurement basis in S′ _BA to Charlie; where qudit represents high-dimensional quantum state;

S10: Charlie measures the particles in S' _BA according to the measurement base, and returns the measurement results to the querying user; the querying user and Bob perform the third safety inspection on the δ particles in S'_BA;

其中，

表示测量结果，该结果为十进制数值；S11: Sort the remaining n particles in S _BA to form a sequence S"_BA; Charlie measures the particles in S" _BA and feeds back the measurement result to Alice _i ; Alice _i restores the position of the measurement result, get recovery sequence

in,

Indicates the measurement result, which is a decimal value;

公布到系统中，其中|q>为Bob手中的qudit，|q>与

均为非正交的量子态，

表示经过量子傅里叶变换的量子态符号，|>表示量子中的Dirac符号；S12: Bob puts non-orthogonal qudit pairs

Publish to the system, where |q> is the qudit in Bob's hand, and |q> is the same as the

are non-orthogonal quantum states,

Represents the quantum state symbol after quantum Fourier transform, |> represents the Dirac symbol in quantum;

和恢复序列S_M采用密钥编码规则进行密钥推测；S13: Alice _i according to the non-orthogonal qudit pair announced by Bob

and recovery sequence S _M using key encoding rules for key guessing;

S14: Distribute the deduced key.

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

Step1: System initialization

(1.1) Negotiate 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 n query users Alice _i (i=1,2,...,n) negotiate the corresponding key encoding rules at the beginning:

表示对量子态0执行量子傅里叶变换后得到的量子态，其中量子傅里叶变换是指量子领域中对量子态的操作；

表示的是对量子态d-1执行量子傅里叶变换后的量子态，d表示维数。where |0> represents quantum state 0,

Represents the quantum state obtained by performing the quantum Fourier transform on the quantum state 0, where the quantum Fourier transform refers to the operation of the quantum state in the quantum field;

represents the quantum state after performing the quantum Fourier transform on the quantum state d-1, where d represents the dimension.

(1.2) Sending sequences S ₁ and S ₂

中随机选择；。其中，n表示数据库的大小；χ表示在第一次安全检测中{Alice₁,Alice₂,...,Alice_n}与Charlie之间交互所需要的单光子乘积态的数量；q表示在第二次安全检测中Bob与Charlie之间交互所需要的单光子乘积态的数量；δ表示在第三次安全检测中Bob与{Alice₁,Alice₂,...,Alice_n}之间交互所需要的单光子乘积态的数量。Charlie prepares a d-dimensional single-photon product state sequence S with length N=n+q+χ+δ, where n+q+δ single-photon product states are prepared according to Bob's requirements, and χ single-photon product states are prepared according to {Alice ₁ ,Alice ₂ ,...,Alice _n } requires preparation, the single-photon product state is

Randomly selected from; . Among them, 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 security check; q represents the The number of single-photon product states required for the interaction between Bob and Charlie in the second security detection; δ represents the interaction between Bob and {Alice ₁ ,Alice ₂ ,...,Alice _n } in the third security detection The number of single-photon product states required.

Charlie将序列S₁发送给Bob，将子序列

分别发送给Alice_i(i＝1,2,...,n)。As shown in Fig. 2.a, n+q+δ single-photon product states in the sequence S form a sequence S ₁ ; as shown in Fig. 2.b, χ single-photon product states form a sequence S ₂ , starting from S ₂ Select the i-th (i=1,2,...,n) column in turn to generate a subsequence

Charlie sends sequence S ₁ to Bob, subsequence

Send to Alice _i (i=1,2,...,n) respectively.

Step2: Particle rearrangement and sending

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

Alice_i(i＝1,2,...,n)首先记录其对应的初始位置并选择对应的测量基，然后各个Alice_i(i＝1,2,...,n)共同选择一个随机数重排粒子

中的qudit，形成序列S_CA。并将S_CA和测量基发送给Charlie，Charlie根据Alice_i(i＝1,2,...,n)告知的测量基对S_CA中的粒子进行测量，并将测量结果反馈给Alice_i(i＝1,2,...,n)，Alice_i(i＝1,2,...,n)将测量结果恢复至重排前位置。Charlie和Alice_i(i＝1,2,...,n)通过序列S_CA中的粒子执行第一次安全检测，调用安全检测过程。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 base, and then each Alice _i (i=1,2,...,n) jointly selects a random Number of rearranged particles

qudit in , forming the sequence S _CA . Send S _CA and measurement base to Charlie, Charlie measures the particles in S _CA according to the measurement base informed by Alice _i (i=1,2,...,n), and feeds back the measurement result to Alice _i ( i=1,2,...,n), Alice _i (i=1,2,...,n) restores the measurement result to the position before rearrangement. Charlie and Alice _i (i=1,2,...,n) perform the first security detection through the particles in the sequence S _CA , calling the security detection process.

For each single-photon product state in the sequence S ₁ that successfully reaches Bob, Bob also records its corresponding initial position and selects the corresponding measurement basis, and then performs quantum reassembly on the received n+q+δ single-photon product states. Row. Secondly, Bob randomly selects q ones from the n+q+δ single-photon product states to form the safety detection sequence S _BC , and sends the S _BC and the measurement base to Charlie, and Charlie pairs the particles in S _BC according to the measurement base informed by Bob Take measurements and feed back the measurements to Bob. Bob restores the measurement to the pre-rearrangement position. At this time, Charlie and Bob perform the second security detection through the particles in the sequence S _BC , and call the security detection process.

序列依次发给Alice_i(i＝1,2,...,n)。每一个用户Alice_i(i＝1,2,...,n)接收到Bob发送过来的

(i＝1,2,...,n)和δ个位置上的测量基，每一个用户Alice_i(i＝1,2,...,n)共同选择一个随机数ζ重排序列

中qudit。各个用户将重排后的序列

形成单光子乘积态S′_BA序列。Alice_i(i＝1,2,...,n)先将S′_BA中δ个位置上的单光子乘积态和测量基发送给Charlie，之后Charlie根据测量基对接收的粒子进行测量，返回测量结果给Alice_i(i＝1,2,...,n)并恢复到原来的位置上。Alice_i(i＝1,2,...,n)和Bob通过S′_BA序列中δ个单光子乘积态执行第三次安全检测，调用安全检测过程。至此只剩下n个单光子乘积态，形成序列S″_BA。Bob composes the remaining n+δ single-photon product states into a sequence S _BA , and forms subsequences between the measurement basis corresponding to the single-photon product states at the δ positions and the 1st, 2nd,...,n columns of S _BA sequence

The sequence is sent to Alice _i (i=1,2,...,n) in turn. Each user Alice _i (i=1,2,...,n) receives the message 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 rearrangement sequence

in qudit. Each user will rearrange the sequence

A sequence of single-photon product states _S'BA 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, and then Charlie measures the received particles according to the measurement basis, and returns The measurement result is given to Alice _i (i=1,2,...,n) and restored to the original position. _{Alice i} (i=1, 2, . So far, only n single-photon product states remain, forming the sequence S″ _BA .

The process of performing security detection includes: setting the 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 security detection; entity B compares the measurement results sent by entity A according to the initial particle information , and calculate the error rate of the sequence according to 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 particles are detected. which is:

Step3: Particle transmission and measurement

(3.1) Charlie's measurement of particles in S″ _BA

序列的长度为n。When the third security check is completed, Alice _i (i=1,2,...,n) randomly selects Z _d or X _d basis for the particles in S″ _BA , and then selects n single particles in S″ _BA The photon product state and the chosen measurement basis are sent to Charlie. Then, Charlie performs corresponding measurement operations 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 result to the position before the rearrangement, and the restored measurement result sequence is

The length of the sequence is n.

测量算子表示为{M_m}＝{M₀,M₁,M₂,M₃}；在测量前量子系统的状态为|2>，则结果m＝2发生的可能性为：A specific implementation manner of measuring the sequence according to the measurement base, the method includes: d=4, the measurement base

The measurement operator is expressed as {M _m }={M ₀ , M ₁ , M ₂ , M ₃ }; the state of the quantum system before the measurement is |2>, then the possibility that the result m=2 occurs is:

表示测量算子M₂的共轭转置，M₂表示测量算子

ω表示

相位；则

的表达式为：where p is the probability,

represents the conjugate transpose of the measurement operator M ₂ , where M ₂ represents the measurement operator

ω means

phase; then

The expression is:

The state after measurement is:

Step4: Key guess

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

其中|q>是Bob手中的qudit，|q>是与

非正交的量子态。Alice_i(i＝1,2,...,n)根据Bob公布的

和自己的测量结果序列

进行密钥推测。如表1所示，表中列举了d＝4维下Alice_i具体的密钥推测规则。Each user Alice _i (i=1,2,...,n) has n measurement result sequences. Bob will publish a non-orthogonal qudit

where |q> is the qudit in Bob's hand, and |q> is the

non-orthogonal quantum states. Alice _i (i=1,2,...,n) according to Bob's published

and its own sequence of measurements

Perform key guessing. As shown in Table 1, the table lists the specific key guessing rules of Alice _i under d=4 dimension.

此时Bob会公布qudit对

其中|2>是Bob所知道的，Bob从

随机选择

和|2>非正交。Alice_i根据自己的测量结果

和Bob公布的

进行猜测，由于|2>通过X₄基进行测量可能得到

但是

通过X₄基测量只能得出

不可能得出

所以Alice_i能肯定知道Bob的量子态为|2>，|2>最终转换成十进制密钥2。Suppose d=4 dimensions, in which it is assumed that Bob's quantum state is |2>, then Bob will send the quantum state to Alice _i , but Alice _i does not know what the specific state of the quantum state is, so he will ask Charlie for the quantum state. Take measurements. At this time, Alice _i will randomly select Z ₄ or X ₄ for Charlie to measure. Assuming that Alice _i chooses X ₄ measurement base and hands it over to Charlie for measurement, the result of Charlie's measurement may be

At this point Bob will announce the qudit pair

where |2> is what Bob knows, and Bob learns from

random selection

and |2> non-orthogonal. Alice _i based on her own measurements

and Bob announced

Take a guess, since |2> measuring through the _X4 base might give

but

Measured by the base of X ₄ only

impossible to draw

So Alice _i can definitely know that Bob's quantum state is |2>, and |2> is finally converted into the decimal key 2.

Table 1 Alice _i key guess in d=4 dimension

Step5: Key post-processing and ciphertext sending

(5.1) Key post-processing

其中

i＝0,1,...,n-1，这里的ι取值可以控制用户所获取的密钥数，然后计算Q′_i＝Q_imod d，最后生成最终密钥K^f，K^f由Q′₀,Q′₁,...,Q′_n-1组成，Bob获取K^f中全部密钥。Alice_i(i＝1,2,...,n)分别执行和Bob相同的操作，如果Alice_i(i＝1,2,...,n)中获取密钥数小于1，那么协议重新开始；否则，Alice_i(i＝1,2,...,n)将分别获得一个不尽相同位置的密钥

其中下标i₀,i₁,...,i_n-1表示位置，0＜＝i₀,i₁,...,i_n-1<＝n-1。After Step4, according to the key coding rules, 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 In 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 ith key of K ^r . First, Bob calculates for each k _i

in

i=0,1,...,n-1, the value of ι here can control the number of keys obtained by the user, then calculate Q' _i =Q _i mod d, and finally generate the final keys K ^f , K ^f Composed of Q′ ₀ , Q′ ₁ ,...,Q′ _n-1 , Bob obtains all the keys in K ^f . Alice _i (i=1,2,...,n) performs the same operations as Bob respectively. If the number of keys obtained in Alice _i (i=1,2,...,n) is less than 1, then the protocol is re-run. Start; otherwise, Alice _i (i=1,2,...,n) will obtain a key in a different position respectively

The subscripts i ₀ , i ₁ ,...,in _-1 represent positions, and 0<=i ₀ ,i ₁ ,...,in _-1 <=n-1.

Step6: Encrypt

(6.1) Generate ciphertext

并试图检索第j₀,j₁,...,j_n-1个项目

其中0＜＝j₀,j₁,...,j_n-1＜＝n-1。Alice_i(i＝1,2,...,n)分别计算移位数s₀,s₁,...s_n-1，其中s_λ＝j_λ-i_λ(λ＝0,1,...,n-1)，把s₀,s₁,...s_n-1发送给Bob，Bob通过s₀,s₁,...s_n-1分别对密钥K^f进行移位，移位后的形成n个

分别用于加密数据库D，形成密文数据库ED⁰,ED¹,...,ED^n-1，其中

Alice _i (i=1,2,...,n) knows the key at the i ₀ ,i ₁ ,...,in _- 1th position in K ^f

and trying 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 respectively, where s _λ =j _λ -i _λ (λ=0,1, ...,n-1), send s ₀ ,s ₁ ,...s _n-1 to Bob, and Bob shifts the key K ^f through s ₀ ,s ₁ ,...s _n-1 respectively Bits, the shifted ones form n

They are respectively used to encrypt database D to form ciphertext databases ED ⁰ , ED ¹ ,..., ED ^n-1 , where

Step7: Quantum Search

(7.1) Application of Grover Algorithm

如果用户Alice₁采用经典算法搜索ED⁰数据库中下标第j₀个密文数据

其中0<＝j₀<＝n-1，那么搜索的时间复杂度为O(n)，这导致搜索效率很差。用户Alice₁通过Grover量子搜索算法搜索密文

将大大提高搜索效率。Alice₁采用Grover算法的具体过程如下：Alice _i (i=1,2,...,n) performs Grover search on the ciphertext database ED ⁱ (i=0,1,...,n-1) respectively, and the ciphertext database ED i (i=0,1,...,n-1)

If user Alice ₁ uses the classical algorithm to search the subscript j _0th ciphertext data 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 through Grover quantum search algorithm

It will greatly improve the search efficiency. The specific process of Alice ₁ using Grover's algorithm is as follows:

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

Step 2: Calculate the initial quantum state |υ>, the calculation formula of the initial quantum state is:

表示σ个H门进行张量积，σ表示比特数，

表示量子中的张量积符号，|x>表示量子态x，n表示密文数据库中的元素个数；Among them, H represents the quantum gate,

represents σ H gates for tensor product, 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 times of G iterations on the initial quantum state |υ> to obtain the current state of the database; the calculation formula is:

Among them, G represents a unitary operator in Grover 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 is looking for;

Step 4: obtain the index subscript j ₀ of the query user according to the state of the database;

Step 5: Obtain the ciphertext to be queried by the query user according to the index subscript.

After running the operator G for k times, the possibility of detecting the quantum state to be measured is:

Step8: Decryption

(8.1) Decrypt to obtain the desired plaintext

密钥对密文

进行解密，获得对应的明文

Alice _i (i=1,2,...,n) passes

key pair ciphertext

Decrypt to get the corresponding plaintext

The above-mentioned embodiments further describe the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above-mentioned embodiments are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modification, equivalent replacement, improvement, etc. made to the present invention within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (10)

1. A multi-user high-dimensional quantum privacy block query method is characterized by comprising the following steps: constructing a multi-user quantum privacy block inquiry system, wherein the system comprises inquiry users { Alice₁,Alice₂,...,Alice_n}, database holders Bob and semi-trusted quantum servers Charlie, Alice_nRepresenting the nth querying user; quantum key distribution method is adopted to distribute quantum key to inquiry user and database holder in the privacy block inquiry system; the database holder and the inquiry user encrypt data in the database by adopting the distributed quantum key to obtain a ciphertext database; searching the ciphertext database by the inquiry user by adopting a Grover quantum search algorithm to obtain a ciphertext; the inquiry user decrypts the ciphertext according to the quantum key to obtain the plaintextText.

2. The multi-user high-dimensional quantum privacy block query method according to claim 1, wherein the process of distributing quantum keys to query users and database holders by using a quantum key distribution method comprises:

s1: initializing a system and constructing a key coding rule;

s2: the semi-credible quantum server Charlie constructs a d-dimensional single-photon product state sequence S, wherein the length of the sequence is N + N + q + chi + delta, N represents the size of a database, q represents the number of single-photon product states required by interaction between Bob and Charlie, chi represents the number of single-photon product states required by interaction between a query user and Charlie, and delta represents the number of single-photon product states required by interaction between Bob and the query user; constructing a subsequence S from a d-dimensional single-photon product state sequence S₁And subsequence S₂In which the subsequence S₁Of length n + q + delta, subsequence S₂The length of (a) is x; in the subsequence S₂Sequentially selecting the ith column, and using the selected ith column as subsequence

Charlie will subsequence S₁Sending to the database holder Bob, and sending the subsequence

Sending the information to a corresponding inquiry user;

s3: querying user record subsequences

And the measurement base corresponding to the sequence, and the subsequence

Rearranging to obtain a new sequence S_CA(ii) a Querying the user' S measurement base and sequence S_CASending the information to Charlie;

s4: charlie based on measurement basisFor the sequence S_CAMeasuring and feeding back the measurement result to Alice_i；

S5：Alice_iAccording to the subsequence

The initial position of the mobile terminal recovers the measurement result; charlie and Alice_iBy the sequence S_CAPerforming a first security detection on the particles;

s6: bob records a subsequence S₁And a measurement base corresponding to the sequence, and a subsequence S₁Rearranging is carried out; randomly selecting particles in q sequences from the rearranged subsequence to form a safety detection sequence S_BCOther particles constituting the sequence S_BA；

S7: bob will S_BCAnd the measuring machine sends the sequence S to Charlie according to the measured base pair_BCThe particles in (1) are measured, and the measurement result is fed back to Bob;

s8: bob according to the subsequence S₁The initial position of the mobile terminal recovers the measurement result; bob and Alice_iBy the sequence S_BCPerforming a second security check on the particles;

s9: bob Slave sequence S_BAExtracting n particles to form a sequence

Obtaining a sequence S_BAMeasuring the base of particles at delta positions, and sequencing the measuring base of particles at delta positions

Sending the information to a query user; querying user pair sequences

The qudit in (1) is rearranged to obtain a sequence

And will sequence

Conversion to Single photon product State S'_BAA sequence; query user will S'_BASending the middle delta particles and the measurement base to Charlie; wherein qudit represents a high-dimensional quantum state;

s10: charlie is according to measured base pair S'_BAThe particles in the database are measured, and the measurement result is returned to the inquiry user; query user and Bob to S'_BACarrying out safety detection on delta particles for the third time;

s11: will S_BAThe remaining n particles in (a) are ordered to form a sequence S ″_BA(ii) a Charlie for S ″)_BAThe particles in the system are measured, and the measurement result is fed back to Alice_i；Alice_iThe position of the measurement result is recovered to obtain a recovery sequence

Wherein,

representing the measurement result, which is a decimal value;

s12: bob couples non-orthogonal qudit

Is published into a system where | q>Is qudit, | q in Bob's hand>And

are all non-orthogonal quantum states and are,

representing symbols of quantum states subjected to quantum Fourier transform>Represents the Dirac symbol in a quantum;

S13：Alice_inon-orthogonal qudit pairs published by Bob

And a recovery sequence S_MPerforming key speculation by using a key coding rule;

s14: the inferred key is distributed.

3. The multi-user high-dimensional quantum privacy block query method according to claim 2, wherein the key encoding rule comprises: bob and n querying users Alice_i(i ═ 1, 2.. times, n) negotiate corresponding key encoding rules, which include:

......

wherein, |0>Which represents the quantum state 0 of the quantum state,

representing the quantum state obtained after performing a quantum fourier transform on quantum state 0,

the quantum state after performing a quantum fourier transform on quantum state d-1 is represented, d representing the dimension.

4. The multi-user high-dimensional quantum privacy block query method as claimed in claim 2, wherein the measurement basis comprises Z_dAnd X_d；Z_dThe expression of (a) is:

X_dthe expression of (a) is:

wherein Z is_dRepresents the measurement base under d, d represents the dimension, | j>Indicating quantum state j, j being a decimal number, X_dRepresenting a measurement basis subjected to a quantum Fourier transform

And k is a decimal value.

5. The method as claimed in claim 2, wherein Charlie measures the sequence according to the measurement basis and comprises:

charlie acquires state | q of quantum system>And construct the measurement operator { M_m}＝{M₀,M₁,...,M_d-1}；

And calculating the probability of the measurement result m-v according to the measurement operator, wherein the probability calculation expression is as follows:

wherein M is_d-1Representing a measurement operator, wherein

d denotes the dimension, m and vAre decimal values, p (v) represents the probability that the measurement is m ═ v,

represents M_vBy conjugate transposition of M_vThe representation of the measurement operator is shown as,<q | and | q |>All represent a quantum state q;

after measurement, the state of the quantum system is:

wherein,

representing measured quantum states

6. The multi-user high-dimensional quantum privacy block query method of claim 2, wherein the process of performing security detection comprises: setting an error threshold tau, and combining Charlie and Alice_iAs entities a and B, respectively; acquiring the number l of particles in a sequence to be detected safely; the entity B compares the measurement results sent by the entity A according to the initial particle information, and calculates the error rate of the sequence according to the number l of particles in the sequence to be detected safely; if the error rate is higher than the set error threshold, the detection is terminated, otherwise, the detection is continued until all the particle detection is finished.

7. The multi-user high-dimensional quantum privacy block query method according to claim 2, wherein the key estimation process comprises: obtaining the quantum state | q of Bob>And sends the quantum state to Alice_i；Alice_iRandomly selecting a measurement base, and combining the measurement base with the received quantum state to send to Charlie; charlie measures the quantum state according to the measurement basis to obtain the measurement junctionFruit

And returns the measurement results to Alice_i(ii) a From

In which one is randomly selected

Will be provided with

And | q>Form a cloth qudit pair

Bob publishes the qudit pair

Wherein

Represents a pair of | κ>Quantum states performing a quantum fourier transform

Alice_iRespectively pairing | q by using selected measurement bases>And

the measurement is carried out to respectively obtain | q>And

from which the quantum state | q of Bob is determined>Using transcoding rules to convert | q>Converting into decimal system to obtain q, which is Alice_iThe resulting key.

8. The multi-user high-dimensional quantum privacy block of claim 2The query method is characterized in that the process of distributing the inferred key comprises the following steps: inquiring user shares a set of asymmetric keys K with Bob^r＝{k₀,k₁,...,k_n-1In which k is_iRepresents K^rThe ith key of (1); bob knows all asymmetric keys in the asymmetric keys, and inquires about the corresponding key which the user knows; bob for each k_iComputing

Wherein,

wherein Q_iIs a decimal numerical value, and iota is a decimal numerical value; according to Q_iCalculating Q'_iQ_imod d, where mod is the remainder symbol; all Q 'are'_iThe key K is collected to obtain the final key K of Bob^f＝{Q′₀,Q′₁,...,Q′_n1}; the inquiry user executes the same operation as Bob, judges the number of keys in the inquiry user, recalculates the keys in the inquiry user if the number of the keys is less than 1, otherwise obtains the keys at different positions

0≤i₀,i₁,...,i_n-1N-1, wherein the subscript i₀,i₁,...,i_n-1Indicating the location.

9. The method of claim 1, wherein the process of encrypting the data in the database by using the quantum key comprises: alice_iObtaining K^fMiddle (i) th₀,i₁,...,i_n-1Key to a location

And retrieve the jth₀,j₁,...,j_n-1An item

Wherein 0 < ═ j₀,j₁,...,j_n-1＜＝n-1；Alice_iSeparately calculating the shift s₀,s₁,...s_n-1Wherein s is_λ＝j_λ-i_λWherein λ is a decimal value in the range {0, 1.., n-1 }; calculating the calculated displacement number s₀,s₁,...s_n-1Sent to Bob, Bob passes s₀,s₁,...s_n-1Respectively to the secret key K^fShifting to form n

Using n number of

Respectively encrypting the data in the database to form a ciphertext database ED⁰,ED¹,...,ED^n-1In which

Representing the (n-1) th ciphertext in the ith ciphertext database.

10. The multi-user high-dimensional quantum privacy block query method according to claim 1, wherein the process of searching the ciphertext by the query user by adopting a Grover quantum search algorithm comprises the following steps:

step 1: acquiring the number of elements in a ciphertext database;

and 2, step: and calculating an initial quantum state | upsilon >, wherein a calculation formula of the initial quantum state is as follows:

wherein, H represents a quantum gate,

represents the product of the H gates, σ represents the number of bits,

representing tensor product sign, | x, in quanta>Representing the quantum state x, wherein n represents the number of elements in the ciphertext database;

and step 3: performing G iteration on the initial quantum state | upsilon > for k times to obtain the state of the current database; the calculation formula is as follows:

wherein, G represents a unitary operator in Grover algorithm, k represents iteration times, theta represents angle, | j₀>Representing a quantum state j₀，j₀Index subscript to be searched by the user is inquired;

and 4, step 4: obtaining index subscript j of query user according to state of database₀；

And 5: and obtaining the ciphertext to be queried of the query user according to the index subscript.

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