CN113794561A - Public key searchable encryption method and system - Google Patents

Abstract

The invention belongs to the field of public key searchable encryption, and provides a public key searchable encryption method and system. The method includes that the receiver is used to generate a retrieval trapdoor and submit it to the cloud server; the sender is used to upload the generated searchable ciphertext and the ciphertext file to the cloud server; the cloud server is used to return all matching searchable secrets The ciphertext file of the encrypted file is sent to the receiver; the process of generating the searchable ciphertext is to calculate the hash value of the keyword attached to each encrypted file; calculate the intermediate parameter of the searchable ciphertext according to the hash value of the keyword ; Uniform random selection of polynomials, combined with the intermediate parameters of the searchable ciphertext, calculate the direct parameters of the searchable ciphertext, and generate the searchable ciphertext. The present invention can ensure better security through Ring-SIS/LWE difficulty assumption based on standard model and lattice problem without sacrificing efficiency, so that the scheme can not only ensure the efficiency of each algorithm but also provide long-term security .

Description

A kind of public key searchable encryption method and system

technical field

The invention belongs to the field of public key searchable encryption, and in particular relates to a public key searchable encryption method and system.

Background technique

The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

Public Key Encryption with Keyword Search (PEKS) is designed to enable retrieval of encrypted files. PEKS allows any user on the system to send encrypted files to the server, providing keywords corresponding to those files. The recipient can use his private key to generate and send a trapdoor for the keyword he wants and enable the server to search the encrypted data to retrieve the file associated with that keyword.

Since the introduction of the PEKS scheme, several PEKS schemes with various characteristics have been proposed. However, the widespread adoption of PEKS schemes in practice is hindered by several obstacles (such as high end-to-end latency and lack of long-term security, etc.). Abdalla et al. proposed a general framework for an anonymous IBE-to-PEKS transformation, and Behnia et al. proposed a general transformation in the random oracle model (ROM ) under the NTRU-based PEKS scheme. Although this scheme has obvious advantages in the efficiency of Test algorithm and PEKS algorithm, the KeyGen algorithm and Trapdoor algorithm of this scheme still cannot guarantee high efficiency.

The inventor found that the current public key searchable encryption method based on Abdalla et al.'s universal anonymous IBE to PEKS transformation still needs to be improved in terms of simultaneously ensuring search efficiency and long-term security of encryption.

SUMMARY OF THE INVENTION

In order to solve the technical problems existing in the above-mentioned background art, the present invention provides a public key searchable encryption method and system, which can simultaneously ensure search efficiency and long-term security of encryption.

In order to achieve the above object, the present invention adopts the following technical solutions:

A first aspect of the present invention provides a public key searchable encryption method, comprising:

The receiver is used to calculate the public key and its corresponding private key used in the public key searchable encryption process according to the preset security parameters, and based on the preset search keyword, generate a retrieval trapdoor and submit it to the cloud server; the sender is used to generate a searchable ciphertext for the keyword attached to each encrypted file according to the public key, and upload the generated searchable ciphertext and the ciphertext file to the cloud server together;

The cloud server is used for retrieving all searchable ciphertexts according to the retrieval trapdoor, returning all matching searchable ciphertext ciphertext files, and sending these matching searchable ciphertext ciphertext files to the receiver;

Among them, the process of generating searchable ciphertext for keywords attached to each encrypted file according to the public key is as follows:

Calculate the hash value of the keyword attached to each encrypted file;

Calculate the intermediate parameter of the searchable ciphertext according to the hash value of the corresponding keyword;

Uniform and random selection of polynomials, combined with the intermediate parameters of the searchable ciphertext, calculate the direct parameters for generating the searchable ciphertext, and generate the searchable ciphertext.

Further, the public key searchable encryption method further includes: the sender, the receiver and the cloud server respectively initialize the operating environment.

Further, the public key and its corresponding private key are generated by the receiver's key generation algorithm KeyGen(1 ^k ).

Further, the public key and its corresponding private key are calculated by generating polynomials and trapdoors associated with them according to preset security parameters, and the trapdoors are generated by a trapdoor generating algorithm according to preset security parameters; The polynomials associated with the gates are randomly generated.

Further, the described process of generating and retrieving trapdoors is:

Calculate the hash value of the pre-set search keyword;

Calculate the intermediate parameter of the retrieval trapdoor according to the hash value of the corresponding keyword;

Based on the intermediate parameters of the retrieval trapdoor and the preimage sampling algorithm, a polynomial is generated, and the polynomial is used as the generation retrieval trapdoor; wherein, the product of the transposition of the intermediate parameter of the retrieval trapdoor and the polynomial is equal to the process of generating the searchable ciphertext A randomly chosen polynomial.

Further, the process that the cloud server retrieves all searchable ciphertexts according to the retrieval trapdoor is:

According to the search trapdoor _tw and the searchable ciphertext s=(b, c ₂ , c ₁ ), calculate the judgment parameter y=c ₂ -b ^T _tw ;

Among them, b, c ₂ , c ₁ are direct parameters of searchable ciphertext, c ₁ ←{0, 1};

而不是0，则y＝1，否则y＝0；其中

表示对q/2的下取整函数；q是整数环的模数，为已知参数；If the judgment parameter y is closer

instead of 0, then y=1, otherwise y=0; where

Represents the rounding function of q/2; q is the modulus of the integer ring, which is a known parameter;

If y=c ₁ , it means that the retrieval trapdoor and the searchable ciphertext match each other, otherwise they do not match.

A second aspect of the present invention provides a public key searchable encryption system, which includes a sender, a receiver, and a cloud server;

The receiver is used to calculate the public key and the corresponding private key used in the public key searchable encryption process according to the preset security parameters, and based on the preset search keyword, generate a retrieval trapdoor and submit it to Cloud Server;

The sender is used to generate a searchable ciphertext for the keyword attached to each encrypted file according to the public key, and upload the generated searchable ciphertext and the ciphertext file to the cloud server together;

The cloud server is used for retrieving all searchable ciphertexts according to the retrieval trapdoor, returning all matching searchable ciphertext ciphertext files, and sending these matching searchable ciphertext ciphertext files to the receiver;

Wherein, the process that the sender generates a searchable ciphertext for the keyword attached to each encrypted file according to the public key is as follows:

Calculate the hash value of the keyword attached to each encrypted file;

Calculate the intermediate parameter of the searchable ciphertext according to the hash value of the corresponding keyword;

Uniform and random selection of polynomials, combined with the intermediate parameters of the searchable ciphertext, calculate the direct parameters for generating the searchable ciphertext, and generate the searchable ciphertext.

Wherein, the process of generating a retrieval trapdoor by the receiver based on a preset search keyword is as follows:

Calculate the hash value of the pre-set search keyword;

Calculate the intermediate parameter of the retrieval trapdoor according to the hash value of the corresponding keyword;

Based on the intermediate parameters of the retrieval trapdoor and the preimage sampling algorithm, a polynomial is generated, and the polynomial is used as the generation retrieval trapdoor; wherein, the product of the transposition of the intermediate parameter of the retrieval trapdoor and the polynomial is equal to the process of generating the searchable ciphertext A randomly chosen polynomial.

Compared with the prior art, the beneficial effects of the present invention are:

The process of generating a searchable ciphertext by the sender according to the public key for the keywords attached to each encrypted file is to calculate the hash value of the keywords attached to each encrypted file; calculate the searchable ciphertext according to the hash value of the corresponding keyword The intermediate parameter of the ciphertext; the polynomial is uniformly and randomly selected, and then combined with the intermediate parameters of the searchable ciphertext, the direct parameters for generating the searchable ciphertext are calculated, and the searchable ciphertext is generated. The present invention is based on the Ring-SIS/LWE difficulty on the lattice assuming that this provides long-term security and is currently considered resistant to attacks by quantum computers, done under the standard model, is IND-CPA secure and computationally consistent; the present invention is compared with the PEKS scheme of Behnia et al., Not only provides a more significant computational efficiency advantage, but also guarantees better security based on the classical assumptions of the Standard Model and lattice problems.

Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will become apparent from the description which follows, or may be learned by practice of the invention.

Description of drawings

The accompanying drawings forming a part of the present invention are used to provide further understanding of the present invention, and the exemplary embodiments of the present invention and their descriptions are used to explain the present invention, and do not constitute an improper limitation of the present invention.

FIG. 1 is a flowchart of a public key searchable encryption method according to an embodiment of the present invention.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and embodiments.

It should be noted that the following detailed description is exemplary and intended to provide further explanation of the invention. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

It should be noted that the terminology used herein is for the purpose of describing specific embodiments only, and is not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly dictates otherwise, the singular is intended to include the plural as well, furthermore, it is to be understood that when the terms "comprising" and/or "including" are used in this specification, it indicates that There are features, steps, operations, devices, components and/or combinations thereof.

PEKS=(KeyGen, Trapdoor, PEKS, Test) encryption scheme mainly includes four algorithms:

(1) KeyGen(1 ^k )→(pk, sk): Key generation algorithm. Assuming that the security parameter of the scheme is k, the algorithm outputs the public key pk and the private key sk by inputting k;

(2) Trapdoor(w, pk, sk)→t _w : Trapdoor generation algorithm. Input the keyword w that the user wants to retrieve, the public key pk and the private key sk, and the algorithm outputs the trapdoor _tw ;

(3) PEKS(w, pk)→s _w : PEKS algorithm. Input the keyword _w and the public key pk, the algorithm outputs a searchable ciphertext sw;

(4) Test(s _w , t′ _w )→d: test algorithm. Input the searchable ciphertext sw and trapdoor _t'w , the algorithm outputs d, if _w =w', d=1, otherwise d=0.

Identity Based Encryption (IBE) is a public key encryption mechanism. Using the user's identity (such as the user's email address) as the public key, the user sends his identity to a trusted third party, and the trusted third party The three parties generate the private key corresponding to the user's identity. We call the trusted third party a private key generator (Private-KeyGenerator, PKG). The IBE=(Setup, Extract, Enc, Dec) encryption scheme mainly includes 4 algorithms:

Setup( ^1k )→(mpk, msk): Key generation algorithm. Assuming that the security parameter of the scheme is k, the algorithm outputs the master public key mpk and the master private key msk by inputting k;

Extract(id, msk, mpk) → sk: Extraction algorithm. Input the user's identity id∈{0, 1} ^k , the master public key mpk and the master private key msk, and the algorithm outputs the user's private key sk;

Enc(m, id, mpk) → c: encryption algorithm. Input the user's identity id and message m∈{0, 1} ^* , the algorithm outputs the ciphertext c;

Dec(c,sk)→m: Decryption algorithm. Enter the ciphertext c and the user's private key sk, and the algorithm outputs the plaintext message m recovered from the ciphertext c.

Abdalla et al. proposed a technique for converting an IBE protocol to a PEKS protocol. That is, if there is an IND-CPA (indistinguishability under chosen plaintext attack) secure anonymous IBE scheme, we can transform it into an IND-CPA secure and computationally consistent PEKS scheme. The conversion method inputs an IBE scheme IBE=(Setup, Extract, Enc, Dec), and returns a PEKS scheme PEKS=(KeyGen, Trapdoor, PEKS, Test). The correspondence between the IBE scheme and the PEKS scheme in the conversion method is as follows Show:

方案中的公钥pk和私钥sk分别是IBE方案的主公钥mpk和主私钥msk；

The public key pk and the private key sk in the scheme are the main public key mpk and the main private key msk of the IBE scheme, respectively;

方案中的关键字w对应于IBE方案的身份id，PEKS方案中与关键字相关联的陷门t_w是IBE方案中分配给身份的私钥sk；

The keyword w in the scheme corresponds to the identity id of the IBE scheme, and the trapdoor _tw associated with the keyword in the PEKS scheme is the private key sk assigned to the identity in the IBE scheme;

PEKS方案的PEKS算法对应于IBE方案的加密算法：

The PEKS algorithm of the PEKS scheme corresponds to the encryption algorithm of the IBE scheme:

PEKS(w, pk) selects C ₂ ∈ {0, 1} ^k , let Enc(C ₂ , w, pk)→C ₁ , return (C ₁ , C ₂ ).

如果Dec(t_w，C₁)＝C₂，Test(C₁，C₂)返回1，否则返回0。

Test(C ₁ , C ₂ ) returns 1 if Dec(t _w , C ₁ )=C ₂ , and 0 otherwise.

Based on this general approach, Behnia et al. propose an NTRU-based PEKS scheme under the random oracle model (ROM). Although this scheme has obvious advantages in the efficiency of Test algorithm and PEKS algorithm, the KeyGen algorithm and Trapdoor algorithm of this scheme still cannot guarantee high efficiency. In order to solve the above problem, the present invention provides a public key A searchable encryption method and system can simultaneously ensure search efficiency and long-term security of encryption.

In order to make the scheme not only ensure the efficiency of each algorithm but also provide long-term security, the present invention constructs a PEKS scheme based on the Ring-SIS/LWE difficulty assumption under the standard model, which proves that the PEKS scheme can be used without sacrificing efficiency. , which guarantees better security by the classical assumptions based on the standard model and lattice problems.

Example 1

Referring to FIG. 1, this embodiment provides a public key searchable encryption method, which specifically includes the following steps:

Step 1: The receiver is used to calculate the public key and its corresponding private key used in the public key searchable encryption process according to the preset security parameters, and based on the preset search keywords, generate a retrieval trapdoor and Submit to the cloud server.

In a specific implementation, the sender, the receiver and the cloud server respectively initialize the operating environment; wherein, the receiver's public key and its corresponding private key used in the running process are generated by the receiver's key generation algorithm;

Wherein, the key generation algorithm is the KeyGen(1 ^k ) algorithm, where k is a security parameter preset by the system, specifically:

是给定的参数。如果a′没有在输入给定，则表示算法在

中均匀选取a′。生成多项式

和与之关联的陷门

以此计算出公钥pk和私钥sk。其中，上标m和k均为已知设定参数。具体包含以下子步骤：The receiver runs the TrapGen(q, σ, h=0) algorithm according to the security parameter k preset by the system, where q is the modulus of the ring, σ is the Gaussian parameter, h∈R _q and

is the given parameter. If a' is not given at the input, it means that the algorithm is

A' is uniformly selected from among them. generator polynomial

and the trapdoor associated with it

Based on this, the public key pk and the private key sk are calculated. Among them, the superscripts m and k are known setting parameters. Specifically, it includes the following sub-steps:

是给定的参数。如果a′没有在输入给定，则表示算法在

中均匀选取a′。该算法生成多项式

和与之关联的陷门

满足a＝(a′^T，-a′^T)^T Run the TrapGen(q, σ, h = 0) algorithm, where q is the modulus of the ring, σ is the Gaussian parameter, h ∈ R _q and

is the given parameter. If a' is not given at the input, it means that the algorithm is

A' is uniformly selected from among them. The algorithm generates polynomials

and the trapdoor associated with it

Satisfy a=(a' ^T , -a' ^T ) ^T

Uniform random selection of polynomial u←R _q ;

Generate the public key pk and private key sk according to the results of the above steps:

Step 2: The sender generates a searchable ciphertext for the keywords attached to each encrypted file according to the public key, and uploads the generated searchable ciphertext and the ciphertext file to the cloud server together;

The trapdoor is generated according to preset security parameters by using a trapdoor generation algorithm. The polynomial associated with the trapdoor is randomly generated.

Among them, the process of generating searchable ciphertext for keywords attached to each encrypted file according to the public key is as follows:

Calculate the hash value of the keyword attached to each encrypted file;

Calculate the intermediate parameter of the searchable ciphertext according to the hash value of the corresponding keyword;

Uniform and random selection of polynomials, combined with the intermediate parameters of the searchable ciphertext, calculate the direct parameters for generating the searchable ciphertext, and generate the searchable ciphertext.

The sender generates a searchable ciphertext s for the keywords attached to each encrypted file according to the public key pk, and uploads the generated searchable ciphertext together with the ciphertext file to the cloud server. Specifically, it includes the following sub-steps:

是一个满秩差分编码(encodingwith Full-Rank Differences，FRD)函数，它可以将

中的元素映射到R_q中的可逆元素；For keyword W, compute h _w = H(w), where the function

is an encoding with Full-Rank Differences (FRD) function, which can convert

Elements in map to reversible elements in R _q ;

Calculate a _w = a ^T + (0, h _w g ^T ) ^T = (a' ^T , h _w g ^T - a' ^T T) ^T where

其中

表示R^m-k(R^k、R)上方差为τ(γ、τ)的高斯分布；Uniform random selection of polynomials

in

Represents a Gaussian distribution with variance τ(γ, τ) over R ^mk (R ^k , R);

和

其中

表示对q/2的下取整函数；calculate

and

in

Represents the rounding down function of q/2;

A searchable ciphertext s=(b, c ₂ , c ₁ ) is generated according to the results of the above steps.

Step 3: The receiver generates a search trapdoor based on the preset search keywords and submits it to the cloud server.

Wherein, the described process of generating retrieval trapdoor is:

Calculate the hash value of the pre-set search keyword;

Calculate the intermediate parameter of the retrieval trapdoor according to the hash value of the corresponding keyword;

Based on the intermediate parameters of the retrieval trapdoor and the preimage sampling algorithm, a polynomial is generated, and the polynomial is used as the generation retrieval trapdoor; wherein, the product of the transposition of the intermediate parameter of the retrieval trapdoor and the polynomial is equal to the process of generating the searchable ciphertext A randomly chosen polynomial.

Specifically, the receiver inputs the keyword w to be searched, generates a retrieval trapdoor _tw ∈ R ^m and submits it to the cloud server. Specifically, it includes the following sub-steps:

For the keyword w, calculate h _w =H(w), where the function H is the FRD function as described above;

Calculate a _w =a ^T +(0, _hw g ^T ) ^T =(a' ^T , h _w g ^T -a' ^T T) ^T ;

其中T，a_w，h_w，u如上所述，ζ，σ，α为给定的高斯参数；Run the preimage sampling SamplePre(T, a _w , hw, ζ, σ, α, u) algorithm ^[8] to generate polynomial x∈R ^m , satisfying

where T, a _w , h _w , u are as described above, ζ, σ, α are given Gaussian parameters;

The search trapdoor _tw =x is generated according to the result of the above steps. Among them, the superscript T all means transposition.

Step 4: The cloud server retrieves all searchable ciphertexts according to the retrieval trapdoor, returns all matching searchable ciphertext ciphertext files and sends them to the receiver.

Wherein, the process that the cloud server retrieves all searchable ciphertexts according to the retrieval trapdoor is:

According to the search trapdoor _tw and the searchable ciphertext s=(b, c ₂ , c ₁ ), calculate the judgment parameter y=c ₂ -b ^T _tw ;

Among them, b, c ₂ , c ₁ are direct parameters of searchable ciphertext, c ₁ ←{0, 1};

而不是0，则y＝1，否则y＝0；其中

表示对q/2的下取整函数；q是整数环的模数，为已知参数；If the judgment parameter y is closer

instead of 0, then y=1, otherwise y=0; where

Represents the rounding function of q/2; q is the modulus of the integer ring, which is a known parameter;

If y=c ₁ , it means that the retrieval trapdoor and the searchable ciphertext match each other, otherwise they do not match.

According to the results of the above steps, the cloud server returns all ciphertext files that meet the trapdoor retrieval conditions.

Table 1 shows the different operation times of PEKS schemes when the security parameter is 80 and the grid dimension is 512: KeyGen, Trapdoor, PEKS and Test.

Table 1

Table 2 shows the different operation times of PEKS schemes when the security parameter is 80 and the grid dimension is 1024: KeyGen, Trapdoor, PEKS and Test.

Table 2

Embodiment 2

This embodiment provides a public key searchable encryption system, which specifically includes a sender, a receiver, and a cloud server;

The receiver is used to calculate the public key and its corresponding private key used in the public key searchable encryption process according to the preset security parameters, and based on the preset search keyword, generate a retrieval trapdoor and submit it to the cloud server; the sender is used to generate a searchable ciphertext for the keyword attached to each encrypted file according to the public key, and upload the generated searchable ciphertext and the ciphertext file to the cloud server together;

The cloud server is used for retrieving all searchable ciphertexts according to the retrieval trapdoor, returning all matching searchable ciphertext ciphertext files, and sending these matching searchable ciphertext ciphertext files to the receiver;

Wherein, the process that the sender generates a searchable ciphertext for the keyword attached to each encrypted file according to the public key is as follows:

Calculate the hash value of the keyword attached to each encrypted file;

Calculate the intermediate parameter of the searchable ciphertext according to the hash value of the corresponding keyword;

Uniform and random selection of polynomials, combined with the intermediate parameters of the searchable ciphertext, calculate the direct parameters for generating the searchable ciphertext, and generate the searchable ciphertext.

Wherein, the process of generating a retrieval trapdoor by the receiver based on a preset search keyword is as follows:

Calculate the hash value of the pre-set search keyword;

Calculate the intermediate parameter of the retrieval trapdoor according to the hash value of the corresponding keyword;

Based on the intermediate parameters of the retrieval trapdoor and the preimage sampling algorithm, a polynomial is generated, and the polynomial is used as the generation retrieval trapdoor; wherein, the product of the transposition of the intermediate parameter of the retrieval trapdoor and the polynomial is equal to the process of generating the searchable ciphertext A randomly chosen polynomial.

In a specific implementation, the process that the cloud server retrieves all searchable ciphertexts according to the retrieval trapdoor is:

According to the search trapdoor _tw and the searchable ciphertext s=(b, c ₂ , c ₁ ), calculate the judgment parameter y=c ₂ -b ^T _tw ;

Among them, b, c ₂ , c ₁ are direct parameters of searchable ciphertext, c ₁ ←{0, 1};

而不是0，则y＝1，否则y＝0；其中

表示对q/2的下取整函数；q是整数环的模数，为已知参数；If the judgment parameter y is closer

instead of 0, then y=1, otherwise y=0; where

Represents the rounding function of q/2; q is the modulus of the integer ring, which is a known parameter;

If y=c ₁ , it means that the retrieval trapdoor and the searchable ciphertext match each other, otherwise they do not match.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (10)

1. a public key searchable encryption method, is characterized in that, comprises: The receiver is used to calculate the public key and its corresponding private key used in the public key searchable encryption process according to the preset security parameters, and based on the preset search keyword, generate a retrieval trapdoor and submit it to the cloud server; the sender is used to generate a searchable ciphertext for the keyword attached to each encrypted file according to the public key, and upload the generated searchable ciphertext and the ciphertext file to the cloud server together; The cloud server is used for retrieving all searchable ciphertexts according to the retrieval trapdoor, returning all matching searchable ciphertext ciphertext files, and sending these matching searchable ciphertext ciphertext files to the receiver; Among them, the process of generating searchable ciphertext for keywords attached to each encrypted file according to the public key is as follows: Calculate the hash value of the keyword attached to each encrypted file; Calculate the intermediate parameter of the searchable ciphertext according to the hash value of the corresponding keyword; Uniform and random selection of polynomials, combined with the intermediate parameters of the searchable ciphertext, calculate the direct parameters for generating the searchable ciphertext, and generate the searchable ciphertext. 2 . The public key searchable encryption method according to claim 1 , wherein the public key searchable encryption method further comprises: the sender, the receiver and the cloud server respectively initialize operating environments. 3 . 3. The public key searchable encryption method according to claim 1, wherein the public key and its corresponding private key are generated by the receiver's key generation algorithm KeyGen( ^1k ). 4. public key searchable encryption method as claimed in claim 1, is characterized in that, generating polynomial and its associated trapdoor are calculated according to preset security parameters, and described trapdoor is calculated by trapdoor generation algorithm according to preset security parameters; the polynomial associated with the trapdoor is randomly generated. 5. public key searchable encryption method as claimed in claim 1 is characterized in that, the process of described generation retrieval trapdoor is: Calculate the hash value of the pre-set search keyword; Calculate the intermediate parameter of the retrieval trapdoor according to the hash value of the corresponding keyword; Based on the intermediate parameters of the retrieval trapdoor and the preimage sampling algorithm, a polynomial is generated, and the polynomial is used as the generation retrieval trapdoor; wherein, the product of the transposition of the intermediate parameter of the retrieval trapdoor and the polynomial is equal to the process of generating the searchable ciphertext A randomly chosen polynomial. 6. The public key searchable encryption method as claimed in claim 1, wherein the process that the cloud server retrieves all searchable ciphertexts according to the retrieval trapdoor is: According to the search trapdoor _tw and the searchable ciphertext s=(b, c ₂ , c ₁ ), calculate the judgment parameter y=c ₂ -b ^T _tw ; Among them, b, c ₂ , c ₁ are direct parameters of searchable ciphertext, c ₁ ←{0, 1}; If the judgment parameter y is closer

instead of 0, then y=1, otherwise y=0; where

Represents the rounding function of q/2; q is the modulus of the integer ring, which is a known parameter; If y=c ₁ , it means that the retrieval trapdoor and the searchable ciphertext match each other, otherwise they do not match. 7. A public key searchable encryption system, comprising a sender, a receiver and a cloud server; The receiver is used to calculate the public key and its corresponding private key used in the public key searchable encryption process according to the preset security parameters, and based on the preset search keyword, generate a retrieval trapdoor and submit it to the cloud server; the sender is used to generate a searchable ciphertext for the keyword attached to each encrypted file according to the public key, and upload the generated searchable ciphertext and the ciphertext file to the cloud server together; The cloud server is used for retrieving all searchable ciphertexts according to the retrieval trapdoor, returning all matching searchable ciphertext ciphertext files, and sending these matching searchable ciphertext ciphertext files to the receiver; Wherein, the process that the sender generates a searchable ciphertext for the keyword attached to each encrypted file according to the public key is as follows: Calculate the hash value of the keyword attached to each encrypted file; Calculate the intermediate parameter of the searchable ciphertext according to the hash value of the corresponding keyword; Uniform and random selection of polynomials, combined with the intermediate parameters of the searchable ciphertext, calculate the direct parameters for generating the searchable ciphertext, and generate the searchable ciphertext. 8. The public key searchable encryption system according to claim 7, wherein the public key and its corresponding private key are calculated according to a preset security parameter to generate a polynomial and a trapdoor associated therewith; the trapdoor Generated by a trapdoor generation algorithm according to preset security parameters; the polynomial associated with the trapdoor is randomly generated. 9. public key searchable encryption system as claimed in claim 7, is characterized in that, the process of described generation retrieval trapdoor is: Calculate the hash value of the pre-set search keyword; Calculate the intermediate parameter of the retrieval trapdoor according to the hash value of the corresponding keyword; Based on the intermediate parameters of the retrieval trapdoor and the preimage sampling algorithm, a polynomial is generated, and the polynomial is used as the generation retrieval trapdoor; wherein, the product of the transposition of the intermediate parameter of the retrieval trapdoor and the polynomial is equal to the process of generating the searchable ciphertext A randomly chosen polynomial. 10. The public key searchable encryption system according to claim 7, wherein the process that the cloud server retrieves all searchable ciphertexts according to the retrieval trapdoor is: According to the search trapdoor _tw and the searchable ciphertext s=(b, c ₂ , c ₁ ), calculate the judgment parameter y=c ₂ -b ^T _tw ; Among them, b, c ₂ , c ₁ are direct parameters of searchable ciphertext, c ₁ ←{0, 1}; If the judgment parameter y is closer

instead of 0, then y=1, otherwise y=0; where

Represents the rounding function of q/2; q is the modulus of the integer ring, which is a known parameter; If y=c ₁ , it means that the retrieval trapdoor and the searchable ciphertext match each other, otherwise they do not match.

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