Homomorphic comparison method, system and equipment based on composite polynomial and medium

Abstract

The invention provides a homomorphic comparison method based on a composite polynomial, and the method comprises the following steps: carrying out the full homomorphic encryption of two pieces of to-be-compared plaintext data, and obtaining the encryption ciphertext corresponding to the two pieces of plaintext data; performing homomorphic operation on the two encrypted ciphertexts to obtain a ciphertext difference of the two encrypted ciphertexts; constructing a component quintic polynomial based on the input precision and the output precision; inputting the ciphertext difference into a component quintic polynomial to obtain a ciphertext result; and performing fully homomorphic decryption on the ciphertext result to obtain a comparison result of the two pieces of plaintext data. According to the method, the composite polynomial approximation sign function is dynamically generated, the calculation depth and complexity are effectively reduced, the convergence speed is increased, meanwhile, the comparison operation precision is improved, and the method can be widely applied to various application scenes.

Description

Technical Field

[0001] The present invention relates to the field of ciphertext data processing, and more specifically to a homomorphic comparison method, system, device and medium based on composite polynomials. Background Art

[0002] Homomorphic encryption technology, as an encryption method that allows direct calculations on encrypted data, has the core advantage of being able to perform various operations on encrypted data without decryption and obtain the same results as plaintext operations. This feature makes homomorphic encryption have broad application prospects in many fields such as cloud computing, finance, and healthcare. However, despite significant progress in homomorphic encryption technology, especially in fully homomorphic encryption (FHE), existing homomorphic comparison technologies still have many defects.

[0003] First, the existing homomorphic comparison methods significantly increase the computational depth when approaching high precision. For example, when Chebyshev polynomials approximate symbolic functions, in order to achieve higher precision, the order of the polynomials needs to be increased, which directly leads to a significant increase in computational depth and thus increases computational complexity. In addition, artificial neural networks also consume a lot of computing resources during training and there is a risk of overfitting, which further limits their application in homomorphic comparison.

[0004] Secondly, the computational complexity of existing homomorphic comparison techniques is high. Methods such as least squares and Newton-Raphson are prone to large errors in the function jump region. In order to reduce these errors, it is often necessary to increase the number of iterations or use more complex algorithms, which undoubtedly increases the computational complexity. At the same time, the iterative process of these methods may be unstable, resulting in slow convergence, further prolonging the calculation time.

[0005] Furthermore, the accuracy error of existing homomorphic comparison technology is large. Since there is a certain amount of noise and error in the encryption process of ciphertext data, these errors may be amplified during the comparison operation, thus affecting the accuracy of the final result. In addition, there are differences in the approximation effect between different methods. Some methods may perform well in certain specific situations, but may produce large errors in other situations.

[0006] Finally, the algorithm applicability of existing homomorphic comparison technologies is poor. Many methods are designed based on specific mathematical models or algorithms, lacking flexibility and universality. When faced with different application scenarios or data types, these methods may require a lot of modifications or optimizations to adapt to new needs. This not only increases the difficulty of technical implementation, but also limits the application and development of homomorphic encryption technology in a wider range of fields.

[0007] Therefore, how to design a homomorphic comparison method based on composite polynomials to overcome the defects of existing homomorphic comparison technologies in terms of computational depth, computational complexity, precision error and algorithm applicability is an urgent problem that technical personnel in this field need to solve. Summary of the invention

[0008] In view of this, the present invention provides a homomorphic comparison method based on composite polynomials, which significantly reduces the calculation depth and complexity by dynamically generating polynomials, improves the accuracy and efficiency of homomorphic comparison, and thus realizes efficient and accurate data comparison in a fully homomorphic encryption environment.

[0009] In order to achieve the above object, the present invention adopts the following technical solution:

[0010] In a first aspect, the present invention provides a homomorphic comparison method based on a composite polynomial, comprising the following steps:

[0011] S1. Perform fully homomorphic encryption on the two plaintext data to be compared, and obtain the encrypted ciphertexts corresponding to the two plaintext data respectively;

[0012] S2, perform homomorphic operation on the two encrypted ciphertexts to obtain the ciphertext difference between the two encrypted ciphertexts;

[0013] S3, constructing a component quintic polynomial based on input precision and output precision;

[0014] S4, inputting the ciphertext difference into a component quintic polynomial to obtain a ciphertext result;

[0015] S5. Perform fully homomorphic decryption on the ciphertext result to obtain a comparison result of two plaintext data.

[0016] Furthermore, the S1 includes:

[0017] Generate private key sk and public key pk through key generation algorithm;

[0018] Combined with the Enc algorithm, the public key pk is used to perform fully homomorphic encryption on the plaintext data X and Y to obtain the corresponding encrypted ciphertext C X and C Y .

[0019] Furthermore, before fully homomorphic encryption is performed, it also includes:

[0020] Determine whether the absolute value of the plaintext data X and Y is greater than the preset value M; if |X|>M, and |Y|>M, scale the plaintext data X and Y to the interval [0,1].

[0021] Furthermore, the S2 includes:

[0022] The encrypted ciphertext C corresponding to the plaintext data XX Perform homomorphic multiplication with -1, and then encrypt the ciphertext C corresponding to the plaintext data Y Y Perform homomorphic multiplication to obtain the ciphertext difference; or,

[0023] The encrypted ciphertext C corresponding to the plaintext data Y Y Perform homomorphic multiplication with -1, and then encrypt the ciphertext C corresponding to the plaintext data X X Perform homomorphic multiplication to obtain the ciphertext difference.

[0024] Furthermore, the S3 includes:

[0025] Generate initialization polynomial ax 5 +bx 3 +cx, the polynomial has the largest derivative at 0, and the function value of the maximum point is 1+∈;

[0026] Combining the error value ∈' between the polynomial and the symbolic function sgn(x), a system of equations is constructed; the system of equations is expressed as:

[0027]

[0028] Among them, x0 and x1 represent the maximum and minimum points respectively;

[0029] Based on the equation group, solve the polynomial coefficients a, b, c and the error value ∈';

[0030] The polynomial coefficients are iteratively adjusted until the error value ∈′ satisfies the output accuracy α, and a component quintic polynomial is generated.

[0031] Furthermore, the S4 includes:

[0032] Generate a set of component quintic polynomials {h i}, where 1≤i≤n; including:

[0033] Generate initialization polynomials h1, h 1([1-∈,1+∈]) =[1-∈1,1+∈1]; and calculate the polynomials h2, h3, …h in turn n , …、

[0034] Among them, ∈1>∈2>…>∈ n ;

[0035] Combined with the preset value W, i The component polynomial h is infinitely close to 0 i Perform compounding to obtain a composite function; wherein the composite function has the same highest degree as the symbolic function sgn(x);

[0036] The ciphertext difference is input into the composite function to obtain the ciphertext result.

[0037] Furthermore, the S5 includes:

[0038] Combined with the Dec algorithm, the ciphertext result is fully homomorphically decrypted using the private key sk to obtain a comparison result of the two plaintext data.

[0039] In a second aspect, the present invention provides a homomorphic comparison system based on a composite polynomial, comprising:

[0040] Fully homomorphic encryption module: used to perform fully homomorphic encryption on the two plaintext data to be compared, and obtain the encrypted ciphertexts corresponding to the two plaintext data respectively;

[0041] Homomorphic operation module: used to perform homomorphic operation on two encrypted ciphertexts to obtain the ciphertext difference between the two encrypted ciphertexts;

[0042] Composite polynomial building block: used to build component quintic polynomials based on input precision and output precision;

[0043] Polynomial evaluation module: used for inputting the ciphertext difference into a component quintic polynomial to obtain a ciphertext result;

[0044] Fully homomorphic decryption module: used to perform fully homomorphic decryption on the ciphertext result to obtain a comparison result of two plaintext data.

[0045] In a third aspect, the present invention provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned homomorphic comparison method based on composite polynomials when executing the computer program.

[0046] In a fourth aspect, the present invention provides a computer-readable storage medium, wherein the storage medium stores a computer program, and when the computer program is executed by a processor, the above-mentioned homomorphic comparison method based on composite polynomials is implemented.

[0047] The descriptions of the second to fourth aspects of the present invention can refer to the detailed description of the first aspect; and the beneficial effects of the descriptions of the second to fourth aspects can refer to the analysis of the beneficial effects of the first aspect, which will not be repeated here.

[0048] It can be seen from the above technical solution that compared with the prior art, the present invention has the following beneficial effects:

[0049] 1. This technical solution realizes the execution of non-arithmetic operations (such as comparison operations) in a fully homomorphic encryption environment that only supports arithmetic operations by constructing component quintic polynomials. By dynamically generating composite polynomials with the least depth consumption, this method significantly reduces the depth and complexity of ciphertext calculations, while improving the accuracy of approximation results. In addition, allowing polynomial combinations of different orders to iterate further accelerates the convergence speed, thereby improving computational efficiency.

[0050] 2. When constructing the polynomial, the requirements of input accuracy and output accuracy are taken into consideration to ensure that the error accuracy requirements can be met after a finite number of iterations. By continuously updating the mapped interval and polynomial coefficients, the finiteness of the dynamic update process is achieved, avoiding unnecessary consumption of computing resources. In addition, the properties of symbolic functions are used for homomorphic operations, reducing the number of homomorphic multiplications and further optimizing resource utilization.

[0051] 3. This technical solution is suitable for application scenarios with large amounts of data. By supporting direct comparison operations on encrypted data, it protects data privacy while ensuring the accuracy and efficiency of data processing, providing a new perspective and broad application prospects for the development of homomorphic encryption technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0053] Figure 1 A flow chart of a homomorphic comparison method based on a composite polynomial provided in an embodiment of the present invention;

[0054] Figure 2 A schematic diagram of an image of a fifth-order polynomial function of an initial component provided by an embodiment of the present invention;

[0055] Figure 3 A schematic diagram of a composite result of a quintic polynomial of some components provided by an embodiment of the present invention;

[0056] Figure 4 A schematic diagram of the composite result of all component quintic polynomials provided in an embodiment of the present invention;

[0057] Figure 5 A framework diagram of a homomorphic comparison system based on a composite polynomial provided in an embodiment of the present invention

[0058] Figure 6 A schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0059] 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.

[0060] The homomorphic comparison method provided in the embodiment of the present application can be applied to a homomorphic comparison server. The above-mentioned homomorphic comparison server can be hardware or software. When the homomorphic comparison server is hardware, it can be implemented as a distributed server cluster providing homomorphic comparison services, or it can be implemented as a single server. When the homomorphic comparison server is software, it can be installed in the servers listed above. It can be implemented as multiple software or software modules, or it can be implemented as a single software or software module, which is not specifically limited here.

[0061] Embodiment 1;

[0062] like Figure 1 As shown, this embodiment provides a homomorphic comparison method based on a composite polynomial, comprising the following steps:

[0063] S1. Perform fully homomorphic encryption on the two plaintext data to be compared, and obtain the encrypted ciphertexts corresponding to the two plaintext data respectively;

[0064] S2, perform homomorphic operation on the two encrypted ciphertexts to obtain the ciphertext difference between the two encrypted ciphertexts;

[0065] S3, constructing a component quintic polynomial based on input precision and output precision;

[0066] S4, inputting the ciphertext difference into a component quintic polynomial to obtain a ciphertext result;

[0067] S5. Perform fully homomorphic decryption on the ciphertext result to obtain a comparison result of two plaintext data.

[0068] In homomorphic comparison operations, the sign function is used as the target function, and its approximation directly determines the accuracy of the comparison result. This method achieves efficient and accurate comparison operations on encrypted data by dynamically generating polynomials and approximating the sign function, significantly reducing the computational depth and complexity, and improving computational efficiency and accuracy.

[0069] The above steps and related technical features are further described in detail below:

[0070] In this embodiment S1, two plaintext data to be compared are fully homomorphically encrypted to obtain encrypted ciphertexts corresponding to the two plaintext data respectively; specifically, the following steps are performed:

[0071] Generate a private key sk and a public key pk through a key generation algorithm; the private key sk is used to decrypt data, and the public key pk is used to encrypt data;

[0072] Combined with the Enc algorithm, the public key pk is used to perform fully homomorphic encryption on the plaintext data X and Y to obtain the corresponding encrypted ciphertext C X and C Y .

[0073] Furthermore, before fully homomorphic encryption is performed, it also includes:

[0074] Determine whether the absolute value of the plaintext data X and Y is greater than the preset value M; if |X|>M, and |Y|>M, scale the plaintext data X and Y to the interval [0,1]. Scaling the plaintext data before performing fully homomorphic encryption can ensure that the encrypted ciphertext size remains within a reasonable range, thereby reducing the computational burden of subsequent homomorphic operations.

[0075] In this embodiment S2, a homomorphic operation is performed on two encrypted ciphertexts to obtain a ciphertext difference between the two encrypted ciphertexts; specifically, the operation includes:

[0076] The encrypted ciphertext C corresponding to the plaintext data X X Perform homomorphic multiplication with -1, and then encrypt the ciphertext C corresponding to the plaintext data Y Y Perform homomorphic multiplication to obtain the ciphertext difference; or,

[0077] The encrypted ciphertext C corresponding to the plaintext data Y Y Perform homomorphic multiplication with -1, and then encrypt the ciphertext C corresponding to the plaintext data X X Perform homomorphic multiplication to obtain the ciphertext difference.

[0078] In this embodiment S3, a component quintic polynomial is constructed based on input precision and output precision; wherein the input precision ε is the minimum effective boundary of the plaintext data X and Y, and the output precision α is the minimum boundary value of the interval range to which the comparison result is mapped;

[0079] Specifically include:

[0080] Generate initialization polynomial ax 5 +bx 3 +cx, the polynomial has the largest derivative at 0, and the function value of the maximum point is 1+∈;

[0081] Combining the error value ∈' between the polynomial and the symbolic function sgn(x), a system of equations is constructed; the system of equations is expressed as:

[0082]

[0083] Among them, x0 and x1 represent the maximum and minimum points respectively;

[0084] Based on the equation group, solve the polynomial coefficients a, b, c and the error value ∈';

[0085] The polynomial coefficients are iteratively adjusted until the error value ∈′ satisfies the output accuracy α, and a component quintic polynomial is generated.

[0086] In the process of solving the polynomial coefficients, the degree of the polynomial is dynamically adjusted according to different needs, not limited to a single degree. In order to make the polynomial iteration quickly converge to the target value 1, the maximum value is set not to exceed 2, which allows the polynomial to fluctuate above and below 1 and gradually reduce the amplitude, thereby converging on both sides at the same time, which is faster than the method that converges only on one side. In addition, this method also allows the combination of polynomials of different degrees of iteration, further improving the calculation efficiency and flexibility.

[0087] In this embodiment S4, the ciphertext difference is input into a component quintic polynomial to obtain a ciphertext result; specifically, it includes:

[0088] Generate a set of component quintic polynomials {h i}, where 1≤i≤n; including:

[0089] like Figure 2 As shown, generate initialization polynomials h1, h 1([1-∈,1+∈]) =[1-∈1,1+∈1]; and calculate the polynomials h2, h3, …h in turn n ,

[0090] …、 Among them, ∈1>∈2>…>∈ n ;

[0091] Combined with the preset value W, i The component polynomial h is infinitely close to 0 i Perform compounding to obtain a composite function; wherein the composite function has the same highest degree as the symbolic function sgn(x);

[0092] The ciphertext difference is input into the composite function to obtain the ciphertext result.

[0093] In this step, if v1 is less than the preset value W, the first t component polynomials are composited, then Among them, 1≤t≤n; Figure 3 The image of the composite polynomial of the first t-4 components is shown in , and it can be seen that the image fluctuates within a certain range. When the composite is continued, Figure 4The result of fully composing the first t component polynomials is shown, and this composed result is almost identical to the graph of the sign function.

[0094] In this embodiment S5, fully homomorphic decryption is performed on the ciphertext result to obtain the comparison result of the two plaintext data.

[0095] It includes: combining with the Dec algorithm, using the private key sk to perform fully homomorphic decryption on the ciphertext result to obtain the comparison result m of the two plaintext data.

[0096] Specifically, in step S2, when the encrypted ciphertext C corresponding to the plaintext data X X is subjected to homomorphic multiplication with -1, and then homomorphic multiplication is performed with the encrypted ciphertext C Y corresponding to the plaintext data Y to obtain the ciphertext difference; in this case, if m is positive, then X < Y, if m is negative, then X > Y, and if m is 0, then X = Y.

[0097] When the encrypted ciphertext C corresponding to the plaintext data Y Y is subjected to homomorphic multiplication with -1, and then homomorphic multiplication is performed with the encrypted ciphertext C X corresponding to the plaintext data X to obtain the ciphertext difference; in this case, if m is positive, then X > Y, if m is negative, then X < Y, and if m is 0, then X = Y.

[0098] In this embodiment, the homomorphic comparison method based on composite polynomials approximates the sign function by dynamically generating and iteratively adjusting the fifth-degree polynomial, achieving efficient and accurate comparison operations on encrypted data. This method significantly reduces the computational depth and complexity, improves the operation efficiency and accuracy, and at the same time maintains the security of the data. Through strategies such as scaling the plaintext data, dynamically adjusting the polynomial degree, and combined iteration, the flexibility and applicability of the method are further enhanced, making it more convenient and reliable to perform data comparison in an encrypted environment.

[0099] Embodiment 2;

[0100] As Figure 5 shown, this embodiment provides a homomorphic comparison system based on composite polynomials, including:

[0101] Fully homomorphic encryption module: used to perform fully homomorphic encryption on the two plaintext data to be compared, respectively obtaining the encrypted ciphertexts corresponding to the two plaintext data;

[0102] Homomorphic operation module: used to perform homomorphic operations on the two encrypted ciphertexts to obtain the ciphertext difference of the two encrypted ciphertexts;

[0103] Composite polynomial construction module: used to construct component fifth-degree polynomials based on the input precision and output precision;

[0104] Polynomial evaluation module: used for inputting the ciphertext difference into a component quintic polynomial to obtain a ciphertext result;

[0105] Fully homomorphic decryption module: used to perform fully homomorphic decryption on the ciphertext result to obtain a comparison result of two plaintext data.

[0106] This embodiment provides a homomorphic comparison system based on a composite polynomial, including a fully homomorphic encryption module, a homomorphic operation module, a composite polynomial construction module, a polynomial evaluation module and a fully homomorphic decryption module. The system encrypts two plaintext data through the fully homomorphic encryption module, the homomorphic operation module generates a ciphertext difference, the composite polynomial construction module constructs a quintic polynomial according to the accuracy requirement, the polynomial evaluation module inputs the ciphertext difference into the polynomial to obtain the ciphertext result, and finally the fully homomorphic decryption module decrypts the ciphertext result to obtain the final comparison result. The system significantly improves the efficiency and accuracy of homomorphic comparison while reducing the computational complexity.

[0107] Embodiment 3;

[0108] like Figure 6 As shown, this embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned homomorphic comparison method based on composite polynomials when executing the computer program.

[0109] Embodiment 4;

[0110] This embodiment provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the above-mentioned homomorphic comparison method based on composite polynomials is implemented.

[0111] In the above embodiments provided in the present application, it should be understood that the disclosed methods, systems, devices and media can be implemented in other ways. The above described methods, systems, devices and media embodiments are only schematic. For example, the division of modules or units is only a logical function division, and there may be other division methods in actual implementation. Each functional unit can be integrated into a processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0112] The units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0113] The computer program includes computer program code, which may be in source code form, object code form, executable file or some intermediate form, etc. Computer readable media may include: any entity or device capable of carrying computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory, random access memory, electric carrier signal, telecommunication signal and software distribution medium, etc.

[0114] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A homomorphic comparison method based on composite polynomials, characterized in that: The following steps are involved: S1. Perform fully homomorphic encryption on the two plaintext data to be compared, and obtain the encrypted ciphertexts corresponding to the two plaintext data respectively; S2, perform homomorphic operation on the two encrypted ciphertexts to obtain the ciphertext difference between the two encrypted ciphertexts; S3, constructing a component quintic polynomial based on input precision and output precision; S4, inputting the ciphertext difference into a component quintic polynomial to obtain a ciphertext result; S5. Perform fully homomorphic decryption on the ciphertext result to obtain a comparison result of two plaintext data.

2. A homomorphic comparison method based on composite polynomials according to claim 1, characterized in that: Said S1 comprises: Generate private key sk and public key pk through key generation algorithm; Combined with the Enc algorithm, the public key pk is used to perform fully homomorphic encryption on the plaintext data X and Y to obtain the corresponding encrypted ciphertext C X and C Y .

3. A homomorphic comparison method based on composite polynomials according to claim 2, characterized in that: Before fully homomorphic encryption, it also includes: Determine whether the absolute value of the plaintext data X and Y is greater than the preset value M; if |X|>M, and |Y|>M, scale the plaintext data X and Y to the interval [0,1].

4. A homomorphic comparison method based on composite polynomials according to claim 1, characterized in that: The S2 comprises: The encrypted ciphertext C corresponding to the plaintext data X X Perform homomorphic multiplication with -1, and then encrypt the ciphertext C corresponding to the plaintext data Y Y Perform homomorphic multiplication to obtain the ciphertext difference; or, The encrypted ciphertext C corresponding to the plaintext data Y Y Perform homomorphic multiplication with -1, and then encrypt the ciphertext C corresponding to the plaintext data X X Perform homomorphic multiplication to obtain the ciphertext difference.

5. The homomorphic comparison method based on composite polynomial according to claim 1, characterized in that: The S3 includes: Generate initialization polynomial ax 5 +bx 3 +cx, the polynomial has the largest derivative at 0, and the function value of the maximum point is 1+∈; Combining the error value ∈' between the polynomial and the symbolic function sgn(x), a system of equations is constructed; the system of equations is expressed as: Among them, x0 and x1 represent the maximum and minimum points respectively; Based on the equation group, solve the polynomial coefficients a, b, c and the error value ∈'; The polynomial coefficients are iteratively adjusted until the error value ∈′ satisfies the output accuracy α, and a component quintic polynomial is generated.

6. A homomorphic comparison method based on composite polynomials according to claim 1, characterized in that: The S4 comprises: Generate a set of component quintic polynomials {h i }, where 1≤i≤n; including: Generate initialization polynomials h1, h 1([1-∈,1+∈]) =[1-∈1,1+∈1]; and calculate the polynomials h2, h3, …h in turn n , Among them, ∈1>∈2>…>∈ n ; Combined with the preset value W, i The component polynomial h is infinitely close to 0 i Perform compounding to obtain a composite function; wherein the composite function has the same highest degree as the symbolic function sgn(x); The ciphertext difference is input into the composite function to obtain the ciphertext result.

7. A homomorphic comparison method based on composite polynomials according to claim 1, characterized in that: The S5 comprises: Combined with the Dec algorithm, the ciphertext result is fully homomorphically decrypted using the private key sk to obtain a comparison result of the two plaintext data.

8. A homomorphic comparison system based on composite polynomials, characterized in that: include: Fully homomorphic encryption module: used to perform fully homomorphic encryption on the two plaintext data to be compared, and obtain the encrypted ciphertexts corresponding to the two plaintext data respectively; Homomorphic operation module: used to perform homomorphic operation on two encrypted ciphertexts to obtain the ciphertext difference between the two encrypted ciphertexts; Composite polynomial building block: used to build component quintic polynomials based on input precision and output precision; Polynomial evaluation module: used for inputting the ciphertext difference into a component quintic polynomial to obtain a ciphertext result; Fully homomorphic decryption module: used to perform fully homomorphic decryption on the ciphertext result to obtain a comparison result of two plaintext data.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the homomorphic comparison method based on composite polynomials is implemented as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the composite polynomial-based homomorphic comparison method according to any one of claims 1 to 7 is implemented.

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