Generation method of finite field irreducible polynomial, electronic equipment and storage medium

Abstract

The invention discloses a finite field irreducible polynomial generation method, electronic equipment and a storage medium, and the method comprises the steps: selecting a base field GF (p), and constructing the self-isomorphic mapping of the base field GF (p); determining an irreducible approximate type and an AS polynomial based on self-isomorphic mapping, and solving an equation Xp-X-alpha = 0 to obtain a root a; generating a first irreducible polynomial f based on the irreducible approximate type IS and the root a, and constructing an algebraic expansion domain L of the base domain GF (p); selecting a random element on the algebraic expansion domain L through a quantum random number, and generating a minimum polynomial g; and generating a polynomial gx based on the minimum polynomial g, finally verifying whether the polynomial gx is an irreducible polynomial, and if yes, outputting the irreducible polynomial. According to the method, the probability that the constructed polynomial is an irreducible polynomial can be greatly improved; and meanwhile, real randomness is realized by utilizing quantum random characteristics, so that the method is further used for quickly constructing a hash function, and a basis is provided for unconditional quantum security.

Description

Technical Field

[0001] The present invention relates to the field of quantum security technology, and in particular to a method for generating irreducible polynomials in a finite field, an electronic device and a storage medium. Background Art

[0002] Hash is an encryption algorithm, also known as hash function or hash function. It is a one-way cryptographic system, that is, an irreversible mapping from plaintext to ciphertext, with only encryption process and no decryption process. There are many kinds of hash algorithms. Generally speaking, the longer the hash algorithm, the higher the security. Only hashes with high enough security, or hashes that no one can successfully achieve collision, are qualified to be considered for use in encryption occasions, and this type of hash algorithm is also called cryptographic hash algorithm.

[0003] The security of the current general hash algorithm scheme is based on the hash function under the preset hash seed, in which the hash function and the seed do not change. When the eavesdropper obtains the ciphertext multiple times, it can find the hash function selected by the communicating parties through statistical methods based on this feature, thereby cracking the keys of the communicating parties. Therefore, the existing hash algorithm scheme cannot meet the requirements of one-time one-key, and when intercepted, it has the disadvantages of being crackable and vulnerable to attacks. In order to cope with the above threats, quantum encryption technology has emerged. Quantum encryption has attracted much attention as an unconditionally secure cryptographic technology. Quantum encryption technology is based on the principle of quantum state non-cloning in quantum mechanics, and uses a randomly changing hash function. In each communication, the two parties generate a different hash function from the last time and exchange them, which can achieve one-time one-key.

[0004] The hash function mentioned in the patent "A quantum digital signature and quantum digital signcryption method" with application number 2021113360202 is generated based on a set of input random numbers and irreducible polynomials, that is, the implementation of the quantum hash algorithm requires the generation of irreducible polynomials first. The current method of generating irreducible polynomials is to continuously use random numbers as the coefficients of each term in the polynomial except the highest term, and then verify the generated polynomial. This method of generating irreducible polynomials by continuously checking whether it is an irreducible polynomial is obviously not efficient enough.

[0005] Therefore, how to improve the efficiency of generating irreducible polynomials becomes a key issue in improving the generation rate of hash functions. Summary of the invention

[0006] Purpose of the invention: In order to solve the problem of low efficiency in generating irreducible polynomials mentioned in the background technology, the purpose of the present invention is to provide a method for generating irreducible polynomials in a finite field, an electronic device and a storage medium. The method of the present invention can greatly increase the probability that the constructed polynomial is an irreducible polynomial; at the same time, by utilizing the random characteristics of quantum, true randomness is achieved, which is then used for the rapid construction of hash functions, providing a basis for unconditional quantum security.

[0007] Technical solution: The present invention provides a method for generating irreducible polynomials in a finite field, comprising the following steps:

[0008] (1) Select a base field GF(p) and construct an automorphism mapping F of the base field GF(p): X→X p , that is, F(x)=X p is an automorphism mapping on the base field GF(p); based on this automorphism mapping, the irreducible concept type is determined And determine the AS polynomial X over the base field GF(p) p -X-α, and for equation X p -X-α=0 Solve to get the root a;

[0009] (2) generating a first irreducible polynomial f based on the irreducible profile IS and the root a, wherein the highest order of the first irreducible polynomial f is consistent with the highest order of the irreducible polynomial to be generated, and the highest order is denoted by k;

[0010] (3) constructing an algebraic extension field L of the base field GF(p) based on the first irreducible polynomial f, wherein the order of the algebraic extension field L is k;

[0011] (4) selecting random elements on the algebraic extension field L by quantum random numbers, and generating a minimum polynomial g based on the selected random elements;

[0012] (5) Generate a polynomial gx based on the minimum polynomial g, and verify whether the polynomial gx is an irreducible polynomial over the base field GF(p). If so, output the irreducible polynomial; if not, return to step (4) and reselect random elements to generate the minimum polynomial.

[0013] Furthermore, the automorphism mapping method for constructing the base field GF(p) is the Euler method.

[0014] Furthermore, the specific process of generating the first irreducible polynomial f based on the irreducible profile IS and the root a is:

[0015] 1) obtaining the number of iterations m based on the value k of the highest order of the irreducible polynomial to be generated;

[0016] 2) Perform m iterations on the irreducible probability model IS and obtain

[0017]

[0018] Among them, the initial value P (0) is (X p -1), Q (0) for For any 0<k≤m, X (k) for P (k) for Q (k) for

[0019] 3) Based on the iterative result and the root a, generate the first irreducible polynomial f = P (m) -aQ (m) .

[0020] Furthermore, the algebraic expansion field L of the base field GF(p) constructed based on the first irreducible polynomial f refers to:

[0021] Let polynomial f = P (m) -aQ (m) = 0, solve the equation P (m) -aQ (m) = 0, add the multiple roots obtained by solving to the base field GF(p) to expand the elements in the base field GF(p); the expanded element set still constitutes a finite field, which is the algebraic expansion field L of the base field GF(p), where the number of elements in the algebraic expansion field L is p m indivual.

[0022] Furthermore, the specific process of selecting random elements by quantum random numbers on the algebraic expansion field L and generating the minimum polynomial g based on the selected random elements is:

[0023] a) Generate t quantum random numbers in chronological order through a quantum random number generator. The set of quantum random numbers is denoted as {q 1 ,q 2 ,…,q j ,…q t}, j∈{1,2,…,t}, generate quantum random number q j The time is t j ;

[0024] b) algebraically expand the field L by p m elements are classified, that is, the elements in the algebraic expansion field L are used to perform a modulo operation with the number of quantum random numbers t, and the result of the modulo operation is used as the classification basis to classify the p elements in the algebraic expansion field L. melements are classified; then the elements with the same remainder obtained by modulo operation with t are classified into one category, and finally p m Elements are classified into t categories;

[0025] c) Suppose there exists L in the i-th category i elements, i∈{1,2,…,t}, then the elements in the i-th class are numbered from 1 to L i ;

[0026] d) When the quantum random number generator is at t j Get a random number q at a time point j When selecting the jth class of the algebraic expansion field element classification, j mod L i )+1 element l, where mod represents the modulus operation;

[0027] e) Compute the minimal polynomial g of element l over the algebraic extension field L.

[0028] Furthermore, the polynomial gx generated based on the minimum polynomial g refers to:

[0029] First, the minimum polynomial g is used as the initial polynomial g0. When there is a coefficient in the initial polynomial g0 that is in the algebraic expansion field L but not in the base field GF(p), the dual element of the coefficient is repeatedly found through the dual relationship of the elements in the algebraic expansion field L to construct the dual polynomial g0′. The dual polynomial g0′ is multiplied by the initial polynomial g0 to obtain the polynomial g1. Repeat the above process, gradually increase the degree of the polynomial and change its coefficients until a polynomial gx is generated, and all the coefficients of the polynomial gx are in the base field GF(p).

[0030] Furthermore, verifying whether the polynomial gx is an irreducible polynomial over the base field GF(p) refers to: verifying whether the highest order of the polynomial gx is k, and verifying whether the polynomial gx is irreducible over the base field GF(p).

[0031] The present invention also includes an electronic device, comprising

[0032] a memory for storing a set of instructions; and

[0033] At least one processor is configured to execute the set of instructions so that the electronic device performs the method as claimed in the preceding claims.

[0034] The present invention also includes a non-transitory computer-readable storage medium storing a set of instructions for a computer, which, when executed, causes the computer to perform the method as claimed in the preceding claims.

[0035] Beneficial effects of the present invention: The method for generating irreducible polynomials in a finite field proposed in the present invention has wide applicability, can be effectively implemented in software and hardware, and greatly improves the probability that the constructed polynomial is an irreducible polynomial; at the same time, it utilizes the quantum random characteristics to achieve true randomness, which is then used for the rapid construction of hash functions, providing a basis for unconditional quantum security. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a schematic diagram of a host according to an embodiment of the present application;

[0037] Figure 2 This is a schematic diagram of the specific implementation steps of this application. DETAILED DESCRIPTION

[0038] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0039] At present, the common method of generating irreducible polynomials is to first take an n-bit (for example, 129-bit) random number with both 1 at the beginning and end as the coefficient of the polynomial, and then use g 2 mod p method to check whether the polynomial is irreducible; if the check result is no, then the random number is not the coefficient of the irreducible polynomial, and you need to take another n-digit random number with both 1 at the beginning and end as the coefficient of the polynomial, and then use g 2 Mod p method is used to check, and the above operation is repeated until the polynomial is verified to be irreducible. It is conceivable that the number of such loop operations and the amount of data are large.

[0040] In view of this, the present application proposes a method for generating irreducible polynomials in a finite field to solve the technical problems that the current generation of irreducible polynomials is inefficient and requires a lot of time and computing power.

[0041] This method is Figure 1 The host 100 shown executes, that is, the host 100 is an electronic device that executes the method.

[0042] like Figure 1 As shown, the host 100 may include: a processor 102, a memory 104, a network interface 106, a peripheral interface 108 and a bus 110. The processor 102, the memory 104, the network interface 106 and the peripheral interface 108 are connected to each other in communication within the host through the bus 110.

[0043] Processor 102 may be a central processing unit (CPU), an image processor, a neural network processor (NPU), a microcontroller (MCU), a programmable logic device, a digital signal processor (DSP), an application specific integrated circuit (ASIC), or one or more integrated circuits. Processor 102 may be used to perform functions related to the technology described in this application. In some embodiments, processor 102 may also include multiple processors integrated into a single logical component. Figure 1 As shown, the processor 102 may include a plurality of processors 102a, 102b, and 102c.

[0044] The memory 104 may be configured to store data (eg, instruction sets, computer codes, intermediate data, etc.). In some embodiments, the simulation test system for simulation test design may be a computer program stored in the memory 104. Figure 1 As shown, the data stored in the memory may include program instructions (for example, program instructions for implementing the method for generating irreducible polynomials in finite fields of the present application) and data to be processed (for example, the memory may store temporary codes generated during the compilation process). The processor 102 may also access the program instructions and data stored in the memory, and execute the program instructions to operate on the data to be processed. The memory 104 may include a volatile storage device or a non-volatile storage device. In some embodiments, the memory 104 may include a random access memory (RAM), a read-only memory (ROM), an optical disk, a magnetic disk, a hard disk, a solid-state drive (SSD), a flash memory, a memory stick, etc.

[0045] The network interface 106 can be configured to provide communication with other external devices to the host 100 via a network. The network can be any wired or wireless network capable of transmitting and receiving data. For example, the network can be a wired network, a local wireless network (e.g., Bluetooth, WiFi, near field communication (NFC) etc.), a cellular network, the Internet or a combination thereof. It is understood that the type of network is not limited to the above specific examples. In some embodiments, the network interface 106 can include any number of network interface controllers (NICs), radio frequency modules, transceivers, modems, routers, gateways, adapters, cellular network chips, etc., in any combination.

[0046] The peripheral interface 108 can be configured to connect the host 100 to one or more peripheral devices to achieve information input and output. For example, the peripheral devices can include input devices such as a keyboard, a mouse, a touch pad, a touch screen, a microphone, and various sensors, and output devices such as a display, a speaker, a vibrator, and an indicator light.

[0047] The bus 110 may be configured to transmit information between various components of the host 100 (e.g., the processor 102, the memory 104, the network interface 106, and the peripheral interface 108), such as an internal bus (e.g., a processor-memory bus), an external bus (USB port, PCI-E bus), etc.

[0048] It should be noted that, although the above host architecture only shows the processor 102, the memory 104, the network interface 106, the peripheral interface 108 and the bus 110, in the specific implementation process, the host architecture may also include other components necessary for normal operation. In addition, it can be understood by those skilled in the art that the above host architecture may also only include the components necessary for implementing the embodiment of the present application, and does not necessarily include all the components shown in the figure.

[0049] like Figure 2 As shown, the present application proposes a method for generating irreducible polynomials in a finite field, which can be performed as follows Figure 1 The host computer performs the following steps of the proposed method:

[0050] (1) Select a base field GF(p) and construct an automorphism mapping F of the base field GF(p): X→X p , that is, F(x)=X p is an automorphism mapping on the base field GF(p); based on this automorphism mapping, the irreducible concept type is determined and determine the Artin-Schreier AS polynomial X over the base field GF(p) p -X-α, and for equation X p -X-α=0 Solve to get the root a;

[0051] The automorphism mapping method for constructing the base field GF(p) may be the Euler method.

[0052] In a finite field, p is the eigenvalue of the finite field, and the number of numbers in the field is at least 2. In cryptographic applications, the base field is generally GF(2). Therefore, in this application, the base field can be GF(2). In the case of GF(2) as the base field, the irreducible concept here is

[0053] The constant α of the AS polynomial satisfies the following formula:

[0054]

[0055] Wherein, p is the eigenvalue of the base field GF(p), for example, the eigenvalue of the base field GF(2) is 2, and k is the value of the highest order of the irreducible polynomial to be generated.

[0056] Let AS polynomial X p -X-α is 0, for equation X p -X-α=0 and solve to obtain the root a of the equation.

[0057] (2) generating a first irreducible polynomial f based on the irreducible profile IS and the root a, wherein the highest order of the first irreducible polynomial f is consistent with the highest order of the irreducible polynomial to be generated, and the highest order is denoted by k;

[0058] The specific process of generating the first irreducible polynomial f based on the irreducible model IS and the root a is:

[0059] 1) The number of iterations m is obtained based on the value k of the highest order of the irreducible polynomial to be generated, and the highest order obtained in each iteration is the pth power of the previous one; for example, the highest order of the irreducible polynomial to be generated is k=128, for the irreducible probability type The highest order obtained in each iteration is the square of the previous one. Therefore, the highest order of 128 requires 7 iterations to obtain (i.e., 2^7=128). The iterative order change process is: 2^1->2^2->2^3->2^4->2^5->2^6->2^7.

[0060] 2) Perform m iterations on the irreducible probability model IS and obtain

[0061]

[0062] Among them, the initial value P (0) is (X p -1), Q (0) for For any 0<k≤m, X (k) for P (k) for Q (k) for

[0063] 3) Based on the iterative result and the root a, generate the first irreducible polynomial f = P (m) -aQ (m) .

[0064] (3) constructing an algebraic extension field L of the base field GF(p) based on the first irreducible polynomial f, wherein the order of the algebraic extension field L is k;

[0065] Specifically, an algebraic expansion field L of the base field GF(p) constructed based on the first irreducible polynomial f refers to: Let polynomial f = P (m) -aQ (m) = 0, solve the equation P (m) -aQ(m) = 0, add the multiple roots obtained by solving to the base field GF(p) to expand the elements in the base field GF(p); the expanded element set still constitutes a finite field, which is the algebraic expansion field L of the base field GF(p), where the number of elements in the algebraic expansion field L is p m indivual.

[0066] (4) Selecting a random element on the algebraic extension field L by using quantum random numbers, and generating a minimum polynomial g based on the selected random element. The specific process is as follows:

[0067] a) Generate t quantum random numbers in chronological order through a quantum random number generator. The set of quantum random numbers is denoted as {q 1 ,q 2 ,…,q j ,…q t}, j∈{1,2,…,t}, generate quantum random number q j The time is t j ;

[0068] b) algebraically expand the field L by p m elements are classified, where the superscript m represents the algebraic meaning of the power; that is, the elements in the algebraic expansion field L are used to perform a modulo operation with the number of quantum random numbers t, and the result of the modulo operation is used as the classification basis to classify the p elements in the algebraic expansion field L. m elements are classified; then the elements with the same remainder obtained by modulo operation with t are classified into one category, so that p can be finally m Elements are classified into t categories;

[0069] c) Suppose there exists L in the i-th category i elements, i∈{1,2,…,t}, for this L i elements, the identification can be to number the elements in the i-th category from 1 to L i ;

[0070] d) When the quantum random number generator is at t j Get a random number q at a time point j When selecting the jth class of the algebraic expansion field element classification, j mod L i )+1 element l, where mod represents the modulus operation; here, the element category in the expansion domain is determined by time, and the specific element in the category is determined by quantum random numbers, thus achieving true randomness;

[0071] e) Compute the minimal polynomial g of element l over the algebraic extension field L.

[0072] (5) Generate a polynomial gx based on the minimal polynomial g and verify whether the polynomial gx is an irreducible polynomial over the base field GF(p). If so, output the irreducible polynomial. If not, return to step (4) and reselect a random element to generate the minimal polynomial.

[0073] Among them, the polynomial gx generated based on the minimum polynomial g is:

[0074] First, the minimum polynomial g is used as the initial polynomial g0. When there is a coefficient in the initial polynomial g0 that is in the algebraic expansion field L but not in the base field GF(p), the dual element of the coefficient is repeatedly found through the dual (conjugate) relationship of the elements in the algebraic expansion field L to construct the dual (conjugate) polynomial g0′. The dual (conjugate) polynomial g0′ is multiplied by the initial polynomial g0 to obtain the polynomial g1. Repeat the above process, gradually increase the degree of the polynomial and change its coefficients until a polynomial gx is generated, and all the coefficients of the polynomial gx are in the base field GF(p).

[0075] Verifying whether a polynomial gx is an irreducible polynomial over the base field GF(p) means: verifying whether the highest order of the polynomial gx is k, and verifying whether the polynomial gx is irreducible over the base field GF(p). If both the highest order and irreducibility are satisfied, the output polynomial gx is an irreducible polynomial of order k over the base field GF(p).

[0076] The probability that the polynomial gx generated by the method of the present invention is an irreducible polynomial of order k on the base field GF(p) is at least 50%. Compared with the current method of blindly selecting a group of random numbers as coefficients of the polynomial to construct the polynomial, the probability that the constructed polynomial is an irreducible polynomial is greatly improved, and the time for constructing the polynomial is shortened.

[0077] The embodiment of the present application also includes an electronic device, which can be Figure 1 The host 100 in the electronic device may include a memory for storing a set of instructions; and at least one processor configured to execute the set of instructions so that the electronic device executes the above-mentioned method for generating irreducible polynomials in a finite field.

[0078] The embodiment of the present application also includes a non-transitory computer-readable storage medium, which stores a set of instructions for a computer, and the set of instructions is used to enable the computer to execute the above-mentioned method for generating irreducible polynomials in a finite field when executed.

[0079] The computer-readable medium of this embodiment includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, read-only compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device.

[0080] It can be seen that the method for generating irreducible polynomials in finite fields proposed in the present invention has wide applicability, can be effectively implemented in software and hardware, and greatly improves the probability that the constructed polynomial is an irreducible polynomial; at the same time, it utilizes the characteristics of quantum randomness to achieve true randomness, which is then used for the rapid construction of hash functions, providing a basis for unconditional quantum security.

Claims

1. A method for generating irreducible polynomials in a finite field, characterized in that: The following steps are involved: (1) Select a base field GF(p) and construct an automorphism mapping F of the base field GF(p): X→X p , that is, F(x)=X p is an automorphism mapping on the base field GF(p); based on this automorphism mapping, the irreducible concept type is determined And determine the AS polynomial X over the base field GF(p) p -X-α, and for equation X p -X-α=0 Solve to get the root a; (2) generating a first irreducible polynomial f based on the irreducible profile IS and the root a, wherein the highest order of the first irreducible polynomial f is consistent with the highest order of the irreducible polynomial to be generated, and the highest order is denoted by k; (3) constructing an algebraic extension field L of the base field GF(p) based on the first irreducible polynomial f, wherein the order of the algebraic extension field L is k; (4) selecting random elements on the algebraic extension field L by quantum random numbers, and generating a minimum polynomial g based on the selected random elements; (5) Generate a polynomial gx based on the minimum polynomial g, and verify whether the polynomial gx is an irreducible polynomial over the base field GF(p). If so, output the irreducible polynomial; if not, return to step (4) and reselect random elements to generate the minimum polynomial.

2. The method for generating irreducible polynomials in a finite field according to claim 1, characterized in that: The automorphism mapping method for constructing the base field GF(p) is the Euler method.

3. The method for generating irreducible polynomials in a finite field according to claim 1, characterized in that: The specific process of generating the first irreducible polynomial f based on the irreducible profile IS and the root a is: 1) obtaining the number of iterations m based on the value k of the highest order of the irreducible polynomial to be generated; 2) Perform m iterations on the irreducible probability model IS and obtain Among them, the initial value P (0) is (X p -1), Q (0) for For any 0<k≤m, X (k) for P (k) for Q (k) for 3) Based on the iterative result and the root a, generate the first irreducible polynomial f = P (m) -aQ (m) .

4. The method for generating irreducible polynomials in a finite field according to claim 3, characterized in that: The algebraic expansion field L constructed based on the first irreducible polynomial f is: Let polynomial f = P (m) -aQ (m) = 0, solve the equation P (m) -aQ (m) = 0, add the multiple roots obtained by solving to the base field GF(p) to expand the elements in the base field GF(p); the expanded element set still constitutes a finite field, which is the algebraic expansion field L of the base field GF(p), where the number of elements in the algebraic expansion field L is p m indivual.

5. The method for generating irreducible polynomials in a finite field according to claim 4, characterized in that: The specific process of selecting random elements through quantum random numbers on the algebraic expansion field L and generating the minimum polynomial g based on the selected random elements is: a) Generate t quantum random numbers in chronological order through a quantum random number generator. The set of quantum random numbers is recorded as {q1,q2,…,q j ,…q t }, j∈{1,2,…,t}, generate quantum random number q j The time is t j ; b) algebraically expand the field L by p m elements are classified, that is, the elements in the algebraic expansion field L are used to perform a modulo operation with the number of quantum random numbers t, and the result of the modulo operation is used as the classification basis to classify the p elements in the algebraic expansion field L. m elements are classified; then the elements with the same remainder obtained by modulo operation with t are classified into one category, and finally p m elements are classified into t categories; c) Suppose there exists L in the i-th category i elements, i∈{1,2,…,t}, then the elements in the i-th class are numbered from 1 to L i ; d) When the quantum random number generator is at t j Get a random number q at a time point j When selecting the jth class of the algebraic expansion field element classification, j mod L i )+1 element l, where mod represents the modulus operation; e) Compute the minimal polynomial g of element l over the algebraic extension field L.

6. The method for generating irreducible polynomials in a finite field according to claim 1, characterized in that: The generating polynomial gx based on the minimum polynomial g refers to: First, the minimum polynomial g is used as the initial polynomial g0. When there is a coefficient in the initial polynomial g0 that is in the algebraic expansion field L but not in the base field GF(p), the dual element of the coefficient is repeatedly found through the dual relationship of the elements in the algebraic expansion field L to construct the dual polynomial g0′. The dual polynomial g0′ is multiplied by the initial polynomial g0 to obtain the polynomial g1. Repeat the above process, gradually increase the degree of the polynomial and change its coefficients until a polynomial gx is generated, and all the coefficients of the polynomial gx are in the base field GF(p).

7. The method for generating irreducible polynomials in a finite field according to claim 6, characterized in that: The verifying whether the polynomial gx is an irreducible polynomial over the base field GF(p) refers to: verifying whether the highest order of the polynomial gx is k, and verifying whether the polynomial gx is irreducible over the base field GF(p).

8. An electronic device, characterized in that: include a memory for storing a set of instructions; and At least one processor is configured to execute the set of instructions so that the electronic device performs the method according to any one of claims 1 to 7.

9. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium stores a set of instructions for a computer, which, when executed, causes the computer to perform the method of any one of claims 1 to 7.

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