Method and apparatus for secure conversion of privacy values
Patent Information
- Application Number
- CN202210295930.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-03-24
- Publication Date
- 2026-09-04
- Estimated Expiration
- 2042-03-24
AI Technical Summary
[0027]The methods and apparatus provided in one or more embodiments of this specification enable secure modulo conversion of the target privacy value in modulo-2 space without performing secure subtraction of the target privacy value in modulo-2 space using Boolean circuits, thus achieving secure modulo conversion of the target privacy value in modulo-2 space more quickly.
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Abstract
Description
Technical Field
[0001] This specification relates to the field of computers through one or more embodiments, and more particularly to a method and apparatus for secure conversion of privacy values. Background Technology
[0002] Secret sharing, also known as secret partitioning or secret sharing, works by splitting a private value into multiple fragments and distributing them among multiple participants. Fragments held by participants exceeding a threshold are merged to recover the original private value. When secret sharing is used in Secure Multi-party Computation (SMPC), the threshold number is typically equal to the total number of participants.
[0003] Some computational tasks may involve integer operations and bitwise operations. To support secure computation for this type of task, it is usually necessary to perform secure modulo conversion on the privacy values in the modulo-2 space involved in bitwise operations. Summary of the Invention
[0004] This specification provides a method and apparatus for secure conversion of privacy values in one or more embodiments.
[0005] In a first aspect, a secure modulo transformation method for privacy values is provided, involving a first participant and a second participant. Each participant holds a first original fragment and a second original fragment of a target privacy value within a modulo-2 space. The method is executed by the first participant. The method includes: performing a multiplication based on secure multi-party computation with the second participant, based on the first original fragment, to obtain a first intermediate fragment, wherein the sum of the first intermediate fragment and a corresponding second intermediate fragment obtained by the second participant is equal to the product of the first original fragment and first data, where the first data is obtained based on the second original fragment; determining a first target fragment based on the first intermediate fragment, such that the sum of the first target fragment and a corresponding second target fragment obtained by the second participant is equal to the target privacy value.
[0006] In one possible implementation, the result of an XOR operation on the first original fragment and the second original fragment is equal to the target privacy value.
[0007] In one possible implementation, the first target fragment is the first intermediate fragment.
[0008] In one possible implementation, the first target fragment is calculated based on the first fragment and the first original fragment.
[0009] In one possible implementation, the step of jointly performing a multiplication based on secure multi-party computation with a second participant to obtain a first intermediate slice based on the first original slice includes: calculating an intermediate value corresponding to the first original slice, wherein the intermediate value corresponding to the first original slice is one of two preset values; exchanging indication information with the second participant to indicate the intermediate values they have calculated; and calculating the first intermediate slice based on the first original slice and the intermediate value indicated by the indication information from the second participant.
[0010] Secondly, a secure modulo transformation method for privacy values is provided, involving a first participant and a second participant. Each participant holds a first original fragment and a second original fragment of the target privacy value within a modulo-2 space. The method is executed by the second participant. The method includes: performing a multiplication based on secure multi-party computation in conjunction with the first participant, according to first data, to obtain a second intermediate fragment, wherein the sum of the second intermediate fragment and the first intermediate fragment obtained by the first participant is equal to the product of the first original fragment and the first data, the first data being obtained based on the second original fragment; determining a second target fragment based on the second intermediate fragment and the second original fragment, such that the sum of the second target fragment and the first target fragment obtained by the first participant is equal to the target privacy value.
[0011] In one possible implementation, the first data is the second original fragment shown.
[0012] In one possible implementation, the first data is 1 or -1 determined based on the second original fragment.
[0013] In one possible implementation, the result of an XOR operation on the first original fragment and the second original fragment is equal to the target privacy value.
[0014] In one possible implementation, the step of jointly performing a multiplication based on secure multi-party computation with the first participant to obtain a second intermediate slice according to the first data includes: calculating an intermediate value corresponding to the first data; exchanging indication information with the first participant to indicate the intermediate values they have each calculated; and calculating the second intermediate slice according to the second original slice and the intermediate value indicated by the indication information from the first participant, wherein the intermediate value calculated by the first participant is one of two preset values.
[0015] Thirdly, a secure modulus conversion device for privacy values is provided, involving a first participant and a second participant. The first participant and the second participant each hold a first original fragment and a second original fragment of the target privacy value within a modulus-2 space. The device is deployed on the first participant. The device includes: a multiplication execution unit configured to jointly perform a multiplication based on secure multi-party computation with the second participant based on the first original fragment to obtain a first intermediate fragment, wherein the sum of the first intermediate fragment and the second intermediate fragment obtained by the second participant is equal to the product of the first original fragment and first data, the first data being obtained based on the second original fragment; and a fragment calculation unit configured to determine a first target fragment based on the first intermediate fragment, such that the sum of the first target fragment and the second target fragment obtained by the second participant is equal to the target privacy value.
[0016] In one possible implementation, the result of an XOR operation on the first original fragment and the second original fragment is equal to the target privacy value.
[0017] In one possible implementation, the first target fragment is the first intermediate fragment.
[0018] In one possible implementation, the first target fragment is calculated based on the first fragment and the first original fragment.
[0019] In one possible implementation, the multiplication execution unit is configured to calculate an intermediate value corresponding to the first original slice, wherein the intermediate value corresponding to the first original slice is one of two preset values; exchange indication information with the second participant to indicate the intermediate values they each calculate; and calculate the first intermediate slice based on the first original slice and the intermediate value indicated by the indication information from the second participant.
[0020] Fourthly, a secure modulus conversion device for privacy values is provided, involving a first participant and a second participant. The first participant and the second participant each hold a first original fragment and a second original fragment of the target privacy value within a modulus-2 space. The device is deployed on the second participant. The device includes: a multiplication execution unit configured to, in conjunction with the first participant, perform a multiplication based on secure multi-party computation to obtain a second intermediate fragment, wherein the sum of the second intermediate fragment and the first intermediate fragment obtained by the first participant is equal to the product of the first original fragment and the first data, and the first data is obtained based on the second original fragment; and a fragment calculation unit configured to determine a second target fragment based on the second intermediate fragment and the second original fragment, such that the sum of the second target fragment and the first target fragment obtained by the first participant is equal to the target privacy value.
[0021] In one possible implementation, the first data is the second original fragment shown.
[0022] In one possible implementation, the first data is 1 or -1 determined based on the second original fragment.
[0023] In one possible implementation, the result of an XOR operation on the first original fragment and the second original fragment is equal to the target privacy value.
[0024] In one possible implementation, the multiplication execution unit is configured to calculate an intermediate value corresponding to the first data; exchange indication information with the first participant to indicate the intermediate values they each calculate; and calculate a second intermediate slice based on the second original slice and the intermediate values indicated by the indication information from the first participant, wherein the intermediate values calculated by the first participant are one of two preset values.
[0025] Fifthly, a computer-readable storage medium is provided having a computer program / instructions stored thereon, wherein when the computer program / instructions are executed in a computing device, the computing device implements the method described in any one of the first aspects.
[0026] In a sixth aspect, a computing device is provided, including a memory and a processor, wherein the memory stores a computer program / instructions, and the processor, when executing the computer program, implements the method described in any one of the first aspects.
[0027] The methods and apparatus provided in one or more embodiments of this specification enable secure modulo conversion of the target privacy value in modulo-2 space without performing secure subtraction of the target privacy value in modulo-2 space using Boolean circuits, thus achieving secure modulo conversion of the target privacy value in modulo-2 space more quickly. Attached Figure Description
[0028] To more clearly illustrate the technical solutions of the embodiments in this specification, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0029] Figure 1 This is a schematic diagram illustrating the technical scenarios provided in the embodiments of this specification;
[0030] Figure 2 This is a schematic diagram of a secure modulus conversion method for privacy values provided in the embodiments of this specification;
[0031] Figure 3 This is a schematic diagram of a security modulus conversion device for privacy values provided in the embodiments of this specification;
[0032] Figure 4 This is a schematic diagram of another privacy value security mode conversion device provided in the embodiments of this specification. Detailed Implementation
[0033] The various non-limiting embodiments provided in this specification will now be described in detail with reference to the accompanying drawings.
[0034] Figure 1 This is a schematic diagram illustrating the technical scenarios provided in the embodiments of this specification. For example... Figure 1 As shown, some computational tasks may involve privacy values a0 held by participant A and a1 held by participant B. Here, a0 and a1 are single-bit data located in modulo-2 space, and a0 and a1 are fragments of the single-bit privacy data a located in modulo-2 space; that is, performing specific bitwise operations on a0 and a1 yields a. t When performing integer operations on 'a' within a space, it may be necessary to generate integers b0 and b1 represented by a bit sequence of length 't' based on a0 and a1, where the sum of integers b0 and b1 equals the privacy value a, and 't' is greater than 1. The process of generating b0 and b1 based on a0 and a1 while ensuring the security of a0 and a1 is also described as a secure modulo transformation of the privacy values a0 and a1.
[0035] In related technologies, module 2 can be generated by participant A. t A random number within the space is designated as b0. Participants A and B use a Boolean circuit based on secret sharing technology to securely compute a-b0, obtaining the value located at modulo 2. t b1 within the space is held by participant B. Performing a secure subtraction of a-b0 via a Boolean circuit requires not only executing the subtraction operation under the Boolean circuit, but also restoring a without revealing the private values a0 and a1, which takes a considerable amount of time and is relatively inefficient.
[0036] This specification provides a secure modulo conversion method and apparatus for privacy values in the embodiments. It enables secure modulo conversion of the target privacy value in modulo-2 space without performing secure subtraction of the target privacy value in modulo-2 space using Boolean circuits, thus achieving faster secure modulo conversion of the target privacy value in modulo-2 space.
[0037] Figure 2 This specification provides a secure modulus conversion method for privacy values in its embodiments. To clearly and accurately describe the technical solution provided in these embodiments, a first participant in the secure modulus conversion is designated as Participant A, and a second participant is designated as Participant B. Participant A holds a first original fragment of the privacy value within the modulus 2 space, and Participant B holds a second original fragment of the target privacy value within the modulus 2 space. The first and second original fragments are the privacy values held by Participant A and Participant B, respectively. Furthermore, Participant A and Participant B can each be implemented as any device, platform, equipment, or cluster of devices with computing / processing capabilities. Figure 2 As shown, the method may include, but is not limited to, steps 22 to 26 below.
[0038] First, in step 22, participant A and participant B jointly perform a multiplication based on secure multi-party computation, each obtaining a first intermediate fragment and a second intermediate fragment. The sum of the first intermediate fragment and the second intermediate fragment is equal to the product of the first original fragment and the first data, which is obtained from the second original fragment.
[0039] Bitwise operations on the first original fragment a0 and the second original fragment a1 can recover the target privacy value a. For example, the result of XORing the first original fragment a0 and the second original fragment a1 is equal to the target privacy value a in the modulo 2 space.
[0040] The first data in the multiplication involved in secure multi-party computation can be either the second original fragment a1, or the value 1 or -1 calculated by participant B based on the second original fragment a1. For example, participant B can use the formula q = (-1). a1The first data point is calculated to have a value of 1 or -1.
[0041] To reduce the communication overhead of joint multiplication based on secure multi-party computation by participants A and B, participant A can calculate the intermediate value corresponding to its first original fragment, and participant B can calculate the intermediate value corresponding to its first data. The intermediate value of participant A can be, for example, one of two preset values. Next, participants A and B exchange indication information indicating their respective calculated intermediate values. Finally, participant A can calculate the first intermediate fragment based on its first original fragment and the intermediate value calculated by participant B, and participant B can calculate the second intermediate fragment based on its first data and the intermediate value calculated by participant A. To further reduce the complexity of subsequent calculations, the intermediate value 'e' calculated by participant A can be relatively small, for example, 1 or -1, meaning the two preset values can be 1 or -1. Furthermore, since the intermediate value calculated by participant A is one of the two preset values, the indication information transmitted by participant A to participant B can be, for example, a 1-bit 0 or 1, thereby reducing the communication overhead of the multiplication process.
[0042] Participant A and Participant B can jointly execute a 2-out-of-1 OT protocol, whereby Participant B receives two randomly arranged values, and Participant A selects a value from these two random values along with its corresponding arrangement number. These two random values can be either two pieces of private data held by Participant B, or two random tags used to encrypt the two pieces of private data held by Participant B. For example, when Participant A and Participant B jointly execute the 2-out-of-1 OT protocol, other participants besides Participant A and Participant B can generate a random tag r0 with arrangement number 0 and a random tag r1 with arrangement number 1, send both r0 and r1 to Participant B, and select one random tag from r0 and r1 as the selection tag / selection value r. i and r i The corresponding permutation number i is sent to participant A. Correspondingly, participant A can calculate the intermediate value e, which is one of two preset values, using the selected value and its corresponding permutation number. Participant B can calculate its corresponding intermediate value f using two random values. More specifically, participant A can, for example, use the formula u = (-1) i The random multiplier u, which takes the value 1 or -1, is calculated using the formula w0 = 2r. i The random addend w0 is calculated and then applied using the formula e = (-1). p u -1The intermediate value e is calculated, where p is the first original shard a0 held by participant A; participant B can calculate the random multiplier v using the formula v = r0 - r1, and the random addend w1 using the formula w1 = -r0 - r1, and calculate the intermediate value using the formula f = qv, where q is the first data held by participant B; finally, participant A can calculate the first intermediate shard c0 using the formula c0 = floor(-ew0 - euf) / 2, and participant B can calculate the second intermediate shard c1 using the formula c1 = ceil(q - ew1) / 2.
[0043] Next, in step 24, participant A determines the first target fragment based at least on the first intermediate fragment; and in step 26, participant B determines the second target fragment based on the second intermediate fragment and the second original fragment. The sum of the first target fragment and the second target fragment is equal to the target privacy value in modulo-2 space.
[0044] When the first data is q, which is the target privacy value a in the modulo-2 space, and the second original fragment a1 in the modulo-2 space, the value of the first target fragment e0 determined by participant A can be, for example, a0-2*c0, and the value of the second target fragment e1 determined by participant B can be, for example, -2f1+a1.
[0045] When the first data is 1 or -1 determined by participant B based on the target privacy value a in the modulo-2 space and the second original fragment a1 in the modulo-2 space, for example, when the first data is determined by participant B using the formula q = (-1) a1 When the calculation is 1 or -1, the value of the first target fragment e0 determined by participant A can be, for example, the value of the first intermediate fragment c0 calculated by participant B, and the value of the second target fragment e1 determined by participant B can be, for example, f1+a1.
[0046] Based on the same concept as the aforementioned method embodiments, this specification also provides a secure modulus conversion device for privacy values, involving a first participant and a second participant. The first participant and the second participant each hold a first original fragment and a second original fragment of the target privacy value within the modulus 2 space. The device is deployed within the first participant. Figure 3As shown, the device includes: a multiplication execution unit 32, configured to jointly perform a multiplication based on secure multi-party computation with a second participant based on the first original fragment to obtain a first intermediate fragment, wherein the sum of the first intermediate fragment and the second intermediate fragment obtained by the second participant is equal to the product of the first original fragment and first data, the first data being obtained based on the second original fragment; and a fragment calculation unit 34, which determines a first target fragment based on the first intermediate fragment, such that the sum of the first target fragment and the second target fragment obtained by the second participant is equal to the target privacy value.
[0047] In one possible implementation, the result of an XOR operation on the first original fragment and the second original fragment is equal to the target privacy value.
[0048] In one possible implementation, the first target fragment is the first intermediate fragment.
[0049] In one possible implementation, the first target fragment is calculated based on the first fragment and the first original fragment.
[0050] In one possible implementation, the multiplication execution unit 32 is configured to calculate an intermediate value corresponding to the first original slice, wherein the intermediate value corresponding to the first original slice is one of two preset values; exchange indication information with the second participant to indicate the intermediate values they each calculate; and calculate the first intermediate slice based on the first original slice and the intermediate value indicated by the indication information from the second participant.
[0051] Based on the same concept as the aforementioned method embodiments, this specification also provides a secure modulus conversion device for privacy values, involving a first participant and a second participant. The first participant and the second participant each hold a first original fragment and a second original fragment of the target privacy value within the modulus 2 space. The device is deployed on the second participant. Figure 4 As shown, the device includes: a multiplication execution unit 42, configured to jointly perform a multiplication based on secure multi-party computation with the first participant according to the first data to obtain a second intermediate fragment, wherein the sum of the second intermediate fragment and the first intermediate fragment obtained by the first participant is equal to the product of the first original fragment and the first data, and the first data is obtained based on the second original fragment; and a fragment calculation unit 44, configured to determine a second target fragment according to the second intermediate fragment and the second original fragment, such that the sum of the second target fragment and the first target fragment obtained by the first participant is equal to the target privacy value.
[0052] In one possible implementation, the first data is the second original fragment shown.
[0053] In one possible implementation, the first data is 1 or -1 determined based on the second original fragment.
[0054] In one possible implementation, the result of an XOR operation on the first original fragment and the second original fragment is equal to the target privacy value.
[0055] In one possible implementation, the multiplication execution unit 42 is configured to calculate an intermediate value corresponding to the first data; exchange indication information with the first participant to indicate the intermediate values they each calculate; and calculate a second intermediate slice based on the second original slice and the intermediate values indicated by the indication information from the first participant, wherein the intermediate values calculated by the first participant are one of two preset values.
[0056] Those skilled in the art will recognize that, in one or more of the examples above, the functions described herein can be implemented using hardware, software, firmware, or any combination thereof. When implemented using software, the computer program corresponding to these functions can be stored in a computer-readable medium or transmitted as one or more instructions / code on a computer-readable medium so that when the computer program corresponding to these functions is executed by a computer, the method provided in any embodiment of this specification, performed by participant A or participant B, can be implemented by the computer.
[0057] This specification also provides a computer-readable storage medium storing a computer program thereon. When the computer program is executed in a computing device, the computing device executes the method provided in any embodiment of this specification, which is performed by participant A or participant B.
[0058] This specification also provides a computing device in its embodiments, including a memory and a processor. The memory stores executable code, and when the processor executes the executable code, it implements the method provided in any embodiment of this specification, which is executed by participant A or participant B.
[0059] The various embodiments in this specification are described in a progressive manner. Similar or identical parts in each embodiment can be referred to interchangeably. Each embodiment focuses on describing the differences from other embodiments. In particular, the apparatus embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments.
[0060] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.
[0061] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made on the basis of the technical solution of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for secure modulo conversion of a privacy value, involving a first participant and a second participant, wherein the first participant and the second participant each hold a first original fragment and a second original fragment of a target privacy value in a modulo-2 space, the method being executed by the first participant, the method comprising: Based on the first original shard, a multiplication based on secure multi-party computation is jointly performed with the second participant based on the first data. This includes: calculating an intermediate value corresponding to the first original shard, wherein the intermediate value corresponding to the first original shard is one of two preset values; exchanging indication information with the second participant to indicate the intermediate values they each calculate; calculating a first intermediate shard based on the first original shard and the intermediate value calculated by the second participant; the intermediate value calculated by the first participant is used by the second participant to calculate a second intermediate shard with the first data; wherein the sum of the first intermediate shard and the second intermediate shard is equal to the product of the first original shard and the first data; and the first data is obtained based on the second original shard. A first target fragment is determined based on the first intermediate fragment, such that the sum of the first target fragment and the second target fragment is equal to the target privacy value. The second target fragment is determined by the second participant based on the second intermediate fragment and the second original fragment.
2. The method according to claim 1, wherein, The result of XORing the first original fragment and the second original fragment is equal to the target privacy value.
3. The method according to claim 1, wherein, The first target fragment is the first intermediate fragment.
4. The method according to claim 1, wherein, The first target fragment is calculated based on the first intermediate fragment and the first original fragment.
5. A method for secure modulo conversion of a privacy value, involving a first participant and a second participant, wherein the first participant and the second participant each hold a first original fragment and a second original fragment of a target privacy value in a modulo-2 space, the method being executed by the second participant, the method comprising: Based on the first data, the first participant and the first participant jointly perform a multiplication based on secure multi-party computation, including: calculating an intermediate value corresponding to the first data, exchanging indication information with the first participant to indicate their respective calculated intermediate values, and calculating a second intermediate shard based on the first data and the intermediate value calculated by the first participant. The intermediate value calculated by the second participant is used by the first participant to calculate a first intermediate shard with the first original shard, wherein the sum of the second intermediate shard and the first intermediate shard is equal to the product of the first original shard and the first data, and the first data is obtained based on the second original shard. A second target fragment is determined based on the second intermediate fragment and the second original fragment, such that the sum of the second target fragment and the first target fragment is equal to the target privacy value. The first target fragment is determined by the first participant based on the first intermediate fragment.
6. The method according to claim 5, wherein, The first data is the second original fragment.
7. The method according to claim 5, wherein, The first data is 1 or -1 determined based on the second original fragment.
8. The method according to claim 5, wherein, The result of XORing the first original fragment and the second original fragment is equal to the target privacy value.
9. A secure modulus conversion device for privacy values, involving a first participant and a second participant, wherein the first participant and the second participant each hold a first original fragment and a second original fragment of a target privacy value in a modulus 2 space, the device being deployed on the first participant, the device comprising: The multiplication execution unit is configured to jointly perform a multiplication based on secure multi-party computation with a second participant based on first data, according to the first original slice. This includes: calculating an intermediate value corresponding to the first original slice, where the intermediate value is one of two preset values; exchanging indication information with the second participant indicating their respective calculated intermediate values; calculating a first intermediate slice based on the first original slice and the intermediate value calculated by the second participant; the intermediate value calculated by the first participant is used by the second participant to calculate a second intermediate slice with the first data; wherein the sum of the first intermediate slice and the second intermediate slice is equal to the product of the first original slice and the first data; and the first data is obtained based on the second original slice. The sharding calculation unit determines a first target shard based on the first intermediate shard, such that the sum of the first target shard and the second target shard is equal to the target privacy value. The second target shard is determined by the second participant based on the second intermediate shard and the second original shard.
10. The apparatus according to claim 9, wherein, The result of XORing the first original fragment and the second original fragment is equal to the target privacy value.
11. The apparatus according to claim 10, wherein, The first target fragment is the first intermediate fragment.
12. The apparatus according to claim 10, wherein, The first target fragment is calculated based on the first intermediate fragment and the first original fragment.
13. A secure modulus conversion device for privacy values, involving a first participant and a second participant, wherein the first participant and the second participant each hold a first original fragment and a second original fragment of a target privacy value in a modulus 2 space, the device being deployed on the second participant, the device comprising: The multiplication execution unit is configured to jointly perform a multiplication based on secure multi-party computation with the first participant based on the first original fragment, according to the first data. This includes: calculating an intermediate value corresponding to the first data; exchanging indication information with the first participant indicating their respective calculated intermediate values; and calculating a second intermediate fragment based on the first data and the intermediate value calculated by the first participant. The intermediate value calculated by the second participant is used by the first participant to calculate a first intermediate fragment with the first original fragment. The sum of the second intermediate fragment and the first intermediate fragment is equal to the product of the first original fragment and the first data. The first data is obtained based on the second original fragment. The sharding calculation unit is configured to determine a second target shard based on the second intermediate shard and the second original shard, such that the sum of the second target shard and the first target shard is equal to the target privacy value, wherein the first target shard is determined by the first participant based on the first intermediate shard.
14. The apparatus according to claim 13, wherein, The first data is the second original fragment.
15. The apparatus according to claim 13, wherein, The first data is 1 or -1 determined based on the second original fragment.
16. The apparatus according to claim 13, wherein, The result of XORing the first original fragment and the second original fragment is equal to the target privacy value.
17. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed in a computing device, the computing device performs the method of any one of claims 1-8.
18. A computing device comprising a memory and a processor, wherein the memory stores a computer program, and the processor, when executing the computer program, implements the method of any one of claims 1-8.
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