Secret sharing compression transmission method, system and terminal equipment

Abstract

The invention discloses a secret sharing compression transmission method and system and terminal equipment, and the transmission method comprises the steps: dividing all secrets into batch secret fragments, and constructing a scrambling-secret embedding-error correction polynomial; respectively substituting the public interpolation points into a scrambling-secret embedding-error correction polynomial to obtain sharing values corresponding to the secret fragments; distributing all sharing values of each secret fragment and the corresponding public interpolation points to each participant; carrying out addition operation or multiplication operation on the sharing value of the batch of secret fragments corresponding to the same public interpolation point so as to obtain secure sharing at each participant; and selecting a sharing point to carry out Reed-Solomon decoding to obtain a secret original value after addition operation or multiplication operation. The method is applied to the field of secret transmission, can support safe, efficient, error-correctable and parallel sharing and calculation of any number of secret data on the premise of limiting the number of participants, and breaks through the communication and calculation bottleneck of the existing secret sharing protocol.

Description

Technical Field

[0001] This invention relates to the field of covert transmission technology, specifically a covert sharing and compressed transmission method, system, and terminal device. Background Technology

[0002] With the development of technologies such as federated learning, IoT collaborative computing, blockchain, and privacy computing, collaborative computing among multiple parties under conditions of mutual distrust has become a critical requirement. To ensure data privacy during transmission and computation, secret-sharing protocols are widely used in secure multi-party computing systems.

[0003] The most commonly used secret sharing method natively only supports sharing a single secret. If multiple secrets need to be shared, a polynomial needs to be constructed independently for each secret and distributed separately, resulting in an exponential increase in communication and computational burden.

[0004] To address this issue, some studies have proposed multi-secret compression schemes that encode multiple secrets into a single high-order polynomial and share them all at once. However, most of these schemes rely on high-order interpolation, requiring a large number of participants to correctly recover the secrets. They are unsuitable for scenarios with a small number of participants and suffer from the following drawbacks: High communication costs: The secret requires construction using traditional methods. A polynomial, generating Each share has a communication complexity of O(n). It is not suitable for bandwidth-constrained devices and edge environments; Participant Number Limit: The secret compression sharing scheme requires a certain number of participants. ,like Very large and If the scope is very small (e.g., only three parties), the recovery conditions cannot be met, and the agreement becomes invalid. The computation lacks parallelism: multi-secret addition or multiplication operations require decoding the secrets before the operation, which cannot be directly parallelized at the sharing layer, resulting in low system performance. Lack of robustness: Once a portion of the share is lost or erroneous, traditional solutions cannot recover the secret, making the system fragile and lacking error correction capabilities. Summary of the Invention

[0005] To address the core technical problems in the existing technology of secure sharing of multiple secrets, such as high communication complexity, poor parallelism, strict limitation on the number of participants, and lack of robustness, this invention provides a secret sharing compressed transmission method, system, and terminal device. Under the premise of limiting the number of participants, it can support secure, efficient, error-correctable, and parallel sharing and computation of any number of secret data, breaking through the communication and computation bottlenecks of existing secret sharing protocols.

[0006] To achieve the above objectives, the present invention provides a secret sharing and compressed transmission method, comprising the following steps: Step 1, Obtain the number of participants and the total amount of secret data possessed by all participating parties. And select within the prime number field Different public interpolation points ; Step 2, divide all the secrets into The secret is batched into secret fragments, and based on the scrambling-embedding-error-correction polynomials used to construct each secret fragment. , , The number of secret data contained in a secret fragment; Step 3, Substituting each of the public interpolation points into the scrambling-embedding-error-correction polynomial of each secret segment, we obtain the corresponding secret segment. Share value , ; Step 4: Distribute all shared values ​​and corresponding public interpolation points of each secret shard to each participant, i.e., each participant receives the shared set as follows: ; Step 5: For each participant, the corresponding public interpolation point... The shared value of each secret shard is added or multiplied to obtain a certain amount for each participant. A secure sharing; Step 6, in All of the participating parties Select at least one from the security sharing. Reed-Solomon decoding is performed at each sharing point to obtain the secret original value after addition or multiplication operations. Let be the total degree of the scrambling-embedding-error-correction polynomial.

[0007] In one embodiment, in step 2, the scrambling-embedding-error-correction polynomial is specifically:

[0008] in, For the first Scrambling-embedding-error-correction polynomials for batch secret fragmentation. The disturbance coefficient is... For the first Batch secret fragments contain A secret data, Redundant symbols used for error correction For privacy threshold, To correct the number of redundant items, It is a prime number field.

[0009] In one embodiment, in step 3, the shared value , representing the first The secret fragments in the first The shared value of a public interpolation point.

[0010] In one embodiment, step 5, the addition operation specifically involves:

[0011] in, For public interpolation points Place Secure sharing of batch secret fragments after additive operations includes A secret data fragment.

[0012] In one embodiment, step 5, the multiplication operation specifically involves: Step 501: Obtain the public interpolation point Place Share value of batch secret shards And let the iteration coefficients ; Step 502, sharing values ​​based on Beaver triplet technology and sharing value Multiply to obtain temporary safe sharing ; Step 503, let Then, make a judgment Is it true or false? If so, temporarily secure sharing As a public interpolation point Place Securely share and output secret fragments after multiplication operations; Otherwise, proceed to step 504; Step 504: Securely share temporary data based on Beaver triplet technology. and sharing value Multiply to obtain a new temporary security sharing Then proceed to step 503 again.

[0013] In one embodiment, the process of multiplying two batches of shared values ​​based on the Beaver triplet technique is as follows: Obtain the interpolation points of each participant. Two shared values ​​to be multiplied And shared shards of Beaver triples pre-generated by each participant. And satisfy ; Calculate the difference value , for: , ; Broadcast by each participating party )and Then, the global difference is recovered and publicly obtained using the Lagrange interpolation method. , for: , ; Each participating party calculates its local value at the public interpolation point. Share value The result of multiplication ,for:

[0014] That is equivalent to a true secret A secure sharing.

[0015] In one embodiment, the process of obtaining the secret original value in step 6 is as follows: Select One point to share:

[0016] Selected The input of each share point to the Reed-Solomon decoder recovers the complete original polynomial:

[0017] The coefficients are polynomials, where the secret coefficients are... That is, the original value of the secret is .

[0018] To achieve the above objectives, the present invention also provides a secret sharing compressed transmission system, which performs secret sharing compressed transmission using the above method. The secret sharing compressed transmission system includes: The protocol input and parameter setting unit is used to obtain the number of participants. and the total amount of secret data possessed by all participating parties. And select within the prime number field Different public interpolation points ; Secret partitioning and polynomial constructive units are used to divide all secrets into... The secret is batched into secret fragments, and based on the scrambling-embedding-error-correction polynomials used to construct each secret fragment. , , The number of secret data contained in a secret fragment; Share generation unit, used to generate Substituting each of the public interpolation points into the scrambling-embedding-error-correction polynomial of each secret segment, we obtain the corresponding secret segment. Share value , ; The sharing and distribution unit is used to distribute all shared values ​​and corresponding public interpolation points of each secret shard to each participant; that is, each participant receives a shared set of values. ; Parallel computing units are used to compute the same public interpolation point corresponding to each participant. The shared value of each secret shard is added or multiplied to obtain a certain amount for each participant. A secure sharing; Secret recovery unit, used in All of the participating parties Select at least one from the security sharing. Reed-Solomon decoding is performed at each sharing point to obtain the secret original value after addition or multiplication operations. Let be the total degree of the scrambling-embedding-error-correction polynomial.

[0019] To achieve the above objectives, the present invention also provides a terminal device, wherein the terminal device is provided with: Memory, used to store programs; A processor is configured to execute the program stored in the memory, and when the program is executed, the processor is configured to perform the method as described above.

[0020] Compared with the prior art, the present invention has the following beneficial technical effects: 1. The secret sharing and compressed transmission method in this invention has low communication complexity. Multiple secrets are embedded in a single polynomial, requiring only one polynomial evaluation to generate the sharing of multiple secrets, thus reducing communication overhead compared to traditional methods. Reduced to ,in It significantly reduces communication costs while also supporting large-scale secret compression and sharing of tens of millions of records; 2. This invention utilizes a batch grouping mechanism, enabling the sharing of any number of secrets even in situations with only three parties, thus breaking the "..." The limitation of "can effectively adapt to real-world scenarios with very few participants"; 3. This invention performs addition and multiplication directly at the sharing layer without decoding and re-encoding using Beaver triples, and also supports parallel multiplication calculations in any batch and any order, effectively maintaining sharing privacy while improving computational efficiency; 4. This invention achieves error detection and correction at the sharing layer by embedding error correction codes into higher-order terms of a polynomial, thereby improving the robustness and availability of the protocol and adapting to network noise and node failures. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art 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 the structures shown in these drawings without creative effort.

[0022] Figure 1 This is a flowchart of the secret sharing and compressed transmission method in an embodiment of the present invention; Figure 2 This is a structural block diagram of the secret sharing compressed transmission system in an embodiment of the present invention; Figure 3 This is a structural block diagram of the terminal device in an embodiment of the present invention.

[0023] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0025] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0026] Example 1 This embodiment discloses a secret-sharing compressed transmission method. By designing a multi-secret batch sharing mechanism, it balances security, efficiency, and robustness, and is suitable for secure multi-party computation in environments with limited bandwidth and a limited number of participants. (Reference) Figure 1The secret sharing and compressed transmission method in this embodiment specifically includes the following steps: Step 1, Obtain the number of participants and the total amount of secret data possessed by all participating parties. And select within the prime number field Different public interpolation points ; Step 2, divide all the secrets into Batch secret fragments, and construct scrambling-embedding-error-correction polynomials for each secret fragment. , , The number of secret data contained in a secret fragment; Step 3, Substituting each public interpolation point into the scrambling-embedding-error-correction polynomial of each secret segment, we obtain the corresponding secret segment. Share value , ; Step 4: Distribute all shared values ​​and corresponding public interpolation points of each secret shard to each participant, i.e., each participant receives the shared set as follows: ; Step 5: For each participant, the corresponding public interpolation point... The shared value of each secret shard is added or multiplied to obtain a certain amount for each participant. A secure sharing; Step 6, in All of the participating parties Select at least one from the security sharing. Reed-Solomon decoding is performed at each sharing point to obtain the secret original value after addition or multiplication operations. Let be the total degree of the scrambling-embedding-error-correction polynomial.

[0027] After dividing all the secrets into During the process of approving secret partitioning, the following must be met: ,in This is a threshold parameter representing the strength of privacy protection in the protocol.

[0028] In practical implementation, to simultaneously achieve multi-secret compression and sharing with a robust error correction mechanism, this embodiment proposes a unified polynomial construction method. This polynomial in a single expression simultaneously carries the following three types of information: low-order random coefficients: providing privacy-preserving perturbations; mid-order coefficients: embedding multiple secrets to be shared; and high-order coefficients: embedding error-correcting redundancy information. Let the... The secret was approved , Let be a prime number field. Then the th The scrambling-embedding-error-correction polynomial for batch secret fragmentation is:

[0029] in, Perturbation coefficients generated for random sources are used to enhance privacy protection. Redundant symbols used for error correction Let be the number of redundant error-correcting terms, representing the error-correcting capability. The total degree of the scrambling-embedding-error-correcting polynomial is: Therefore, recovering this batch of secrets and completing the error correction will require at least the collection of [data / information]. A sharing point.

[0030] In the specific implementation of step 3, the shared value , representing the first The secret fragments in the first The shared value of a public interpolation point.

[0031] After distributing all shared values ​​of each secret shard and their corresponding public interpolation points to each participant, each participant receives [a certain amount] at each public interpolation point. Each share refers to the collection of shares received by each participant. Because this embodiment uses a compressed secret sharing scheme, The secret is compressed into a polynomial, requiring only evaluation. Each time (per batch), only one construction is needed in total. Therefore, the communication complexity of this embodiment is _ polynomials. In traditional secret-sharing schemes, because each secret requires a separately constructed polynomial, it needs to be sent... Each share has a communication complexity of O(n). And because Therefore, the secret sharing and compressed transmission method in this embodiment significantly reduces communication costs while also supporting large-scale secret compression and sharing at the level of tens of millions. For example, if there are A secret, each batch ,but Compared to the previous transmission requirements, In this embodiment, the secret sharing compression transmission method only requires one sharing. Sharing reduces communication overhead by 90%.

[0032] The secret sharing and compressed transmission method in this embodiment, in addition to confidentiality and compressed sharing, also supports parallel addition and multiplication operations on the secret, and does not require decoding or restoring the original secret between sharing operations, which greatly improves the execution efficiency in secure multi-party computation scenarios.

[0033] In practice, the secret parallel addition operation refers to the operation performed by the participating parties on each public interpolation point. The batch of secret fragments is directly added locally to obtain the corresponding secure share, namely:

[0034] in, For public interpolation points Place Secure sharing of batch secret fragments after additive operations includes A secret data fragment, which does not require restoration during the process. It can be directly calculated, and multiple secret addition operations support batch processing and parallelization, which can significantly improve computational throughput.

[0035] During the multiplication of the secret, because the two multiplication operations have a certain degree of... Multiplying polynomials will result in a product of degree 2. This exceeds the original sharing structure, making it impossible to directly recover the secret later. Therefore, this embodiment uses Beaver triplet technology for multiplication operations. The multiplication operation process in this embodiment is as follows: Step 501: Obtain the public interpolation point Place Share value of batch secret shards And let the iteration coefficients ; Step 502, sharing values ​​based on Beaver triplet technology and sharing value Multiply to obtain temporary safe sharing ; Step 503, let Then, make a judgment Is it true or false? If so, temporarily secure sharing As a public interpolation point Place Securely share and output secret fragments after multiplication operations; Otherwise, proceed to step 504; Step 504: Securely share temporary data based on Beaver triplet technology. and sharing value Multiply to obtain a new temporary security sharing Then proceed to step 503 again.

[0036] In the specific implementation process, the process of multiplying the two batches of shared values ​​based on the Beaver triplet technique is as follows: Obtain the interpolation points of each participant. Two shared values ​​to be multiplied And shared shards of Beaver triples pre-generated by each participant. And satisfy ; Calculate the difference value , for: , ; Broadcast by each participating party )and Then, the global difference is recovered and publicly obtained using the Lagrange interpolation method. , for: , ; Each participating party calculates its local value at the public interpolation point. Share value The result of multiplication ,for:

[0037] That is equivalent to a true secret A secure sharing.

[0038] In the specific implementation of step 6, the process of obtaining the secret original value through Reed-Solomon decoding is as follows: Select One point to share:

[0039] It is worth noting the subscript of the above sharing points. Compared with the aforementioned public interpolation points Safe sharing subscript Not equivalent. Public interpolation point Safe sharing subscript All refer to The th public interpolation point One publicly shared interpolation point. The index of the shared point mentioned above. This refers to the selected The first of the sharing points There are several sharing points, and different sharing points may be the same public interpolation point for different participants; In the selected Among the sharing points, the most is If the input is incorrect, Reed-Solomon decoding can be used. This decoding algorithm is often used in error correction scenarios to recover polynomials. During the decoding process, the input... Each sharing point can automatically identify and correct secure sharing in erroneous sharing points. The specific implementation process of automatically identifying and correcting erroneous sharing points during this decoding process is a conventional technique in Reed-Solomon decoding in this field, so it will not be described in detail in this embodiment. Finally, by interpolating using the correct share point values, the complete original polynomial can be recovered, as follows:

[0040] The coefficients are polynomials, where the secret coefficients are... That is, the original value of the secret is , which represents the secret after addition or multiplication.

[0041] It is worth noting that, although this embodiment Figure 1 The steps are shown sequentially as indicated by the arrows, but they are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order in which these steps are performed; they can be executed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0042] Example 2 Based on the secret sharing compressed transmission method in Embodiment 1, this embodiment discloses a secret sharing compressed transmission system, referencing... Figure 2 The secret sharing compressed transmission system includes a protocol input and parameter setting unit, a secret fragmentation and polynomial construction unit, a sharing generation unit, a sharing distribution unit, a parallel computing unit, and a secret recovery unit, specifically: The protocol input and parameter setting unit is used to obtain the number of participants. and the total amount of secret data possessed by all participating parties. And select within the prime number field Different public interpolation points ; Secret partitioning and polynomial constructs are used to divide all secrets into... Batch secret fragments, and construct scrambling-embedding-error-correction polynomials for each secret fragment. , , The number of secret data contained in a secret fragment; The sharing generation unit is used to... Substituting each public interpolation point into the scrambling-embedding-error-correction polynomial of each secret segment, we obtain the corresponding secret segment. Share value , ; The sharing and distribution unit is used to distribute all shared values ​​of each secret shard and their corresponding public interpolation points to each participant; that is, each participant receives a shared set of values. ; Parallel computing units are used to compute the same public interpolation point corresponding to each participant. The shared value of each secret shard is added or multiplied to obtain a certain amount for each participant. A secure sharing; Secret recovery unit is used in All of the participating parties Select at least one from the security sharing. Reed-Solomon decoding is performed at each sharing point to obtain the secret original value after addition or multiplication operations. Let be the total degree of the scrambling-embedding-error-correction polynomial.

[0043] In this embodiment, the specific working processes and principles of the protocol input and parameter setting unit, the secret fragmentation and polynomial construction unit, the sharing generation unit, the sharing distribution unit, the parallel computing unit, and the secret recovery unit are the same as those in Embodiment 1, and therefore will not be described again in this embodiment. Each unit module can be implemented entirely or partially through software, hardware, or a combination thereof. Each unit module can be embedded in or independent of the processor in the computer device in hardware form, or it can be stored in the memory of the computer device in software form, so that the processor can call and execute the operations corresponding to the above unit modules.

[0044] Example 3 like Figure 3 The diagram illustrates a terminal device disclosed in this embodiment, comprising a transmitter, a receiver, a memory, and a processor. The transmitter transmits instructions and data, the receiver receives instructions and data, the memory stores computer-executed instructions, and the processor executes the computer-executed instructions stored in the memory to implement the method described in Embodiment 1 above.

[0045] It is important to note that the aforementioned memory can be either standalone or integrated with the processor. When the memory is set up independently, the terminal device also includes a bus for connecting the memory and the processor.

[0046] The above description is only a preferred embodiment of the present invention and does not limit the scope of protection of the present invention. All equivalent structural transformations made under the inventive concept of the present invention using the contents of the present invention specification and drawings, or direct / indirect applications in other related technical fields, are included within the scope of protection of the present invention.

Claims

1. A method for secret sharing and compressed transmission, characterized in that, Includes the following steps: Step 1, Obtain the number of participants and the total amount of secret data possessed by all participating parties. And select within the prime number field Different public interpolation points ; Step 2, divide all the secrets into The secret is batched into secret fragments, and based on the scrambling-embedding-error-correction polynomials used to construct each secret fragment. , , The number of secret data contained in a secret fragment; Step 3, Substituting each of the public interpolation points into the scrambling-embedding-error-correction polynomial of each secret segment, we obtain the corresponding secret segment. Share value , ; Step 4: Distribute all shared values ​​and corresponding public interpolation points of each secret shard to each participant, i.e., each participant receives the shared set as follows: ; Step 5: For each participant, the corresponding public interpolation point... The shared value of each secret shard is added or multiplied to obtain a certain amount for each participant. A secure sharing; Step 6, in All of the participating parties Select at least one from the security sharing. Reed-Solomon decoding is performed at each sharing point to obtain the secret original value after addition or multiplication operations. Let be the total degree of the scrambling-embedding-error-correction polynomial.

2. The secret sharing and compressed transmission method according to claim 1, characterized in that, In step 2, the scrambling-embedding-error-correction polynomial is specifically: in, For the first Scrambling-embedding-error-correction polynomials for batch secret fragmentation. The disturbance coefficient is... For the first Batch secret fragments contain A secret data, Redundant symbols used for error correction For privacy threshold, To correct the number of redundant items, It is a prime number field.

3. The secret sharing and compressed transmission method according to claim 2, characterized in that, In step 3, the shared value , representing the first The secret fragments in the first The shared value of a public interpolation point.

4. The secret sharing and compressed transmission method according to claim 3, characterized in that, In step 5, the addition operation specifically involves: in, For public interpolation points Place Secure sharing of batch secret fragments after additive operations includes A secret data fragment.

5. The secret sharing and compressed transmission method according to claim 3, characterized in that, In step 5, the multiplication operation specifically involves: Step 501: Obtain the public interpolation point Place Share value of batch secret shards And let the iteration coefficients ; Step 502, sharing values ​​based on Beaver triplet technology and sharing value Multiply to obtain temporary safe sharing ; Step 503, let Then, make a judgment Is it true or false? If so, temporarily secure sharing As a public interpolation point Place Securely share and output secret fragments after multiplication operations; Otherwise, proceed to step 504; Step 504: Securely share temporary data based on Beaver triplet technology. and sharing value Multiply to obtain a new temporary security sharing Then proceed to step 503 again.

6. The secret sharing and compressed transmission method according to claim 5, characterized in that, The process of multiplying two batches of shared values ​​based on the Beaver triplet technique is as follows: Obtain the interpolation points of each participant. Two shared values ​​to be multiplied And shared shards of Beaver triples pre-generated by each participant. And satisfy ; Calculate the difference value , for: , ; Broadcast by each participating party )and Then, the global difference is recovered and publicly obtained using the Lagrange interpolation method. , for: , ; Each participating party calculates its local value at the public interpolation point. Share value The result of multiplication ,for: That is equivalent to a true secret A secure sharing.

7. The secret sharing compressed transmission method according to claim 4, 5, or 6, characterized in that, The process of obtaining the secret original value in step 6 is as follows: Select One point to share: Selected The input of each share point to the Reed-Solomon decoder recovers the complete original polynomial: The coefficients are polynomials, where the secret coefficients are... That is, the original value of the secret is .

8. A secret sharing compressed transmission system, characterized in that, Secret sharing and compressed transmission is performed using the method described in any one of claims 1 to 7, wherein the secret sharing and compressed transmission system comprises: The protocol input and parameter setting unit is used to obtain the number of participants. and the total amount of secret data possessed by all participating parties. And select within the prime number field Different public interpolation points ; Secret partitioning and polynomial constructive units are used to divide all secrets into... The secret is batched into secret fragments, and based on the scrambling-embedding-error-correction polynomials used to construct each secret fragment. , , The number of secret data contained in a secret fragment; Share generation unit, used to generate Substituting each of the public interpolation points into the scrambling-embedding-error-correction polynomial of each secret segment, we obtain the corresponding secret segment. Share value , ; The sharing and distribution unit is used to distribute all shared values ​​and corresponding public interpolation points of each secret shard to each participant; that is, each participant receives a shared set of values. ; Parallel computing units are used to compute the same public interpolation point corresponding to each participant. The shared value of each secret shard is added or multiplied to obtain a certain amount for each participant. A secure sharing; Secret recovery unit, used in All of the participating parties Select at least one from the security sharing. Reed-Solomon decoding is performed at each sharing point to obtain the secret original value after addition or multiplication operations. Let be the total degree of the scrambling-embedding-error-correction polynomial.

9. A terminal device, characterized in that, The terminal device is equipped with: Memory, used to store programs; A processor for executing the program stored in the memory, wherein when the program is executed, the processor is configured to perform the method as described in any one of claims 1 to 7.

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