A function secret sharing method of a boolean interval inclusion function

Abstract

The application discloses a function secret sharing method of a Boolean type interval containing function and belongs to the field of big data security calculation and privacy protection; firstly, a distributed computing scene of two servers which do not collude with each other and a user end is built; then, the user end initiates an evaluation request signal to the two servers, carries an input share and which is secret shared by an ASS algorithm, and executes a Boolean type interval containing function bDICF to generate a pair of server side keys and respectively and respectively send the keys to the two servers. Finally, the two servers respectively randomly mask the respective input shares, obtain masked inputs, combine the held keys and, perform the evaluation algorithm of the two ibDCF on the masked inputs, obtain share and of the evaluation result of whether belonging to the interval, and return respective output shares to the client, and the client XOR reconstructs a plaintext judgment result. The application reduces communication overhead and calculation complexity while completing nonlinear interval operation under single round communication.

Description

Technical Field

[0001] This invention belongs to the field of secure computing and privacy protection of big data, and relates to a method for sharing function secrets of Boolean interval contained functions. Background Technology

[0002] With the development of big data and large models, the demand for privacy protection is constantly increasing. In secure multi-party computation (MPC) and privacy-preserving machine learning, comparison operations are common non-linear operations, such as LeakyReLU, decision tree branching, and threshold judgment; Distributed Comparison Function (DCF) is another important technology. [1] These operations can be performed efficiently. However, in more complex scenarios, simple comparisons are no longer sufficient, and there is an urgent need for an MPC method that can efficiently perform range inclusion operations while ensuring data security.

[0003] With the continuous development of Functional Secret Sharing (FSS), researchers have proposed various optimization schemes for the design of Distributed Interval Containment Functions (DICF). While existing DICF schemes have made some progress in reducing communication rounds, they suffer from key structure redundancy, significant space overhead, and limited adaptability to interval containment functions. This high resource consumption is particularly pronounced when processing large-scale data, making them difficult to apply in resource-constrained or real-time-critical scenarios.

[0004] Therefore, how to achieve efficient, general, and scalable interval inclusion function computation while ensuring security remains an important problem that needs to be solved in the fields of MPC and privacy-preserving machine learning.

[0005] Existing DICF methods require optimizing the range comparison gates of two DCF keys to require only one DCF key, but they have the following drawbacks:

[0006] 1. In the original FSS scheme, each DCF key contains Correction each Each contains at least one element of length 1. Group elements are bitwise, and group element operations are typically slower than ordinary integer operations. Therefore, this not only increases computational costs but also results in longer key lengths, leading to higher storage and communication costs.

[0007] 2. In the key evaluation phase, the protocol needs to perform iterative computation for each bit of the input. In each iteration, not only Boolean operations (such as XOR) are needed, but also addition and subtraction of group elements. As the dimension of the input increases, these operations will linearly accumulate, causing high evaluation computation delay.

[0008] The professional terms are explained as follows:

[0009] MPC: Secure Multi-Party Computation, as a cryptographic technology, allows multiple participants to jointly complete a computing task while keeping their own input data private. MPC ensures that no one can obtain the private input of others except for the calculation result, thus realizing data privacy protection.

[0010] SS:Secret Sharing, a cryptographic method that splits a secret (such as data or parameters) into multiple "shares" and distributes them to multiple participants. A single share itself does not contain useful information, and only when a certain number of shares are combined can the original secret be recovered.

[0011] FSS: Function Secret Sharing. An extended secret sharing method, mainly used for secure computation of nonlinear functions.

[0012] DCF: Distributed Comparison Function. The comparison function is "split" into multiple keys, each participant holds a key and performs local calculation, only when the results are added together, the correct comparison result can be obtained. The definition of the comparison function is usually:

[0013]

[0014] where is the threshold, and the DCF output is used to determine whether the comparison relationship is satisfied.

[0015] DICF: Distributed Interval Containment Function. A function secret sharing protocol based on FSS, used to determine whether an input value falls within a certain interval.

[0016] bDICF: Boolean Distributed Interval Containment Function. It is a lightweight and improved version of DICF, specifically optimized for efficiency and key size, outputting a boolean value, which can significantly reduce communication and storage overhead. Summary of the Invention

[0017] In existing DICF schemes, the correction word CW that makes up the key is of length . The group elements are 36 bits long, which increases the key complexity and leads to low computational efficiency in the evaluation phase. Furthermore, the output of the evaluation phase is of length 36 bits. Using a group element with a specific number of bits would lead to high communication costs. Therefore, this invention proposes a function secret sharing method for Boolean interval containment functions, focusing on Boolean outputs and specifically for interval comparison scenarios involving only outputs of 0 or 1. By reconstructing the key composition and replacing the group element correction word with a Boolean correction word, it is possible to complete nonlinear interval operations in a single round of communication while reducing communication overhead and computational complexity.

[0018] The method for sharing the function secrets within the Boolean interval contains the following steps:

[0019] Step 1: Set up two servers that do not collude with each other. and and distributed computing scenarios on the user end;

[0020] The user end is a trusted entity responsible for holding the plaintext input and algorithm parameters, and for dividing the input plaintext dataset into two shares. and Send them to the corresponding servers respectively. and ;

[0021] The two servers determine their respective information shares based on a key evaluation algorithm. and Each assessment was conducted separately to determine whether the share fell within the specified range. Share of the assessment results and The result is returned to the user, who then XORs it to reconstruct the plaintext judgment result. .

[0022] Step 2: The user sends an evaluation request signal to both servers, carrying the input share after being secretly shared using the ASS algorithm. and ;

[0023] Step three, the user end executes the Boolean interval containing function bDICF to generate a pair of server side keys , and respectively issues to two servers.

[0024] The specific process is:

[0025] Step 301, the user end initializes parameters; including security parameters , random input / output masks and ; interval values of plaintext interval comparison[ , ];

[0026] Step 302, first offset the interval boundary using the security parameters and the input / output masks, expand the right end point to construct an extended boundary auxiliary value , calculate the mask intermediate value ;

[0027] , , ,

[0028] Step 303, calculate the parameters for generating ibDCF keys ;

[0029]

[0030] Among them, represents the number of bits, represents the integer ring, represents the integer ring of module .

[0031] Step 304, using the initialization parameters and the parameters , call the key generation algorithm Gen of ibDCF to generate a key pair ;

[0032] Gen

[0033] is an incremental Boolean distributed comparison function;

[0034] Step 305, based on the mask intermediate value , and introduce the Boolean correction term to correct the boundary condition, together with the mask shared value, embedded in the key;

[0035]

[0036] Step 306: Split the Boolean correction term to obtain two shares:

[0037]

[0038]

[0039] The two parties each hold a shared share. and , Represents an integer ring modulo 2.

[0040] Step 307: Set the share and key pair of the Boolean correction term. Combined into the final key ;

[0041] The formula is: .

[0042] Step 4: The two servers will each input their respective shares. and Randomly select masks to obtain mask inputs. Combined with the key held and For mask input Perform two evaluations using the ibDCF algorithm to determine whether the share falls within the range. Share of the assessment results and ;

[0043] The specific steps are as follows:

[0044] Step 401: Each server parses its own key to obtain... and ;

[0045] Step 402: Mask the input Based on the left and right boundary points of the interval , Comparison values ​​are obtained by translation. and :

[0046]

[0047]

[0048] Step 403: Call the evaluation function Eval respectively. exist and Perform an interval comparison operation to obtain the share of the Boolean comparison results for the left and right endpoints. and ;

[0049] Eval

[0050] Eval

[0051] Step 404, calculating the comparison flag , for judging whether the input is between and .

[0052]

[0053] Step 405, combining the comparison flag with the share and , and the correction term share , to synthesize the output share by the XOR rule;

[0054]

[0055] Step five, the two servers return the respective output shares to the client, and the client XORs them to reconstruct the plaintext judgment result .

[0056] If , it indicates that the input is in the interval , otherwise it is not in the interval.

[0057] The advantages of the present application are:

[0058] 1. In the generation and discrimination of secure images, the bDICF used in the present application realizes multiple acceleration compared with the prior art, and the running time is significantly reduced in the secure training process, significantly improving the computing efficiency.

[0059] 2. In the secure training and data synthesis process, the bDICF used in the present application reduces the communication volume by multiple times, significantly reduces the communication overhead, can significantly reduce the data transmission cost across servers, and improves the scalability and stability of the system.

[0060] 3. The quality of the generated result is close to the plaintext training. The bDICF can reduce numerical errors and gradient jitter, ensure the training of the generator and discriminator to be more stable, so as to generate higher quality images, which are closer to the plaintext training results, and achieve the best score on some data sets. While ensuring privacy security, the quality of the generated image is not lost, ensuring the accuracy and practicality of the result.

[0061] 4. Overall cost savings and enhanced feasibility. By reducing runtime and communication volume, bDICF significantly outperforms existing technologies in terms of hardware and software resource consumption, thus lowering deployment costs. Experiments have verified the feasibility of bDICF for security training and data synthesis in a real-world environment, demonstrating its high application and promotion value. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of a function secret sharing method for Boolean interval contained functions according to the present invention;

[0063] Figure 2 This is a flowchart illustrating a method for sharing function secrets within a Boolean interval containing functions, as described in this invention. Detailed Implementation

[0064] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0065] This invention provides a function secret sharing method (bDICF) for Boolean interval contained functions, such as... Figure 1 and Figure 2 As shown, the specific steps are as follows:

[0066] Step 1: Set up two servers that do not collude with each other. and and distributed computing scenarios on the user end;

[0067] The user end is a trusted entity responsible for holding the plaintext input and algorithm parameters, and for dividing the input plaintext dataset into two shares. and Send them to the corresponding servers respectively. and ;

[0068] The two servers only receive their respective share of information and do not collude with each other throughout the process, providing a platform for subsequent key distribution and evaluation.

[0069] The two servers determine their respective information shares based on a key evaluation algorithm. and Each assessment was conducted separately to determine whether the share fell within the specified range. Share of the assessment results and The result is returned to the user, who then XORs it to reconstruct the plaintext judgment result. .

[0070] Step two, the user end initiates an evaluation request signal to two servers, carrying the input shares after secret sharing by ASS algorithm and ;

[0071] When it is necessary to determine whether a plaintext input falls within the interval , the client initiates an evaluation request signal to two servers. The request carries the input shares and , which lay the foundation for subsequent comparison and interval determination in the ciphertext.

[0072] Step three, the user end executes the Boolean interval inclusion function bDICF to generate a pair of server-side keys and respectively issues them to the two servers.

[0073] The specific process is as follows:

[0074] Step 301, the user end initializes parameters; including security parameters , random input / output masks and ; interval values for plaintext interval comparison , ;

[0075] Step 302, first offset the interval boundaries using the security parameters and input / output masks, expand the right endpoint to construct an extended boundary auxiliary value , and calculate the mask intermediate value ;

[0076] , , ,

[0077] Step 303, calculate the parameters for generating ibDCF keys ;

[0078]

[0079] wherein represents the number of bits, represents the integer ring, represents the integer ring modulo .

[0080] Step 304, use the initialization parameters and parameters to call the key generation algorithm Gen of ibDCF to generate a key pair ;

[0081] Gen

[0082] Incremental Boolean type distributed comparison function;

[0083] Step 305, based on the mask intermediate value , and introduce a Boolean correction term to correct the boundary condition, together with the mask shared value embedded in the key;

[0084]

[0085] Step 306, the Boolean correction term is divided into two shares:

[0086]

[0087]

[0088] Two participants hold the shared shares and , represent the integer ring modulo 2.

[0089] Step 307, the share of the Boolean correction term and the key pair are combined into the final key ;

[0090] The formula is: .

[0091] Step four, two servers will randomly mask the input shares and respectively, get the masked input , combined with the held key and , twice ibDCF evaluation algorithm is carried out on the masked input , get the share and whether the share belongs to the interval evaluation result.

[0092] The specific steps are:

[0093] Step 401, each server will analyze the key held respectively, get and ;

[0094] Step 402, the masked input according to the left and right two boundary points of the interval , Translation: Obtain comparison value by translation and :

[0095]

[0096]

[0097] Step 403, call evaluation function Eval respectively Perform interval comparison operation on and to obtain the share of the Boolean comparison result of the left and right endpoints and ;

[0098] Eval

[0099] Eval

[0100] Step 404, calculate comparison flag , used to determine whether it is between and .

[0101]

[0102] Step 405, combine comparison flag with shares and , and correction share , to synthesize output share by XOR rule;

[0103]

[0104] The entire evaluation is only in the ciphertext, without exposing any plaintext intermediate quantity.

[0105] Step five, two servers return their respective output shares to the client, and the client XOR reconstructs the plaintext judgment result .

[0106] If , it means that the input is located in the interval , otherwise it is not in the interval.

[0107] In this way, the function secret sharing scheme of the Boolean interval inclusion function of "initiate request-key generation-ciphertext evaluation-plaintext judgment" is completed.

[0108] The DICF in the prior art can be implemented by the following core parts:

[0109] (1) In the key generation phase:

[0110] The security parameters , input offset and output offset are taken as inputs of the function Gen ;

[0111] First, the boundary offset for generating the DCF key is calculated , and the DCF generation function is called to generate the DCF key pair :

[0112] Gen

[0113] For the interval , the offset interval endpoints , are set, and .

[0114]

[0115] In the integer domain , the uniform random sampling and are taken as correction terms , and the correction terms satisfy:

[0116]

[0117] For any participant, the DCF key and the correction term are combined to obtain the complete key . .

[0118] Let .

[0119] (2) In the key evaluation phase:

[0120] First, the key evaluation phase function Eval is used to split the key, and the key is decomposed into the DCF key and the correction term : the segmentation formula is: .

[0121] Then, the input after the cyclic offset is calculated , and is set for left endpoint comparison, and is set for right endpoint comparison; .

[0122] For and Two DCF evaluations result in and :

[0123] The specific formula is: Eval , Eval ;

[0124] Both parties calculate as output, and and are summed to obtain the interval judgment result.

[0125] In this scheme, the DCF key of each party is composed of the following parts:

[0126]

[0127] Among them, is a random value, and and are group elements, which increases the key size and calculation complexity.

[0128] In the prior art, (1) in the key generation phase, the original correction word is composed of a large-scale group element, and the key length is too large. The present application replaces it with a Boolean element and reconstructs the correction word CW, thereby significantly reducing the size of the key. At the same time, this improvement also reduces the dependence on large integer group operations in the key generation and propagation process, and reduces the calculation complexity in the evaluation phase.

[0129] (2) In the key evaluation phase, the present application also introduces a Boolean element to improve the evaluation algorithm. Unlike the prior art, which requires transmission and processing of group elements, this scheme only needs to transmit and calculate Boolean data during the evaluation process, avoiding large number operations and redundant communication. Therefore, the communication volume of the protocol is greatly reduced, and the evaluation efficiency is significantly improved, especially suitable for large-scale distributed security computing scenarios.

[0130] The Boolean distributed interval inclusion function bDICF of the present application has two main calculation stages:

[0131] (1) In the key generation phase, the client generates the bDICF key of each server using the bDICF key generation algorithm, and feeds back to each server. Each server's corresponding bDICF key includes the share of the input parameter.

[0132] (2) Key evaluation phase, two servers that do not collude with each other will evaluate the user input share according to the key evaluation algorithm and , to obtain the share of the evaluation result of whether the share belongs to the interval , and .

[0133] The implementation of the bDICF of the present application will utilize the ibDCF algorithm, which is an incremental Boolean distributed comparison function, which is an improved version of the DCF, mainly for interval comparison.

[0134] (1) First, introduce the key generation phase of ibDCF:

[0135] Key generation algorithm Gen , the specific content is as follows:

[0136]

[0137] It is worth noting that because the output of ibDCF is Boolean , the control word can be designed as , where and are both Boolean control bits used to replace group operations, and are bit-level Boolean correction items that can significantly reduce the key size.

[0138] In the key generation phase of the bDICF of the present application, first, a input mask is generated using a pseudo-random generator (PRG) to mask the interval boundary, and an extended boundary is constructed. By combining the original boundary with the offset, the intermediate value of the mask is generated. Then, the key generation algorithm of ibDCF is called to generate the key component, and the Boolean correction item is introduced to correct the errors that may occur in the boundary condition, and is embedded in the key together with the mask shared value, the specific process is as follows:

[0139]

[0140] Algorithm process:

[0141] 1. Calculate the auxiliary variables , , , , where is used for subsequent ibDCF operations that only support the form of , , , respectively , , are the masked representations.

[0142] 2. Compute parameters for generating ibDCF key .

[0143] 3. Call ibDCF key generation algorithm Gen , generate ibDCF key pair .

[0144] 4. Compute correction term , use Boolean indicator function and mask to ensure output is correct and randomized.

[0145] 5. Split correction term , so that two participants hold share and respectively.

[0146] 6. Combine correction term and ibDCF key together to form final key.

[0147] (2) Key evaluation phase

[0148] First introduce the key evaluation algorithm Eval of ibDCF.

[0149]

[0150] In the evaluation phase of the bDICF of the present application, the server receives the masked input and parses the key, constructs two comparison values and . By calling the evaluation function of ibDCF twice, the protocol performs interval comparison operations on and , and generates intermediate shared results. Finally, by combining the comparison flag with the correction term , the final result is synthesized using XOR and modulo 2 operations.

[0151]

[0152] Detailed analysis as follows

[0153] Algorithm parameters: : participant identifier; : key held by the participant; : input masked at random.

[0154] Algorithm process:

[0155] 1. Analyze the key, decompose the key held by each party into and .

[0156] 2. The masked input According to the left and right endpoints of the interval , Do translation to get and .

[0157] 3. Call Eval Evaluation function, and save the result as .

[0158] 4. Call Eval Evaluation function, and save the result as .

[0159] 5. Calculate the comparison flag , used to determine Whether between and .

[0160] 6. Synthesize , , , , To form the final output share.

[0161] Because the output of the existing ibDCF only needs a boolean value, the correction part in the correction word can be completely replaced by a boolean element, so as to avoid group element operation, shorten the key, and also greatly reduce the communication overhead in the transmission process, improve the efficiency.

[0162] Finally, the calculated evaluation result is returned to the user by each server respectively, and the user reconstructs the plaintext evaluation result by using the additive homomorphism property of secret sharing locally.

[0163] The function secret sharing method bDICF of the Boolean interval inclusion function of the application, firstly, the communication amount in the model training and data synthesis and other secure computing stages is reduced by several times compared with the traditional DICF, which can effectively reduce the communication overhead in the secure multi-party computing stage, meet the data security computing demand in the bandwidth limited environment; secondly, it remains stable under large-scale batch input, supports high-precision gradient update and effective loss calculation, can guarantee the stability of the training process, the output result is close to the plaintext training precision, and the data synthesis quality is improved.

Claims

1. A method of function secret sharing of a Boolean interval inclusion function, characterized by, The specific steps are as follows: Step one, build a distributed computing scenario including two servers that do not collude with each other and , and a user end; Step two, the user end initiates an evaluation request signal to the two servers, carrying the input share after the ASS algorithm secret sharing and ; Step three, the user end executes the Boolean type interval containing function bDICF to generate a pair of server side keys and respectively issues to two servers; The specific process is as follows: Step 301, user terminal initializes parameters; including security parameters , random input / output mask and ; Interval values for plaintext interval comparison , ] Step 302, offset the interval boundary first with the security parameter and the input / output mask, expand the right end point to construct an extended boundary auxiliary value , calculate the mask intermediate value ; , , , Step 303, computing parameters for generating ibDCF keys ; wherein, representing the number of bits, representing the ring of integers, representing the modulus of the ring of integers; Step 304, using the initialization parameters and parameters , calling the key generation algorithm Gen of the ibDCF , generating a key pair ; Gen Incremental Boolean type distributed comparison function; Step 305, based on the mask intermediate value and introducing a Boolean correction term to correct the boundary conditions, together with the mask shared value, embedded in the key; In step 306, the Boolean correction term is divided into two shares: Two participants each hold a share and , denotes the ring of integers modulo 2; Step 307, combining the share of the Boolean correction term and the key pair combining into a final key ; The formula is: ; Step four, two servers will be their respective input shares and respectively randomly masked, get masked input , combined with the key and , on the masked input two ibDCF evaluation algorithm, get the evaluation results of the share whether belongs to the interval share and ; Step five, both servers return their output shares to the client, which XORs them to reconstruct the plaintext decision and back to the client, which XORs them to reconstruct the plaintext decision ; If then it is indicated that the input lies in the interval otherwise not.

2. The method of claim 1, wherein, In the step one, the user end is a trusted entity, responsible for holding the plaintext input and algorithm parameters, and dividing the input plaintext data set into two shares and , respectively sent to the corresponding server and ; The two servers determine their respective information shares based on a key evaluation algorithm. and Each assessment was conducted separately to determine whether the share fell within the specified range. Share of the assessment results and The result is returned to the user, who then XORs it to reconstruct the plaintext judgment result. .

3. The method of claim 1, wherein, The step four is specifically as follows: Step 401, each server parses the key it holds to obtain and ; Step 402, mask the input According to the left and right boundary points of the interval , Make a translation to get the comparison value And : Step 403, respectively call evaluation function Eval In And Perform interval comparison operation, get the share of the Boolean comparison result of the left and right endpoints And ; Eval Eval Step 404, calculating comparison flag , for judging whether between and ; Step 405, combine comparison tokens and shares and and correction term shares , combine output shares by XOR rule ; 。

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