A method and system for privacy-preserving aggregation of discrete gaussian noise secure sampling

Abstract

The application discloses a discrete Gaussian noise security sampling method and system for multi-party privacy aggregation, and comprises the following steps: each participant provides a uniform bit stream; the uniform bit stream is subjected to security sampling to obtain a secure uniform bit stream; geometric noise is sampled and converted based on the secure uniform bit stream to obtain discrete Laplace noise; and the discrete Laplace noise is subjected to rejection sampling based on the secure uniform bit stream to obtain discrete Gaussian noise. The method and system can guarantee malicious security.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of information security, and particularly relates to a discrete Gaussian noise secure sampling method and system for multi-party privacy aggregation. BACKGROUND

[0002] In today's big data era, with the development of artificial intelligence, cloud computing, Internet of Things and other technologies, data has become a new production factor, and has very important value in economy, society and technology. On the other hand, with the wide application of data, the problem of data privacy has become increasingly prominent. The leakage of data privacy will lead to personal property damage, enterprise secret leakage, and even national security threats. In today's era, how to realize data utilization and data sharing under the premise of protecting data privacy is a very important problem, which has important significance for promoting productivity development, protecting the legal rights and interests of individuals and organizations, and maintaining national interests.

[0003] Differential privacy is a widely used privacy protection mechanism that can analyze and utilize aggregated data without revealing individual data. A common method to achieve differential privacy is to add random noise to the aggregated data and release the noisy results, so that attackers cannot infer individual data privacy from the query results. Multi-party differential privacy refers to the scenario where data is held by multiple parties and the differential privacy mechanism is constructed by all participating parties. The implementation of multi-party differential privacy includes central differential privacy and local differential privacy. The principle of central differential privacy is that each party submits the original data to the center node for aggregation and noise addition. The principle of local differential privacy is that each party adds noise to the original data and submits it to the center node for aggregation. Both of the above methods have certain defects, among which, central differential privacy requires the center node to be a trusted node, otherwise the original data of each party will be leaked to the center node. Local differential privacy adds excessive noise, which will reduce the usability of the final data. To solve the problems of the above two schemes, one solution is to use secure multi-party computing technology to simulate a trusted center node and securely implement the aggregation-noise addition process in central differential privacy. This scheme combines the advantages of central differential privacy and local differential privacy, can protect the data privacy of each party without a trusted center node, and at the same time avoids adding excessive noise and improves the usability of data.

[0004] One of the keys of the above-mentioned secure multi-party computation based scheme is the secure sampling of noise. In differential privacy, Laplace noise and Gaussian noise are two most commonly used noise types, in which Gaussian noise is more suitable for implementing differential privacy mechanism for high-dimensional aggregation applications. Gaussian noise is further divided into continuous Gaussian noise and discrete Gaussian noise. Continuous Gaussian noise takes a range of real numbers, while discrete Gaussian noise takes a range of integers. Compared with continuous Gaussian noise, discrete Gaussian noise can be naturally represented by computers and provides better differential privacy guarantee. Currently, the existing secure sampling scheme of discrete Gaussian noise only guarantees semi-honest security guarantee, and in the face of malicious attackers, the existing sampling scheme cannot guarantee security. SUMMARY

[0005] The purpose of the present application is to provide a discrete Gaussian noise secure sampling method and system for multi-party privacy aggregation, and to apply the secure sampling method and system to federated learning to ensure malicious security.

[0006] To achieve the above-mentioned purpose of the application, the embodiment provides a discrete Gaussian noise secure sampling method for multi-party privacy aggregation, comprising the following steps:

[0007] Each participant provides a uniform bit stream;

[0008] Securely sampling the uniform bit stream to obtain a secure uniform bit stream;

[0009] Sampling and converting the geometric noise based on the secure uniform bit stream to obtain discrete Laplace noise;

[0010] Rejecting sampling the discrete Laplace noise based on the secure uniform bit stream to obtain discrete Gaussian noise.

[0011] Preferably, securely sampling the uniform bit stream to obtain a secure uniform bit stream comprises:

[0012] Using secure multi-party computation technology to perform XOR operation on the uniform bit stream to obtain a secure uniform bit stream.

[0013] Preferably, the sampling and converting the geometric noise based on the secure uniform bit stream to obtain discrete Laplace noise comprises:

[0014] Sampling the geometric noise distribution based on the secure uniform bit stream to obtain geometric noise;

[0015] Converting the geometric noise into discrete Laplace noise.

[0016] Preferably, the sampling the geometric noise distribution based on the secure uniform bit stream to obtain geometric noise comprises:

[0017] Defining a geometric noise distribution fG (x; q) = (1 - q) * q x x e N, wherein q represents a geometric noise distribution parameter, and takes a value of q = e -1 / t t is a discrete Laplace distribution parameter, x represents a noise point in the geometric noise distribution, and N represents a natural number;

[0018] sampling a series of Bernoulli distributions based on the geometric noise distribution and in combination with secure uniform bit stream to obtain a series of bits b i wherein i = 0, 1,..., κ - 1, and κ represents a parameter for controlling the range of the geometric noise;

[0019] bit b i as the i-th bit in binary representation, and the result of sequentially splicing all the bits is the geometric noise in binary representation.

[0020] Preferably, the conversion of the geometric noise into the discrete Laplace noise comprises:

[0021] maintaining the original geometric noise unchanged with a probability of 50%, and taking the original geometric noise as negative with a probability of the remaining 50%, to realize the processing of the geometric noise;

[0022] adopting a secure multi-party computation technology to judge whether the geometric noise after the processing is 0, if yes, then discarding the geometric noise with a probability of 50% or accepting the geometric noise with a probability of the remaining 50%, and if not, then accepting the geometric noise, and the finally accepted geometric noise is the discrete Laplace noise.

[0023] Preferably, the rejection sampling of the discrete Laplace noise based on the secure uniform bit stream to obtain the discrete Gaussian noise comprises:

[0024] sampling the discrete Laplace noise based on the secure uniform bit stream to obtain an acceptance bit, which is used to judge whether to reject the noise;

[0025] rejecting the sampling of the discrete Laplace noise according to the acceptance bit, specifically comprising: if the acceptance bit corresponding to the noise is 0, then discarding the noise, otherwise accepting the noise, and the accepted noise is the discrete Gaussian noise.

[0026] Preferably, the sampling of the discrete Laplace noise based on the secure uniform bit stream to obtain the acceptance bit comprises:

[0027] adopting a secure multi-party computation technology to calculate u = g(s), wherein s represents the discrete Laplace noise, σ represents a discrete Gaussian noise distribution parameter, and g(s) represents:

[0028]

[0029] sampling a series of Bernoulli distributions based on discrete Laplace noise and combined with secure uniform bitstream obtaining a series of bits b i ′ wherein i = 0, 1, …, l-1, l is the number of bits of u in binary representation, and the parameter r takes the value of:

[0030]

[0031] calculating and outputting acceptance bits by using secure multi-party computation technology wherein u i is the i-th bit of u in binary representation.

[0032] Preferably, the sampling a series of Bernoulli distributions based on geometric noise distribution and combined with secure uniform bitstream and the sampling a series of Bernoulli distributions based on discrete Laplace noise and combined with secure uniform bitstream both rely on the secure sampling of Bernoulli distribution B(p);

[0033] The Bernoulli distribution B(p) is defined as:

[0034]

[0035] wherein p represents the Bernoulli distribution parameter, x represents the Bernoulli distribution midpoint, and f B (x; p) represents the Bernoulli distribution. The sampling process of the above Bernoulli distribution B(p) relies on a secure uniform bitstream, specifically:

[0036] The Bernoulli distribution parameter p is approximately expressed as μ-bit binary form p = 0.p1p2…p μ wherein μ is the precision parameter;

[0037] μ secure uniform bits r1, r2, …, r μ are taken, and r = 0.r1r2…r μ is approximately expressed as a uniform random number in the interval [0, 1] in binary form;

[0038] The secure multi-party computation technology is used to perform size judgment operation on r and p. If r < p, output 1, otherwise output 0 as the sampling result;

[0039] The sampling process based on the Bernoulli distribution B(p) is performed when sampling a series of bits b i , p is replaced by The above sampling process is performed when sampling a series of bits b′ i , and is replaced by The above sampling process is performed.

[0040] To achieve the above-mentioned object of the application, the embodiment provides a discrete Gaussian noise secure sampling system for multi-party privacy aggregation, comprising: an input module, a uniform bit sampling module, a discrete Laplace noise sampling module and a discrete Gaussian noise sampling module.

[0041] The input module is used for accepting a uniform bit stream provided by each participant.

[0042] The uniform bit sampling module is used for securely sampling the uniform bit stream to obtain a secure uniform bit stream.

[0043] The discrete Laplace noise sampling module is used for sampling and converting geometric noise based on the secure uniform bit stream to obtain discrete Laplace noise.

[0044] The discrete Gaussian noise sampling module is used for rejecting sampling of the discrete Laplace noise based on the secure uniform bit stream to obtain discrete Gaussian noise.

[0045] Compared with the prior art, the application has at least the following beneficial effects:

[0046] (1) The application can provide malicious security by securely sampling the uniform bit stream, and resist attacks by malicious participants.

[0047] (2) The sampling method of the application mainly contains efficient bit operation operations, which can avoid high-overhead floating point operation operations and complex transcendental function operation operations.

[0048] (3) The application can flexibly realize sampling of discrete Gaussian noise with different parameters. BRIEF DESCRIPTION OF DRAWINGS

[0049] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description only constitute some embodiments of the application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0050] Figure 1 is a flowchart of the discrete Gaussian noise secure sampling method for multi-party privacy aggregation provided by the embodiment;

[0051] Figure 2 is a flowchart of the discrete Gaussian noise secure sampling method for multi-party privacy aggregation provided by the embodiment;

[0052] Figure 3 is a structural schematic diagram of the discrete Gaussian noise secure system for multi-party privacy aggregation provided by the embodiment. DETAILED DESCRIPTION

[0053] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the protection scope of the present application.

[0054] The technical concept of the present application is that, in view of the defect that the existing discrete Gaussian noise secure sampling scheme only guarantees semi-honest security, the embodiments of the present application provide a discrete Gaussian noise secure sampling method and system for multi-party privacy aggregation to guarantee malicious security.

[0055] As shown in Figure 1 and Figure 2 , the embodiments provide a discrete Gaussian noise secure sampling method for multi-party privacy aggregation, which comprises the following steps:

[0056] Step 1: Each participant provides a uniform bit stream.

[0057] In the embodiments, each participant provides a uniform bit stream as input.

[0058] Step 2: Securely sampling the uniform bit stream to obtain a secure uniform bit stream.

[0059] In the embodiments, when securely sampling, the secure multi-party computing technology is used to perform XOR operation on the uniform bit stream to obtain a secure uniform bit stream. This process is the basis for guaranteeing malicious security. Under the condition that only one participant honestly provides a uniform bit stream, even if the remaining malicious participants provide non-uniform bits, the secure sampling in step 2 can still guarantee that the obtained bits are uniform bits.

[0060] Step 3: Sampling and converting the geometric noise based on the secure uniform bit stream to obtain discrete Laplace noise.

[0061] In the embodiments, the discrete Laplace noise distribution L(t) is defined as:

[0062]

[0063] t is a discrete Laplace distribution parameter, and the selected parameter t is:

[0064]

[0065] represents the integer closest to the noise point x, represents the smallest integer not less than x, and σ represents the parameter of the discrete Gaussian noise.

[0066] In an embodiment, sampling and converting geometric noise based on a secure uniform bit stream to obtain the above discrete Laplace noise includes:

[0067] (a) Sampling the geometric noise distribution based on the secure uniform bit stream to obtain geometric noise, specifically including:

[0068] (a-1) Defining the geometric noise distribution f G (x; q) = (1 - q)·q x x ∈ N, where q represents the geometric noise distribution parameter, and the value is q = e -1 / t , x represents the noise point in the geometric noise distribution, and N represents natural numbers;

[0069] (a-2) Sampling a series of Bernoulli distributions based on the geometric noise distribution and in combination with the secure uniform bit stream to obtain a series of bits b i , where i = 0, 1,..., κ - 1, and κ represents the parameter for controlling the geometric noise range;

[0070] In an embodiment, sampling to obtain a series of bits b i requires the sampling process of the Bernoulli distribution B(p). Specifically, the Bernoulli distribution B(p) is defined as:

[0071]

[0072] where p represents the Bernoulli distribution parameter, x represents the point in the Bernoulli distribution, and f B (x; p) represents the Bernoulli distribution. The sampling process of the above Bernoulli distribution B(p) depends on the secure uniform bit stream. Specifically:

[0073] Approximately represent the Bernoulli distribution parameter p in μ-bit binary form p = 0.p1p2...p μ , where μ is the precision parameter; take μ secure uniform bits r1, r2,..., r μ , to obtain r = 0.r1r2...r μ , and r is approximately represented as a uniform random number in the interval [0, 1] in binary form; use secure multi-party computing technology to perform a size comparison operation on r and p. If r < p, output 1, otherwise output 0 as the sampling result; when sampling a series of bits b i , replace p with Execute the above sampling process to obtain a series of bits b i ;

[0074] (a-3) Use the bit b i as the i-th bit in binary representation, and the result obtained by sequentially concatenating all bits is the geometric noise in binary representation.

[0075] (b) converting the geometric noise into discrete Laplace noise, specifically comprising:

[0076] (b-1) keeping the original geometric noise unchanged with a probability of 50%, and taking the negative of the original geometric noise with a probability of the remaining 50%, to achieve the processing of the geometric noise. This process puts the original noise into positive and negative signs with equal probability, aiming to expand the noise range from non-negative numbers to integers.

[0077] (b-2) using secure multi-party computation technology to determine whether the geometric noise after the above processing is 0, if it is 0, then discard the geometric noise with a probability of 50% or accept the geometric noise with a probability of the remaining 50%, if it is not 0, then accept the geometric noise, and the final accepted geometric noise is discrete Laplace noise. The purpose of this process is to remove the double counting problem of 0 when expanding the noise range.

[0078] Step 4, rejecting sampling of the discrete Laplace noise based on the secure uniform bit stream to obtain discrete Gaussian noise.

[0079] In an embodiment, the discrete Gaussian noise distribution N(σ) is defined as:

[0080]

[0081] where σ represents the discrete Gaussian distribution parameter, x represents the noise point, Z represents an integer, and n represents the summation variable.

[0082] In an embodiment, the discrete Laplace noise is rejected sampled based on the secure uniform bit stream to obtain the above discrete Gaussian noise, comprising:

[0083] (c) sampling the discrete Laplace noise based on the secure uniform bit stream to obtain an acceptance bit, which is used to determine whether to reject the noise, specifically comprising:

[0084] (c-1) using secure multi-party computation technology to calculate u=g(s), where s represents the discrete Laplace noise, σ represents the discrete Gaussian noise distribution parameter, and g(s) represents:

[0085]

[0086] (c-2) based on the discrete Laplace noise and combined with the secure uniform bit stream, a series of Bernoulli distributions are sampled to obtain a series of bits b i ′ where i=0,1,…,l-1, l is the number of bits of u in binary representation, and the parameter r takes the value:

[0087]

[0088] In an embodiment, a series of bits b is sampled i ′ The sampling process of the Bernoulli distribution B(p) described above is needed, specifically, when a series of bits b' is sampled i , will be replaced by The sampling process described above is performed to obtain a series of bits b i ′ .

[0089] (c-3) Calculate and output acceptance bits using secure multi-party computation technology Where u i is the i-th bit of u in binary representation.

[0090] (d) Rejection sampling of discrete Laplace noise according to acceptance bits, specifically including:

[0091] If the noise corresponds to an acceptance bit of 0, the noise is discarded, otherwise the noise is accepted, and the accepted noise is used as discrete Gaussian noise.

[0092] It should be noted that secure multi-party computation technology is a privacy protection mechanism for cooperative computing, and the specific scenario is n participants P1, P2, …, P n need to jointly compute a function f(x1, x2, …, xn) n , where x i is the input provided by participant P i . Secure multi-party computation technology can ensure that the input of each party will not be leaked to the other parties under the premise of correct calculation results, and this process does not require a trusted central node.

[0093] The discrete Gaussian noise secure sampling method for multi-party privacy aggregation provided in the embodiment takes the uniform bit stream of each participant as input, uses secure multi-party computation technology to perform XOR operation on the uniform bits input by each participant, generates a secure uniform bit stream, and at the same time, generates Bernoulli samples by sampling the Bernoulli distribution using the secure uniform bit stream, securely samples geometric noise bit by bit using the Bernoulli samples, and converts the geometric noise into discrete Laplace noise; Bernoulli samples are securely sampled to obtain acceptance bits, and discrete Laplace noise and acceptance bits are used for secure rejection sampling to generate discrete Gaussian noise. This process can provide malicious security and resist attacks by malicious participants, and uses efficient bit operation operations to avoid high-overhead floating-point operation operations and complex transcendental function operation operations. By configuring different parameters, flexible sampling of discrete Gaussian noise can be achieved.

[0094] Based on the same inventive concept, the embodiments also provide a discrete Gaussian noise secure sampling system for multi-party privacy aggregation, which includes Figure 3As shown, it comprises an input module, a uniform bit sampling module, a discrete Laplace noise sampling module and a discrete Gaussian noise sampling module;

[0095] The input module is configured to accept uniform bit streams provided by each participant; the uniform bit sampling module is configured to securely sample the uniform bit streams to obtain secure uniform bit streams; the discrete Laplace noise sampling module is configured to sample and convert geometric noise based on the secure uniform bit streams to obtain discrete Laplace noise; and the discrete Gaussian noise sampling module is configured to reject sample the discrete Laplace noise based on the secure uniform bit streams to obtain discrete Gaussian noise.

[0096] It should be noted that the discrete Gaussian noise secure sampling device for multi-party privacy aggregation provided by the above embodiment should be illustrated by the division of the above functional modules when performing discrete Gaussian noise secure sampling, and the above functions can be completed by different functional modules according to needs, i.e., the internal structure of the terminal or server is divided into different functional modules to complete all or part of the functions described above. In addition, the discrete Gaussian noise secure sampling device for multi-party privacy aggregation provided by the above embodiment and the discrete Gaussian noise secure sampling method embodiment belong to the same concept, and the specific implementation process is described in detail in the discrete Gaussian noise secure sampling method embodiment for multi-party privacy aggregation, which will not be repeated here.

[0097] The specific embodiments described above have explained the technical solutions and beneficial effects of the present application. It should be understood that the above description is only the most preferred embodiment of the present application and is not intended to limit the present application. Any modification, supplement and equivalent replacement made within the principle range of the present application should be included in the protection scope of the present application.

Claims

1. A discrete Gaussian noise secure sampling method for multi-party privacy aggregation, characterized in that, It includes the following steps: Each participant provides a uniform bit stream; Perform secure sampling on the uniform bit stream to obtain a secure uniform bit stream, including: using secure multi-party computation technology to perform an exclusive OR operation on the uniform bit stream to obtain a secure uniform bit stream; Sample and transform geometric noise based on the secure uniform bit stream to obtain discrete Laplace noise, including: sampling the geometric noise distribution based on the secure uniform bit stream to obtain geometric noise; transforming the geometric noise into discrete Laplace noise, specifically including: Keeping the original geometric noise unchanged with a probability of 50%, and taking the negative of the original geometric noise with the remaining 50% probability to achieve the processing of geometric noise; using secure multi-party computation technology to judge whether the processed geometric noise is 0. If it is 0, then discard the geometric noise with a probability of 50% or accept the geometric noise with the remaining 50% probability. If it is not 0, then accept the geometric noise, and the finally accepted geometric noise is discrete Laplace noise; Perform rejection sampling on the discrete Laplace noise based on the secure uniform bit stream to obtain discrete Gaussian noise.

2. The discrete Gaussian noise secure sampling method for multi-party privacy aggregation according to claim 1, characterized in that, The sampling of the geometric noise distribution based on the secure uniform bit stream to obtain geometric noise includes: Define the geometric noise distribution f G (x; q) = (1-q)·q x x∈N, where q represents the geometric noise distribution parameter, with a value of q=e -1 / t t is the discrete Laplace distribution parameter, x represents the noise point in the geometric noise distribution, and N represents a natural number; Based on geometric noise distribution and combined with a series of Bernoulli distributions sampled from a secure uniform bitstream. Obtain a series of bits b i , where i = 0, 1, ..., κ-1, and κ represents the parameter controlling the range of geometric noise; Bit b i As the i-th bit in the binary representation, the result of sequentially concatenating all bits is the geometric noise in the binary representation.

3. The discrete Gaussian noise secure sampling method for multi-party privacy aggregation according to claim 1, characterized in that, The rejection sampling of the discrete Laplace noise based on the secure uniform bit stream to obtain discrete Gaussian noise includes: Sampling the discrete Laplace noise based on the secure uniform bit stream to obtain an acceptance bit, and this acceptance bit is used to judge whether to reject the noise; Perform rejection sampling on the discrete Laplace noise according to the acceptance bit, specifically including: if the acceptance bit corresponding to the noise is 0, then discard the noise, otherwise accept the noise, and the accepted noise is used as discrete Gaussian noise.

4. The discrete Gaussian noise secure sampling method for multi-party privacy aggregation according to claim 3, characterized in that, The sampling of the discrete Laplace noise based on the secure uniform bit stream to obtain an acceptance bit includes: Using secure multi-party computation technology to calculate u = g(s), where s represents the discrete Laplace noise, σ represents the discrete Gaussian noise distribution parameter, and g(s) is expressed as: Based on discrete Laplace noise and combined with a series of Bernoulli distributions sampled from a secure uniform bitstream. Obtain a series of bits b i ′ Where i = 0, 1, ..., l-1, l is the number of bits in the binary representation of u, and the parameter r takes the following values: Calculate and output the received bits using secure multi-party computation techniques. Among them, u i Let be the i-th bit of u in binary representation.

5. The discrete Gaussian noise secure sampling method for multi-party privacy aggregation according to claim 2 or 4, characterized in that, Based on geometric noise distribution and combined with a series of Bernoulli distributions sampled from a secure uniform bitstream. and a series of Bernoulli distributions based on discrete Laplace noise combined with secure uniform bitstream sampling. All rely on safe sampling of the Bernoulli distribution B(p); The Bernoulli distribution B(p) is defined as: Where p represents the Bernoulli distribution parameter, x represents the midpoint of the Bernoulli distribution, and f B (x; p) represents the Bernoulli distribution. The sampling process for the Bernoulli distribution B(p) depends on a secure uniform bit stream, specifically: The Bernoulli distribution parameter p can be approximated in μ-bit binary form as p = 0, p1, p2, ..., p μ Where μ is the precision parameter; Take μ secure uniform bits r1, r2, ..., r μ We get r = 0.r1r2…r μ r is approximately represented as a uniform random number in binary form within the interval [0,1]. Using secure multi-party computation technology to perform a size judgment operation on r and p. If r < p, then output 1, otherwise output 0 as the sampling result; Based on the sampling process of Bernoulli distribution B(p), a series of bits b are sampled. i When, replace p with Perform the above sampling process, sampling a series of bits b i ′ When, it will be replaced with Perform the above sampling process.

6. A discrete Gaussian noise secure sampling system for multi-party privacy aggregation, characterized in that, It includes: An input module, a uniform bit sampling module, a discrete Laplace noise sampling module, and a discrete Gaussian noise sampling module; The input module is used to accept the uniform bit stream provided by each participant; The uniform bit sampling module is used to perform secure sampling on the uniform bit stream to obtain a secure uniform bit stream, including: using secure multi-party computation technology to perform an exclusive OR operation on the uniform bit stream to obtain a secure uniform bit stream; The discrete Laplace noise sampling module is used to sample and transform geometric noise based on the secure uniform bit stream to obtain discrete Laplace noise, including: sampling the geometric noise distribution based on the secure uniform bit stream to obtain geometric noise; transforming the geometric noise into discrete Laplace noise, specifically including: The original geometric noise is kept unchanged with a 50% probability, and the original geometric noise is negative with a remaining 50% probability to process the geometric noise. Secure multi-party computation is used to determine whether the geometric noise after the above processing is 0. If it is 0, the geometric noise is discarded with a 50% probability or accepted with a remaining 50% probability. If it is not 0, the geometric noise is accepted. The final accepted geometric noise is discrete Laplace noise. The discrete Gaussian noise sampling module is used to reject sampling of discrete Laplace noise based on a secure uniform bit stream to obtain discrete Gaussian noise.

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