Threshold homomorphic password federated gradient secure aggregation method

Abstract

The invention relates to a threshold homomorphic password federated gradient secure aggregation method, system and device, and the method comprises the steps: obtaining an aggregation gradient plaintext based on an online participant set, a threshold value and a network connection time limit; obtaining an online participant set and a threshold value, inputting the online participant set and the threshold value into a T-N threshold homomorphic encryption model, and then encrypting and collecting the online participant set and the threshold value to an aggregation party to generate ciphertext data; an aggregation party collects encryption parameters through an aggregation algorithm in combination with ciphertext data and aggregation gradient plaintext, and a T-N threshold homomorphic encryption model can expand a new private key with a threshold access characteristic on the basis of multi-party homomorphic encryption, so that under the condition that a certain proportion of participants are offline, a new private key with a threshold access characteristic can be expanded, and the encryption efficiency is improved. And the rest participants can still decrypt the ciphertext by using the new private key with the threshold access characteristic, and then the aggregation gradient plaintext is obtained by cooperating with calculation for aggregation, so that the time of iterative convergence to an expected value is shortened.

Description

Technical Field

[0001] The present application relates to the field of data security, and in particular to a threshold homomorphic cryptographic federated gradient security aggregation method, system and device. Background Art

[0002] A typical federated learning system usually includes multiple participants, which are divided into a parameter aggregator and multiple model trainers according to their roles. The steps of the training protocol process are summarized as follows:

[0003] (1) The training party uses local data to train local model parameters;

[0004] (2) Encrypt the parameters and collect them to the aggregator;

[0005] (3) The aggregator aggregates the encryption parameters through the aggregation algorithm and updates the global model parameters;

[0006] (4) The aggregator sends the updated global model parameters to the trainer;

[0007] (5) Iterate the above steps until the model converges to the expected value.

[0008] Among them, step 1 training local model parameters is basically consistent with classical machine learning, and step 3 aggregation algorithm realizes gradient processing, transmission and aggregation to prevent leakage of sensitive information, which becomes the key to federated learning.

[0009] Researchers mainly optimize the central aggregation process, which is mainly divided into three directions: introducing secure aggregation to strengthen privacy protection, lossy compression of aggregated values ​​to improve communication efficiency, and adding noise and updating to achieve differential privacy. From the perspective of attack, attackers also attack the aggregation process, such as gradient leakage, that is, analyzing the relevant features of the original data by stealing the uploaded data of other nodes, or data poisoning, that is, uploading carefully constructed malicious data to affect the global model or the local model of other nodes. The aggregation method has become the core that affects the parameter security and execution efficiency of federated learning. How to design an efficient and secure aggregation method has become a research focus and hotspot. The existing aggregation scheme has two defects. First, it cannot take into account both security and performance. Once the training party cannot participate in the aggregation step, the training process will fail. Second, there is an assumption that the aggregator is trustworthy, not only correctly executes the aggregation step, but also will not collude with some training parties to steal the data of other participants.

[0010] The main reason is that in real federated learning scenarios, some training parties may not be able to be online all the time due to network delays or failures, resulting in multiple training parties being unable to coordinate with a recognized trusted third party.

[0011] The above contents are only used to assist in understanding the technical solution of the present invention and do not constitute an admission that the above contents are prior art. Summary of the invention

[0012] The embodiments of the present application provide a threshold homomorphic cryptographic federated gradient security aggregation method, system and device to solve the problem in the related art that in real federated learning scenarios, some training parties may not be able to be online all the time due to network delays or failures, resulting in multiple training parties being unable to coordinate with a recognized trusted third party.

[0013] In a first aspect, a threshold homomorphic cryptographic federated gradient security aggregation method is provided, which includes:

[0014] Based on the online participant collection, the threshold value and the network connection time limit, a gradient ciphertext set is obtained;

[0015] Based on the gradient ciphertext set, the online participant set and the threshold, the aggregated gradient plaintext is obtained;

[0016] Obtain the online participant collection and threshold value, and input them into the TN threshold homomorphic encryption model, which is then encrypted and aggregated to the aggregator to generate ciphertext data;

[0017] The aggregator aggregates encryption parameters by using an aggregation algorithm and combining the ciphertext data and the aggregate gradient plaintext.

[0018] Further, based on the online participant collection, the threshold value and the network connection time limit, a gradient ciphertext set is obtained, which specifically includes the following steps:

[0019] Check whether the number of online participants in the online participant set is greater than a threshold;

[0020] If so, terminate;

[0021] Otherwise, each participant uses the local training model to obtain the gradient m i , and then use the multi-party homomorphic encryption message encryption algorithm to convert the gradient m i Encrypt to obtain the corresponding gradient ciphertext; then send the gradient ciphertext of each participant to other participants;

[0022] Get the gradient ciphertext set obtained within the network connection time limit.

[0023] Furthermore, based on the gradient ciphertext set, the online participant set and the threshold, the aggregated gradient plaintext is obtained, which specifically includes the following steps:

[0024] Check whether the number of online participants in the online participant set is greater than a threshold;

[0025] If so, terminate;

[0026] Otherwise, the gradient ciphertext set is decrypted based on the gradient ciphertext set and combined with the secret recovery algorithm; then the decrypted gradient ciphertext set is used to obtain the aggregated gradient plaintext based on the ciphertext decryption algorithm of the multi-party homomorphic encryption scheme.

[0027] Furthermore, the online participant collection and threshold value are obtained and input into the TN threshold homomorphic encryption model, and then encrypted and collected to the aggregation party to generate ciphertext data, including the following steps:

[0028] Perform algorithm settings;

[0029] Based on the set of participating parties and the threshold, a private key is generated using a multi-party homomorphic encryption private key generation algorithm;

[0030] Based on the set of participants and the threshold, a public key is generated using a multi-party homomorphic encryption public key generation algorithm;

[0031] The private key fragment of each participant is sent to other participants using a secret sharing algorithm; other participants use a secret recovery algorithm to decrypt and obtain the private key fragment;

[0032] The original private key, public key and private key fragment of each participant are used as the corresponding ciphertext data;

[0033] Repeat the above operation to obtain the ciphertext data of the online participants, and collect them to the aggregator to generate ciphertext data.

[0034] Furthermore, generating the public key specifically includes the following steps:

[0035] Check whether the number of online participants in the online participant set is greater than a threshold;

[0036] If so, terminate;

[0037] Otherwise, select T participants with the same threshold value to run the threshold access private key construction algorithm in the TN threshold homomorphic encryption model to obtain the calculation result;

[0038] Run the multi-party homomorphic encryption public key generation algorithm in the TN threshold homomorphic encryption model, and input the calculation result to obtain the public key.

[0039] Furthermore, generating the private key includes the following steps: selecting T participants with consistent threshold values ​​to run the multi-party homomorphic encryption private key generation algorithm in the TN threshold homomorphic encryption model to obtain a calculation result; and then running the private key secret sharing algorithm based on the calculation result to obtain the private key.

[0040] Furthermore, the secret sharing algorithm comprises the following steps:

[0041] Each participant P i Randomly select polynomial coefficients ci,1 ,c i,2 ,...,c i,T―1 ←R q Each participant P i send To each participant P j Each participant P i Receiving Party P j The private key fragment And calculate

[0042] Furthermore, the secret recovery algorithm comprises the following steps:

[0043] For any subset of participants Each participant P i calculate

[0044] Secondly, a federated gradient security aggregation system based on threshold homomorphic cryptography is provided, including:

[0045] The first module is used to obtain a gradient ciphertext set based on a collection of online participants, a threshold value, and a network connection time limit;

[0046] The second module is used to obtain the aggregated gradient plaintext based on the gradient ciphertext set, the online participant set and the threshold value;

[0047] The third module is used to obtain the online participant collection and threshold value, and input them into the TN threshold homomorphic encryption model, and then encrypt and aggregate them to the aggregation party to generate ciphertext data;

[0048] The fourth module is used for the aggregation party to aggregate encryption parameters through an aggregation algorithm and in combination with the ciphertext data and the aggregated gradient plaintext.

[0049] In a third aspect, an electronic device is provided, comprising a processor, a memory, and a federated gradient security aggregation program based on threshold homomorphic cryptography stored in the memory and executable by the processor, wherein when the federated gradient security aggregation program based on threshold homomorphic cryptography is executed by the processor, the steps of the threshold homomorphic cryptography federated gradient security aggregation method are implemented.

[0050] The beneficial effects of the technical solution provided by this application include:

[0051] The embodiments of the present application provide a threshold homomorphic cryptographic federated gradient security aggregation method, system and device, which obtains a gradient ciphertext set based on a collection of online participants, a threshold value and a network connection time limit; obtains an aggregated gradient plaintext based on the gradient ciphertext set, the collection of online participants and the threshold value; obtains the collection of online participants and the threshold value, and inputs them into a TN threshold homomorphic encryption model, and then encrypts and aggregates them to an aggregator to generate ciphertext data; the aggregator aggregates encryption parameters through an aggregation algorithm and in combination with the ciphertext data and the aggregated gradient plaintext, wherein the TN threshold homomorphic encryption model can expand a new private key with a threshold access feature on the basis of multi-party homomorphic encryption, so that when a certain proportion of participants are offline, the remaining participants can still decrypt the ciphertext using the new private key with the threshold access feature, and then aggregate the aggregated gradient plaintext in cooperation with the calculation, thereby speeding up the time for the iteration to converge to the expected value. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0053] Figure 1 A flowchart of a threshold homomorphic cryptographic federated gradient security aggregation method provided in an embodiment of the present application. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0055] The embodiments of the present application provide a threshold homomorphic cryptographic federated gradient security aggregation method, system and device to solve the problem in the related art that in real federated learning scenarios, some training parties may not be able to be online all the time due to network delays or failures, resulting in multiple training parties being unable to coordinate with a recognized trusted third party.

[0056] See also Figure 1 , a threshold homomorphic cryptographic federated gradient security aggregation method, comprising:

[0057] Step 100: Obtain a gradient ciphertext set CT based on a collection of online participants, a threshold value T, and a network connection timeout;

[0058] Step 101: Based on the gradient ciphertext set CT, the online participant set and the threshold T, an aggregated gradient plaintext m is obtained;

[0059] Step 102: Obtain the online participant collection and threshold value T, and input them into the TN threshold homomorphic encryption model, and then encrypt and aggregate them to the aggregation party to generate ciphertext data;

[0060] Step 103: The aggregator aggregates encryption parameters by using an aggregation algorithm and combining the ciphertext data and the aggregate gradient plaintext m.

[0061] In the above steps, the TN threshold homomorphic encryption model can expand a new private key with threshold access characteristics based on multi-party homomorphic encryption, so that when a certain proportion of participants are offline, the remaining participants can still decrypt the ciphertext using the new private key with threshold access characteristics, and then aggregate the aggregated gradient plaintext m obtained by calculation, thereby speeding up the time for the iteration to converge to the expected value.

[0062] In some preferred embodiments, step 100, based on the online participant collection P online , threshold T and network connection timeout Timeout, obtain the gradient ciphertext set CT, specifically including the following steps:

[0063] Verify the set of online participants P online Whether the number of online participants is greater than the threshold T;

[0064] If so, terminate;

[0065] Otherwise, each participant uses the local training model to obtain the gradient m i , and then use ct i =MHE.Enc(pk i ,m i ) The multi-party homomorphic encryption message encryption algorithm converts the gradient m i Encrypt to obtain the corresponding gradient ciphertext; then send the gradient ciphertext of each participant to other participants;

[0066] Get the gradient ciphertext set CT obtained within the network connection time limit Timeout.

[0067] Its main function is gradient distribution: the trainers execute the multi-party homomorphic encryption message encryption algorithm TMHE.Enc on their respective gradient information and send the results to the aggregator; the network connection timeout can be set, and the aggregator collects the ciphertext data sent by the trainers within the time limit.

[0068] The execution program can be:

[0069] Input: Participant Set P online , threshold T, timeout

[0070] Output: Gradient ciphertext set CT

[0071] 1) Select participant P as the aggregator, where or third party

[0072] 2)

[0073] 3) P i Train the model locally and obtain the gradient m i

[0074] 4)P i Execute ct i =MHE.Enc(pk i ,m i )

[0075] 5)P i ct i Send to P j

[0076] 6) end for

[0077] 7) P obtains the gradient ciphertext set CT within the Timeout

[0078] 8) Return to CT.

[0079] In some preferred embodiments, step 101, based on the gradient ciphertext set CT and the online participant set P online and threshold T, to obtain the aggregated gradient plaintext m, which specifically includes the following steps:

[0080] Verify the set of online participants P online Whether the number of online participants is greater than the threshold T;

[0081] If so, terminate;

[0082] Otherwise, the gradient ciphertext set CT is decrypted based on the gradient ciphertext set CT and combined with the T.Combine secret recovery algorithm; then the decrypted gradient ciphertext set CT is based on MHE.Dec(s'1,s'2,...,s' T ,ct) The ciphertext decryption algorithm of the multi-party homomorphic encryption scheme obtains the aggregated gradient plaintext m.

[0083] Its main function is gradient aggregation: the aggregator performs homomorphic encryption on the ciphertext gradient, and performs decryption based on the online status of the training party to obtain the aggregated plaintext gradient, and sends it to the training party. The execution program is roughly as follows:

[0084] Input: Online participant set P online , threshold T, gradient ciphertext set CT

[0085] Output: Aggregate gradient plaintext m

[0086] 1) Based on CT, perform TMHE.Add ciphertext addition and TMHE.Mul ciphertext multiplication locally to generate ct

[0087] 2) If the test is satisfied, continue, otherwise terminate

[0088] 3) Select T participants

[0089] 4) for i = 1:1:T

[0090] 5) Execute T.Combine

[0091] 6) end for

[0092] 7) Execution

[0093] 8) Return m.

[0094] In some preferred embodiments, step 102, obtaining a collection of online participants P online and threshold T, and input them into the TN threshold homomorphic encryption model, and then encrypt and aggregate them to the aggregation party to generate ciphertext data, including the following steps:

[0095] Perform TMHE.Setup algorithm settings;

[0096] Using the participant collection P online , threshold value T, TMHE.SecKeyGen multi-party homomorphic encryption private key generation algorithm generates a private key;

[0097] Using the participant collection P online , threshold value T, TMHE.PubKeyGen multi-party homomorphic encryption public key generation algorithm generates a public key;

[0098] The private key fragment of each participant is sent to other participants using the T.Thresholdize secret sharing algorithm; other participants use the T.Combine secret recovery algorithm to decrypt and obtain the private key fragment;

[0099] The original private key, public key and private key fragment of each participant are used as the corresponding ciphertext data;

[0100] Repeat the above operation to obtain the online participant collection P online The ciphertext data is collected and aggregated to the aggregation party to generate ciphertext data.

[0101] The above steps realize the expansion of a new private key with threshold access characteristics based on multi-party homomorphic encryption, so that when a certain proportion of participants are offline, the remaining participants can still decrypt the ciphertext using the new private key with threshold access characteristics. The method of transformation is that each participant uses the Shamir secret sharing scheme to distribute the original private key fragments to other participants, and each participant receives the original private key fragments of other participants and reassembles the new private key with threshold access characteristics. Without relying on a trusted third party, gradient aggregation can be performed by the training party or third party participating in federated learning, where the threshold characteristics meet the requirement that the model training will not be affected when some training parties are offline, thereby improving the fault tolerance of the training process. Under the mainstream FATE federated learning framework, the computational performance of the algorithm is verified and comparative indicators are given.

[0102] Since there are many special professional terms above, the following is an explanation:

[0103] T.Setup algorithm settings: Each participant P i Related public points α i ∈R q ,(threshold key and threshold signature) for any i≠j,α j ―α i is the unit element.

[0104] T.Thresholdize secret sharing: Each participant P i Randomly select polynomial coefficients c i,1 ,c i,2 ,...,c i,T―1 ←R q Each participant P i send To each participant P j Each participant P i Receiving Party P j The private key fragment And calculate

[0105] T. Combine secret recovery: for any subset of participants Each participant P i calculate

[0106] (TN) The threshold homomorphic encryption scheme is based on the multi-party homomorphic encryption MHE algorithm and adds the multi-party homomorphic encryption T algorithm with threshold access to the private key.

[0107] TMHE.Setup algorithm setting: Run the multi-party homomorphic encryption algorithm setting MHE.Setup and the threshold access private key algorithm setting T.Setup.

[0108] TMHE.SecKeyGen private key generation: Run the multi-party homomorphic encryption private key generation algorithm (s1, s2, ..., s N )←MHE.SecKeyGen; Run the private key secret sharing algorithm T.Thresholdize(s1,s2,...,s N ).

[0109] TMHE.PubKeyGen public key generation:

[0110] 1) Get the set of online participants P online .

[0111] 2) Check if the number of online participants is greater than the threshold value T, otherwise terminate.

[0112] 3) Select T participants and run the threshold access private key construction algorithm (s'1, s'2, ..., s' T )←T.Combine.

[0113] 4) Run the multi-party homomorphic encryption public key generation algorithm

[0114] MHE.PubKeyGen(s'1,s'2,...,s' T ).

[0115] TMHE.Enc message encryption: Run the multi-party homomorphic encryption message encryption algorithm MHE.Enc.

[0116] TMHE.Dec ciphertext decryption:

[0117] 1) Get the set of online participants P online .

[0118] 2) Check if the number of online participants is greater than the threshold value T, otherwise terminate.

[0119] 3) Select T participants and run the threshold access private key construction algorithm (s'1, s'2, ..., s' T )←T.Combine.

[0120] 4) Run the ciphertext decryption algorithm MHE.Dec(s'1,s'2,...,s' T ,ct).

[0121] TMHE.Add ciphertext addition: same as MHE.Add(ct1,ct2).

[0122] TMHE.Mul ciphertext multiplication: same as MHE.Mul(ct1,ct2).

[0123] In the second aspect, a federated gradient security aggregation system based on threshold homomorphic cryptography includes:

[0124] The first module is used to online , threshold T and network connection timeout, obtain the gradient ciphertext set CT;

[0125] The second module is used to calculate the gradient ciphertext set CT and the online participant set P. online and threshold T, obtain the aggregated gradient plaintext m;

[0126] The third module is used to obtain the online participant collection P online and threshold T, and input into the TN threshold homomorphic encryption model, then encrypted and collected to the aggregation party to generate ciphertext data;

[0127] The fourth module is used for the aggregation party to aggregate encryption parameters through an aggregation algorithm and in combination with the ciphertext data and the aggregate gradient plaintext m.

[0128] An electronic device comprises a processor, a memory, and a federated gradient security aggregation program based on threshold homomorphic cryptography stored in the memory and executable by the processor, wherein when the federated gradient security aggregation program based on threshold homomorphic cryptography is executed by the processor, the steps of a threshold homomorphic cryptography federated gradient security aggregation method are implemented.

[0129] An electronic device may include a processor, a memory, a communication interface, and a communication bus.

[0130] The communication bus may be of any type and is used to interconnect the processor, the memory, and the communication interface.

[0131] The communication interface includes input / output (I / O) interface, physical interface and logical interface, etc., which are used to realize the interconnection of devices inside the AAAA device, and the interface used to realize the interconnection between the AAAA device and other devices (such as other computing devices or user devices). The physical interface can be an Ethernet interface, a fiber optic interface, an ATM interface, etc.; the user device can be a display (Display), a keyboard (Keyboard), etc.

[0132] The memory can be various types of storage media, such as random access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), flash memory, optical storage, hard disk, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), etc.

[0133] The processor may be a general-purpose processor, and the general-purpose processor may call the AAAA program stored in the memory and execute the AAAA method provided in the embodiment of the present application. For example, the general-purpose processor may be a central processing unit (CPU). The method executed when the AAAA program is called may refer to the various embodiments of the AAAA method of the present application, and will not be repeated here.

[0134] In the description of the present application, it should be noted that the terms "upper", "lower", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present application. Unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be a connection between the two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present application can be understood according to the specific circumstances.

[0135] It should be noted that, in this application, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0136] The above description is only a specific implementation of the present application, so that those skilled in the art can understand or implement the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest range consistent with the principles and novel features applied for herein.

Claims

1. A threshold homomorphic cryptographic federated gradient security aggregation method, characterized in that: It includes: Based on the online participant collection, the threshold value and the network connection time limit, a gradient ciphertext set is obtained; Based on the gradient ciphertext set, the online participant set and the threshold, the aggregated gradient plaintext is obtained; Obtain the online participant collection and threshold value, and input them into the TN threshold homomorphic encryption model, which is then encrypted and aggregated to the aggregator to generate ciphertext data; The aggregator aggregates encryption parameters by using an aggregation algorithm and combining the ciphertext data and the aggregate gradient plaintext.

2. The threshold homomorphic cryptographic federated gradient security aggregation method according to claim 1, characterized in that: Based on the online participant collection, the threshold value and the network connection time limit, a gradient ciphertext set is obtained, which specifically includes the following steps: Check whether the number of online participants in the online participant set is greater than a threshold; If so, terminate; Otherwise, each participant uses the local training model to obtain the gradient m i , and then use the multi-party homomorphic encryption message encryption algorithm to convert the gradient m i Encrypt to obtain the corresponding gradient ciphertext; then send the gradient ciphertext of each participant to other participants; Get the gradient ciphertext set obtained within the network connection time limit.

3. The threshold homomorphic cryptographic federated gradient security aggregation method according to claim 1, characterized in that: Based on the gradient ciphertext set, the online participant set and the threshold, the aggregated gradient plaintext is obtained, which specifically includes the following steps: Check whether the number of online participants in the online participant set is greater than a threshold; If so, terminate; Otherwise, the gradient ciphertext set is decrypted based on the gradient ciphertext set and combined with the secret recovery algorithm; then the decrypted gradient ciphertext set is used to obtain the aggregated gradient plaintext based on the ciphertext decryption algorithm of the multi-party homomorphic encryption scheme.

4. The threshold homomorphic cryptographic federated gradient security aggregation method according to claim 1, characterized in that: Obtain the online participant collection and threshold value, input them into the TN threshold homomorphic encryption model, and then encrypt and aggregate them to the aggregator to generate ciphertext data, including the following steps: Perform algorithm settings; Based on the set of participating parties and the threshold, a private key is generated using a multi-party homomorphic encryption private key generation algorithm; Based on the set of participants and the threshold, a public key is generated using a multi-party homomorphic encryption public key generation algorithm; The private key fragment of each participant is sent to other participants using a secret sharing algorithm; other participants use a secret recovery algorithm to decrypt and obtain the private key fragment; The original private key, public key and private key fragment of each participant are used as the corresponding ciphertext data; Repeat the above operation to obtain the ciphertext data of the online participants, and collect them to the aggregator to generate ciphertext data.

5. The threshold homomorphic cryptographic federated gradient security aggregation method according to claim 4, characterized in that: Generating the public key specifically includes the following steps: Check whether the number of online participants in the online participant set is greater than a threshold; If so, terminate; Otherwise, select T participants with the same threshold value to run the threshold access private key construction algorithm in the TN threshold homomorphic encryption model to obtain the calculation result; Run the multi-party homomorphic encryption public key generation algorithm in the TN threshold homomorphic encryption model, and input the calculation result to obtain the public key.

6. The threshold homomorphic cryptographic federated gradient security aggregation method according to claim 4, characterized in that: Generating the private key comprises the following steps: T participants with the same threshold are selected to run the multi-party homomorphic encryption private key generation algorithm in the TN threshold homomorphic encryption model to obtain a calculation result; then the private key secret sharing algorithm is run based on the calculation result to obtain the private key.

7. The threshold homomorphic cryptographic federated gradient security aggregation method according to claim 4, characterized in that: The secret sharing algorithm comprises the following steps: Each participant P i Randomly select polynomial coefficients c i,1 ,c i,2 ,...,c i,T―1 ←R q Each participant P i send To each participant P j Each participant P i Receiving Party P j The private key fragment And calculate 8. The threshold homomorphic cryptographic federated gradient security aggregation method according to claim 1, characterized in that: The secret recovery algorithm comprises the following steps: For any subset of participants Each participant P calculates 9. A federated gradient security aggregation system based on threshold homomorphic encryption, characterized in that: include: The first module is used to obtain a gradient ciphertext set based on a collection of online participants, a threshold value, and a network connection time limit; The second module is used to obtain the aggregated gradient plaintext based on the gradient ciphertext set, the online participant set and the threshold value; The third module is used to obtain the online participant collection and threshold value, and input them into the TN threshold homomorphic encryption model, and then encrypt and aggregate them to the aggregation party to generate ciphertext data; The fourth module is used for the aggregation party to aggregate encryption parameters through an aggregation algorithm and in combination with the ciphertext data and the aggregated gradient plaintext.

10. An electronic device, characterized in that: The invention comprises a processor, a memory, and a federated gradient security aggregation program based on threshold homomorphic cryptography stored in the memory and executable by the processor, wherein when the federated gradient security aggregation program based on threshold homomorphic cryptography is executed by the processor, the steps of the threshold homomorphic cryptography federated gradient security aggregation method according to any one of claims 1 to 8 are implemented.

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