LU601634B1 - Multi-party fully homomorphic encryption-based data sharing method and system - Google Patents
Multi-party fully homomorphic encryption-based data sharing method and systemInfo
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- LU601634B1 LU601634B1 LU601634A LU601634A LU601634B1 LU 601634 B1 LU601634 B1 LU 601634B1 LU 601634 A LU601634 A LU 601634A LU 601634 A LU601634 A LU 601634A LU 601634 B1 LU601634 B1 LU 601634B1
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
- H04L9/3093—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving Lattices or polynomial equations, e.g. NTRU scheme
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- G—PHYSICS
- G06—COMPUTING OR CALCULATING; COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/008—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols involving homomorphic encryption
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
- H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
- H04L9/085—Secret sharing or secret splitting, e.g. threshold schemes
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
- H04L2209/46—Secure multiparty computation, e.g. millionaire problem
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Abstract
The present invention discloses a multi-party fully homomorphic encryption-based data sharing method and system. The method comprises: each party's user terminal generates its own private key using a private key generation algorithm; each party's user terminal generates a collective public key for a designated data sharing task through a protocol; a relinearization public key is generated; each party's user terminal encrypts its own data using the collective public key and transmits the ciphertext to a server; the server performs homomorphic computation on the uploaded ciphertext data and returns the computation result to each user terminal; the server executes a relinearization operation on the ciphertext using the relinearization public key after each homomorphic multiplication computation; and each user terminal executes a joint decryption protocol to decrypt the computation result or designates a recipient to perform decryption. This method and system not only ensure the privacy and security of each party's data but also enable data sharing, achieving efficiency comparable to single-key fully homomorphic encryption while supporting participation by thousands of parties. Furthermore, the decryption process is flexible, providing a method for decryption by a designated recipient.
Description
MULTI-PARTY FULLY HOMOMORPHIC ENCRYPTION-BASED DATA SHARING 11601636
METHOD AND SYSTEM
The present invention relates to the field of data encryption technologies, and particularly to a multi-party fully homomorphic encryption-based data sharing method and system.
In the context of big data and cloud computing environments, users are concerned about the leakage of their sensitive data, financial service providers worry about the theft of proprietary service models, and malicious actors may exploit vulnerabilities to steal data for profit. Consequently, there is an urgent market demand for methods and tools that ensure secure computation.
Fully homomorphic encryption (FHE) enables arbitrary computations on ciphertexts without decryption, thereby achieving privacy-preserving outsourced data processing.
However, conventional FHE cannot support multi-party collaboration. For example, multiple banks may seek to assess a user’s financial creditworthiness. While each bank can independently train a machine learning model based on its own data, sharing data among them could yield a more accurate joint model. Yet, due to security concerns, direct data sharing between institutions is infeasible.
To address this, multi-key fully homomorphic encryption (MK-FHE) was proposed.
Although MK-FHE is theoretically promising, it suffers from inefficiency: ciphertext size and computational overhead grow linearly and quadratically with the number of participating keys, respectively. These scalability limitations in both time and space hinder its practical adoption.
In view of these challenges, the present invention is proposed.
The objective of the present invention is to provide a multi-party fully homomorphic encryption-based data sharing method and system, which ensures the privacy and security of each party's data while enabling data sharing. Compared to multi-key fully homomorphic encryption, the method generates smaller keys and ciphertexts, achieves efficiency comparable to single-key fully homomorphic encryption, and supports participation by 11601636 thousands of parties. Additionally, it offers flexible decryption by providing a method for decrypting data for designated recipients.
To address the above issues, an embodiment of the present invention provides a multi-party fully homomorphic encryption-based data sharing method, in which multiple user terminals participate. The method comprises:
Fach user terminal generates its own private key using a private key generation algorithm and stores the private key;
Each user terminal generates a collective public key for a data sharing task through a collective public key generation protocol, wherein the data sharing task is established in a server by at least one user terminal;
Each user terminal generates a re-linearization public key through a re-linearization public key generation protocol; and
Each user terminal encrypts its own data using the collective public key and transmits the ciphertext to the server.
The server performs homomorphic computation on the ciphertext data uploaded by the user terminals and returns the computation result to each user terminal; wherein the homomorphic computation includes homomorphic addition and homomorphic multiplication, and the server executes a re-linearization operation on the ciphertext using the re-linearization public key after each homomorphic multiplication computation.
Each user terminal executes a joint decryption protocol to decrypt the said computation result and thereby obtain the decrypted result, or each participant, upon receiving the said computation result and the recipient's public key, executes a key exchange protocol to generate a new ciphertext, which 1s then decrypted by the designated recipient.
On the other hand, an embodiment of the present invention further provides a multi-party fully homomorphic encryption-based data sharing system, comprising user terminals and servers participating in multi-party data sharing, wherein each user terminal and server execute the steps in the aforementioned multi-party fully homomorphic encryption-based data sharing method.
Compared with the prior art, the present invention achieves multi-party fully homomorphic encryption (MFHE) without any performance degradation relative to 11601636 single-party fully homomorphic encryption. Each user generates their own private key using multi-party homomorphic encryption, and a shared public key 1s then generated through a collective public key protocol. When data sharing is required, the parties encrypt their data using the shared public key and transmit the encrypted data to a shared platform (server). The shared platform performs homomorphic computations on the encrypted data from all parties and returns the computation results to the participants. Finally, the parties execute a joint decryption protocol to obtain the decrypted final result. This system ensures both the privacy and security of each party's data while enabling secure data sharing.
FIG. 1 is a schematic diagram of a multi-party fully homomorphic encryption-based data sharing system according to an embodiment of the present invention.
Specific Embodiment of the Invention
The principles and spirit of the present invention will be described below with reference to several exemplary embodiments illustrated in the accompanying drawings. It should be understood that these embodiments are described solely to enable those skilled in the art to better understand and consequently implement the present invention, and are in no way intended to limit the scope of the invention in any manner.
With reference to FIG. 1, an embodiment of the present invention provides a data sharing method based on multi-party fully homomorphic encryption (MFHE), which can be implemented in the data sharing system shown in FIG. 1.The data sharing system comprises multiple user terminals participating in data sharing (i.e., participating parties).
For example, several banks may collaborate to establish a financial credit profile for a specific user. While each bank may independently train machine learning models using its own user data, superior models can be developed through collaborative data sharing. In this configuration, the multi-party user terminals may comprise respective banking institution terminals. All user terminals communicate with a server that hosts a data sharing platform, wherein each user terminal may initiate data sharing tasks on said platform.
In accordance with embodiments of the disclosed invention, a data sharing method ee utilizing multi-party fully homomorphic encryption includes:
A data sharing method based on multi-party fully homomorphic encryption, comprising the participation of a plurality of user terminals and including:
S1: Each user terminal generates and stores its own private key using a private key generation algorithm.
Let P = {P,, P,,..., Py} be a set of N participating parties, each possessing respective message (xq, Xz, ..., Xn). Let f(xy, X2,… , Xy) = y represent an input function provided by an input party.
Each user terminal P; uniformly and randomly selects a polynomial si from Rj as its private key, where R3 = Z3[X]/(X™ + 1) is a polynomial quotient ring with the modulus (X™+1) and its coefficients are uniformly distributed in{-1, 0,1}, andnisa power of 2.
It should be noted that, prior to the commencement of step S1, each user terminal is required to register its own account on the data-sharing platform by accessing the server.
S2: Each user terminal generates a collective public key for the data-sharing task through a joint public key generation protocol.
The data-sharing task is established in advance by at least one user terminal on the server. For example, User A creates a data-sharing task in the system, and the system generates a unique data-sharing task ID for the task. To enable other users to participate in the data-sharing task, User A may transmit the data-sharing task ID to the user terminals of other participating parties via the server.
Step S2 specifically includes: (1) Under the common random string (CRS) model, each user terminal (each participant) obtains a common polynomial pi, where Di is uniformly and randomly sampled from Ra = Za[X]/(X" + 1),denotes a polynomial quotient ring in which each polynomial 1s taken modulo (x " +1) with coefficients uniformly distributed Se over 14) where n is a power of 2; and q serves as the ciphertext coefficient modulus. (2) Each user terminal P; uniformly and randomly samples a noise term eifrom an error distribution x and broadcasts p,, =—(p,s, +e) to the other participating user terminals, where y is a discrete Gaussian distribution over R,. (3) Each user terminal computes p,= >, p, and generates a collective public key pk =(p,.p,) ; said collective public key is held and publicly shared by each user terminal; the private key corresponding to the collective public key is s= = ] where the notation[ ], denotes reduction modulo ge
S3: Each user terminal generates a relinearization public key via a relinearization key generation protocol
Step S3 specifically comprises: (1) Let w=(w,w',...,w') be the public parameter of all user terminals, where ” represents the base (for example, W=2 indicates the binary system), and /=[log,(q) |; wherein the symbol | | denotes the ceiling function; (2) In the Common Reference String (CRS) model, each user terminal (each participant) obtains a common value aeR,. (3) Each user terminal P; uniformly and randomly selects e,, from x and u; from R,, then broadcasts h, =—ma+sw+e,, to the other user terminals. (4) Each user terminal computes h= >" h_, then uniformly and randomly selects e,,,e,, from x’, and broadcasts hy to the other user terminals. (5) Each user terminal: computes h,=> h,, and h; => h,, ; uniformly and randomly selects e,, from 4’; and broadcasts h; (us), +e,, to the other user terminals.
(6) Each user terminal: computes h'= } h;; generates a relinearization oe public key rlk=(r,.5)=(h,+h"h;) and publishes it; and wherein the relinearization public key is configured to reduce ciphertext length after each homomorphic multiplication operation.
S4: Each user terminal encrypts its own data using the collective public key and transmits the ciphertext to the server.
Step S4 specifically comprises: (1) Let the message space be R, = Z;|X]/(X" + 1), where t is the plaintext modulus; for the collective public key pk=(p,p,), to encrypt a message m me R,, uniformly and randomly select »* from , and uniformly and randomly select eo* and ei* from 7. (2) Compute ct=(c1,c2)= (La /ilm+u po ve up +e );output the ciphertext ct,where the symbol | Jdenotes the floor operation (rounding down to the nearest integer).
S5: The server performs homomorphic computations on the ciphertext data uploaded by each user terminal and returns the computation results to the respective user terminals; wherein the homomorphic computations include homomorphic addition and homomorphic multiplication, and wherein the server, after each execution of a homomorphic multiplication computation, applies a relinearization operation to the ciphertext using the relinearization public key.
Step S5 specifically comprises: (1)Homomorphic addition: given cf=(c,,¢;) and of =(c,.e), compute and output ct, = ( +66 + a); (2)Homomorphic multiplication: given cf=(c,,c,) and ct = (conc ) , compute and output ct_, = Le (696060 + cic) , where the notation [ |, denotes modulo q. q
(3)Ciphertext relinearization operation: given ct = (cc, €, ),rlk = (nn); express cz in base w representation, namely c,= Sep” ; compute and output cto, = C + She + Zn? . a
Step S6: Key Exchange (1) Let the ciphertext to be decrypted be ct = (0,6) ° (2) Each user terminal Pi uniformly and randomly samples a noise term e from an error distribution X, computes ” 7948, and broadcasts it to the other participating parties. (3) Calculate a 2h and (cc) =(c +h.) .output the target ciphertext to be decrypted" = (ce) = (c + hy, hy)
If the ciphertext is to be jointly decrypted by all participating parties, execute Step S7: each user terminal performs a joint decryption protocol to decrypt the computation result, thereby obtaining the decrypted result.
Step S5 specifically comprises: (1) Defining the ciphertext requiring decryption as cr =(c,.¢,); (2) each user terminal P; uniformly samples a noise term el from an error distribution 7 , computes a value h, = se, +e,, and broadcasts h, = sc, +e to other participants. (3) Calculate a 2 and (cc) (+46) ; (4) Output the decryption result Le (c, mod q)
Furthermore, the inventors have considered that in certain scenarios, such as
IoT environments, the primary functions of terminal physical devices are to collect data and transmit it to the server. In such cases, the user terminals do not See need to decrypt the final computation results, as this neither ensures data security nor 1s necessary. Therefore, when the ciphertext is not jointly decrypted by all participating parties but rather decrypted by a designated recipient, the method proceeds to Step S8 after Step S6: (1) Let s be the recipient's private key, wherein the recipient receives a ciphertext c/=(c,,c,) corresponding to the private key s. m = Le ral] (2) the recipient performs computation of 1 t
As demonstrated in Step S7 and Step S8, the system provides two distinct decryption methods corresponding to different application scenarios: (1) a joint decryption approach where participating parties collaboratively execute a joint decryption protocol to obtain decrypted results; and (ii) a designated recipient approach where only pre-authorized receivers perform decryption.
For Scenario 1 (Joint Decryption): Under the first operational scenario, upon receiving the computation results, all participating parties execute a joint decryption protocol to obtain the decrypted plaintext.
For Scenario 2 (Designated Recipient Decryption):
Under the second operational scenario, after receiving both the computation results and the recipient's public key, the participating parties perform a key exchange protocol to generate a new ciphertext, wherein said new ciphertext is decryptable exclusively by the designated recipient.
Wherein multiple users desire to contribute their data for collaborative Se analytics while preserving data privacy, the system constructs a privacy-preserving data sharing platform utilizing the aforementioned multi-party fully homomorphic encryption (FHE) scheme.
Each user encrypts their own data and transmits it to a shared system (server). This system can be regarded as a cloud platform (cloud server). After receiving the encrypted data from each user, the shared system performs corresponding computations. Upon completion of the computation, the results are returned to the respective users. The users then jointly decrypt the results to obtain the computed output. This system not only protects the data privacy and security of all participating parties but also enables data sharing and computation among users, thereby amplifying the value of the data.
Fully Homomorphic Encryption (FHE) enables arbitrary computations to be performed on ciphertexts. By utilizing FHE, multiple institutions can share their data in encrypted form and conduct various data analyses directly on the ciphertexts. This allows for the acquisition of more accurate data models without the need for decryption.
This fully homomorphic encryption (FHE)-based data sharing system is highly flexible and convenient, as it allows computation to be delegated to any party— even an untrusted third party —without leaking any training data to the computing entity. Furthermore, the FHE-based approach imposes no additional assumptions or constraints, offering significantly greater flexibility and ease of use compared to alternative methods (e.g., secure multi-party computation). ee
This makes it particularly suitable for military applications, where secure and efficient data collaboration is critical.
The present disclosure illustrates the inventive concept through specific examples, and the descriptions of the aforementioned embodiments are provided solely to facilitate understanding of the core principles of the invention.
It should be noted that any obvious modifications, equivalent substitutions, or other improvements made by those of ordinary skill in the art without departing from the inventive concept shall fall within the scope of protection of the present invention.
Claims (8)
1. A multi-party fully homomorphic encryption-based data sharing method, characterized in that it involves multiple user terminals, the method comprising: Each user terminal generates and stores its own private key using a private key generation algorithm; Each user terminal generates a collective public key for a designated data sharing task through a collective public key generation protocol, wherein the data sharing task 1s established in advance on a server by at least one user terminal; Each user terminal generates a relinearization public key through a relinearization public key generation protocol; Each user terminal encrypts its own data using the collective public key and transmits the ciphertext to the server; The server performs homomorphic computation on the ciphertext data uploaded by each user terminal and returns the computation result to each user terminal, wherein the homomorphic computation includes homomorphic addition and homomorphic multiplication, and the server executes a relinearization operation on the ciphertext using the relinearization public key after each homomorphic multiplication computation; Each user terminal executes a joint decryption protocol to decrypt the computation result and obtain the decrypted result; or, after receiving the computation result and a recipient’s public key, each participating party executes a key exchange protocol to generate a new ciphertext, which is decryptable by a designated recipient.
2. The multi-party fully homomorphic encryption-based data sharing method according to claim 1, characterized in that said each party user terminal generating its own private key through a private key generation algorithm comprises:
Each user terminal Pi uniformly and randomly selects a polynomial si from R3 as its private key, wherein R3 is a polynomial quotient ring, R3 =7, [X]/(X" + 1) ‚The polynomial modulus is(Xn+1) and its coefficients are uniformly distributed over{-1, 0,1}, where n is a power of 2.
3. The multi-party fully homomorphic encryption-based data sharing method according to claim 1, characterized in that the generation of the collective public key for the data sharing task by each party's user terminal through a collective public key generation protocol comprises: (1) Under the common reference string (CRS) model, each user terminal obtains a common polynomial P1, wherein P1 is uniformly and randomly selected from a polynomial quotient ring Ry = Zg[X]/(X™ + 1); where: each polynomial in Rg is taken modulo(X™ + 1), the coefficients are uniformly distributed ov. , n is a power , of two; and q is the ciphertext modulus; (2) Each user terminal P; uniformly and randomly selects a noise term €; from an error distribution,broadcasts it to the other user terminals p,; = —( DS, + e,) ‚ Wherein xis a discrete Gaussian distribution over R, (3)Each user terminal computes p, = > Po; generates a collective public key Prep pk = ( Po» P,) , wherein the collective public key is held by and publicly available to each user terminal, wherein a private key corresponding to the collective public key is s= = ] wherein the notation [ ], denotes modulo g operation. BP Le, 4 The multi-party fully homomorphic encryption-based data sharing method according to claim 1, characterized in that the generation of the re-linearization public key by each party's user terminal through a re-linearization public key generation protocol comprises: (1) Let w= CEE be the common parameter of all parties' user terminals. Where W isthe base. /= [10g,(g) | ; wherein the symbol [ | denotes a ceiling function: (2)In the random oracle model, each user terminal obtains a common ae R° ; (3)Each user terminal P; uniformly and randomly selects e,, from x ‚and uniformly and randomly selects uw, from R;,;broadcasts h, =—ua+sw+e,, to the other user terminals. (
4)Each user terminal computes h = > h, ; then selects ©. uniformly at random Prep from X ‚and broadcasts both h,,=sh+e,, and h,,=sa+e,, to the other user terminals. (5)Each user terminal computes h, = > h,, and h => h,, : then selects e,, Prep Prep uniformly at random from x’ ‚and broadcasts h, = (x, —s,)h, +e,, to the other user terminals. (6)Each user terminal computes h'= h’, generates a re-linearization public key - rlk = (1,1) = (hs +h,h, ). and publishes it.
5. The multi-party fully homomorphic encryption-based data sharing method according to claim 1, characterized in that said each party's user terminal encrypting their own data using said collective public key comprises: (1)Let the message space be R; = Z;|X]/(X" + 1), where t is the plaintext modulus. To encrypt a message me R,, select u“ uniformly at random from R,, and select eo* and eı* uniformly at random from 7. (2)"Compute ct=(cy, &;)= (Lg/t1m+u'p,+e;, up +e), output the ciphertext ct , where the symbol | | denotes a floor function.
6. The multi-party fully homomorphic encryption-based data sharing method according to claim 1, characterized in that the homomorphic computation comprises: (1)Homomorphic addition: given ct=(c,,c,) and ct = (06 ). compute and output ct, = (co + Ca, + a); (2)Homomorphic multiplication: given cf=(c,,¢,) and ct = (co ci) , compute and
1 . . . ' . output ct_, = Le (6960606 + cine) , where the notation [ |, denotes modulo q. q q (3)Ciphertext relinearization operation: given ct = (Co, C, c,), rlk = (,, r) ; express ca in I base w_ representation, namely c,= X cw” ; compute and output b=0 - ®) ®) Clin = C + Dach 16 + Dre : ho b=0
7. The multi-party fully homomorphic encryption-based data sharing method according to claim 1, characterized in that the step of each user terminal executing a joint decryption protocol to decrypt the computation result and obtain the decrypted result comprises: . ,_ct= (ce ¢) (1)The ciphertext that needs to be decrypted is
(2)Each user terminal P; uniformly and randomly selects noise e from the error distribution x, computes h; = s,c, +e,, and broadcasts it to the other participating parties ; (3)Compute Ah = Sn, and (cc) =(c, +h,c).
- . Lt. (4)Output the decryption result |-(c, mod q) q After receiving the computation results and the recipient's public key, each participating party executes the key exchange protocol to generate a new ciphertext, which includes: . ct = (Co, ¢) PR . . (1) Let the current ciphertext be , with its corresponding public key pk = (2 oP ) and private key s= > s, | ; the target ciphertexts public key is BeP q pk = (pp). (2)Each party 7 uniformly and randomly selects a polynomial u, from Æ, samples e,, uniformly from the error distribution x , and computes h,=sc+up,+e, and h,=up, +e, using the noise term e,,, then broadcasts them to all other participating parties. h => hy, h=}h, (3)Compute J and J , then output the target ciphertext ct = (ce) =(c, +h,h,). The designated recipient can decrypt the new ciphertext, which includes: (1) Let s be the recipient's private key. The ciphertext received by the recipient is ct= (co c ), where this ciphertext corresponds to the private key s. ‚ f m = Le ral] (2) The recipient computes 1 .
8. A multi-party fully homomorphic encryption-based data sharing system, characterized by comprising multiple user terminals and servers participating in data sharing; wherein: Each user terminal generates its own private key using a private key generation algorithm and stores it securely;
Each user terminal generates a collective public key for the data sharing task through a 11601636 collective public key generation protocol, wherein the data sharing task is established in the server by at least one user terminal;
Each user terminal generates a relinearization public key through a relinearization public key generation protocol;
Each user terminal encrypts its own data using the collective public key and transmits the ciphertext to the server;
The server performs homomorphic computations on the ciphertext data uploaded by each user terminal and returns the computation results to the respective user terminals; wherein the homomorphic computations include homomorphic addition and homomorphic multiplication, and the server is required to execute a relinearization operation on the ciphertext using the relinearization public key after each homomorphic multiplication computation;
Each user terminal executes a joint decryption protocol to decrypt the computation results and thereby obtain the decrypted outcome; alternatively, each participating party, upon receiving the computation results and a recipient's public key, performs a key switching protocol to generate a new ciphertext, which is then decryptable by a designated recipient.
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