4DETAILED ACTION
This Office Action is in response to the communication filed on 12/15/2025.
Claims 1-3, 6-11 and 14-20 are pending.
Claims 1-3, 7-8, 10, 14-15 and 18-19 have been amended.
Claims 4-5 and 12-13 have been canceled.
Claims 1-3, 6-11 and 14-20 are rejected.
A request for continued examination under 37 CFR 1.114, including the fee set forth in 37 CFR 1.17(e), was filed in this application after final rejection. Since this application is eligible for continued examination under 37 CFR 1.114, and the fee set forth in 37 CFR 1.17(e) has been timely paid, the finality of the previous Office action has been withdrawn pursuant to 37 CFR 1.114. Applicant's submission filed on 12/15/2025 has been entered.
The Examiner cites particular sections in the references as applied to the claims below for the convenience of the applicant(s). Although the specified citations are representative of the teachings in the art and are applied to the specific limitations within the individual claim, other passages and figures may apply as well. It is respectfully requested that, in preparing responses, the applicant(s) fully consider the references in their entirety as potentially teaching all or part of the claimed invention, as well as the context of the passage as taught by the prior art or disclosed by the Examiner.
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Examiner’s Notes
Examiner’s note: (instant [0070] In a secure multi-party computation process, in step 31, the first party performs a mapping operation and homomorphic encryption on first plaintext data to obtain a first converted ciphertext in a Montgomery state); Therefore, being mapped is being interpreted as being in a Montgomery state.
Note
On Pages 13 and 14 of Remarks, applicant cites paragraphs 0060 and 0061. Please confirm the specifications are complete and correct.
The specifications examiner is able to reference read recite:
“[0060] FIG. 2 is a schematic diagram illustrating performing a modular exponentiation operation by using Montgomery reduction. In the example in FIG. 2, assume that g is an integer in integer ring Z and e and m are positive integers, in the example, g^e mod m attempts to be calculated, i.e. modular exponentiation of g attempts to be performed.
[0061] As shown in FIG. 2, the modular exponentiation operation is performed by applying Montgomery reduction, and an operation process mainly includes the following steps.”
Claim Objections
The claim objections have been withdrawn due to applicant’s amendments.
Claim Rejections - 35 USC § 112
The 112 rejections have been withdrawn due to applicant’s amendments.
Response to Arguments
Applicant's arguments filed 12/25/2025 regarding the 101 rejections have been fully considered but they are not persuasive.
Applicant states on pages 8-9 of Remarks “Unlike the over-simplified examples provided in the Office Action and Advisory Action, these claimed steps cannot be performed in the human mind” which seems to indicate that the examples which Examiner provided can be performed in the human mind. BRI only requires one example which can be performed by the human mind.
Applicant argues on pages 10-11 of Remarks that the converting a plaintext into Montgomery form and then performing homomorphic encryption and modular multiplication amounts to significantly more because such practice is not conventional or routine. However, Zhang discloses all of these processes which would seem to indicate that at least Mr. Zhang, who is someone skilled in the art, had previously considered these concepts in a system together.
“secure multi-party computation” and “homomorphic encryption operations” do not require what applicant argues. The guidance is “additional generic computer elements, explain that the generically recited computer elements do not add a meaningful limitation to the abstract idea because they amount to simply implementing the abstract idea on a compute”. applicant only recites “device” and “device” is generic, applicant is implementing the concept on a generic “device”. If applicant had specific hardware recitations it would be difficult for to make abstract idea arguments.
Applicant's arguments filed 12/15/2025 have been fully considered but they are not persuasive.
Applicant argues that Ahmed does not teach or suggest that “the encrypted search request is in the Montgomery state at the time it is transmitted” by the client device or that “instead of converting the first converted ciphertext in the Montgomery state back to the integer ring, sending, by the first device of the first party, the first converted ciphertext in the Montgomery state to a second device of a second party…”
First, examiner points out that (1) the claims do not recite “client device” (2) the claims do not recite encrypting (3) claim 1 does not recite what operation are being performed at the second device/party.
Second, the rejection is an obviousness rejection where the combination need only suggest the combination.
Zhang and Ahmed both teach Montgomery reduction for improved efficiency and homomorphic encryption for data security. Both references teach both concepts which reasonably suggests the order of operations which applicant argues.
Further Zhang explicitly discloses converting data to Montgomery form and further teaches that homomorphic encryption can be applied to data which before sharing the data to provide data privacy. Amend explicitly discloses a user encrypting data [0382] “A user is provided with an encryption module on his or her client device which is adapted to perform the requisite encryption”. The combination of these two references at least suggests converting to Montgomery form then encrypting before sending the data to a third party
On Page 13-14 of Remarks applicant argues that a Zhang in view of Ahmed does not teach or suggest a client converting to Montgomery state and encrypting data (forming encrypted Montgomery data) which is sent to a 3rd party for processing.
Examiner disagrees because Zhang teaches that Montgomery form can be used to improve computational efficiency and explains that data can be homomorphic encrypted so that the data can be used to perform federated learning without the party performing the federated learning being able to see the underlaying data.
This means that Zhang teaches Montgomery reduction (for improved efficiency) and homomorphic encryption (for improved security). In order for the encryption to be useful the data must be encrypted before it is sent to the 3rd party. Meaning the data is encrypted by the client for security and Montgomery reduction is applied for efficiency.
Zhang does not explicitly teach the actual transfer of data from one party to another party however Ahmed does.
In Summary Examiner believes that applicant is saying the claimed invention is:
User-side (1) Montgomery reduction and (2) homomorphically encrypting data
Server-side processing of the reduced encrypted data.
Examiner is saying that Zhang teaches the (1) Montgomery reduction and (2) homomorphically encrypting and Amend teaches (3) sending of data which has been (1) reduced and (2) encrypted. It would be obvious to send that data to a server after both operation have been performed. In order to provide improved efficiency at the cloud and data security while offloading the processing to the cloud.
Additionally applicant’s claims are broader than what applicant is arguing the invention is. Examiner suggests reciting all steps including which party is performing what operations.
Regarding the 101 rejection Applicant argues that the amended limitations amount to more than an abstract idea because the claims, as recited, demonstrate a specific and practical implementation, as well as an inventive concept, and not an abstract idea.
Examiner issues the 101 rejection because the claims, while potentially specific, practical and inventive, recite steps which can be performed in the human mind, using pen and paper, in the simplest implementation.
The Claims recite the steps of:
Performing mapping and performing encryption
Easily done in the mind for example:
The Montgomery form of the residue class a with respect to R is aR mod N, that is, it is the representative of the residue class aR. For example, suppose that N = 17 and that R = 100. The Montgomery forms of 3, 5, 7, and 15 are 300 mod 17 = 11, 500 mod 17 = 7, 700 mod 17 = 3, and 1500 mod 17 = 4.
Sending the resulting data to a second party
Easily done verbally and/or extra solution activity
At the second party, performing a homomorphic operation
This can be addition which, in its simplest form, can be performed in the human mind (for example 2+2=4)
Claim 10 simply involves a third party
Examiner recommends amending to include steps which cannot be performed by the human mind which as amending the claims to recite hardware structural elements interacting and perform the various steps recited in the claim.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 1, 10 and 14 are rejected under 35 U.S.C. 101 because the claimed invention is directed to Abstract Idea without significantly more. The claims recite generically computer elements which does not add a meaningful limitation to the abstract idea because they amount to simply implementing the abstract idea on a computer. This judicial exception is not integrated into a practical application because the steps can be categorized as mental steps or processes for mental step/organizing human activity. For example, performing mapping could reasonably be implemented manually and the sending step amounts to mere data gathering amounts and routine and conventional. The claims recite generically computer elements which does not add a meaningful limitation to the abstract idea because they amount to simply implementing the abstract idea on a computer. The claims do not include additional elements that are sufficient to amount to significantly more than the judicial exception because sending, mapping encrypting and processing data are all mental processes which can be performed in a human mind. The additional elements recited “device” amount to generic computer elements and fails to integrate the judicial exceptions into a practical application. Dependent claims 2-9, 11-13 and 15-20 are also rejected under the same rationale because they recited similar steps performing mapping and do not cure the deficiencies failing to integrate the abstract idea into practical application.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
The factual inquiries for establishing a background for determining obviousness under 35 U.S.C. 103 are summarized as follows:
1. Determining the scope and contents of the prior art.
2. Ascertaining the differences between the prior art and the claims at issue.
3. Resolving the level of ordinary skill in the pertinent art.
4. Considering objective evidence present in the application indicating obviousness or nonobviousness.
Claims 1-20 are rejected under 35 U.S.C. 103 as being unpatentable over Zhang (U.S. 20220147873), in view of Ahmed (U.S. 20190036678).
Regarding claim 1,
Zhang discloses: A computer-implemented method for secure multi-party computation, comprising: (Zhang [0005, 0021, 0030-0033] federated learning, privacy-preserving computation, Paillier encryption algorithm which are related to the privacy-preserving computation of federated learning, and other implementation scenarios that require a large number of large integer modular multiplication operations and modulus with larger bits, etc; [0033] a multi-operator parallel processing device for federated learning in accordance with the present disclosure)
converting, by a first device of a first party participating in the secure multi-party computation, first plaintext data to a Montgomery state by using a first mapping operation to obtain a first converted plaintext, wherein the first mapping operation converts data from an integer ring to the Montgomery state; (Zhang [0005-0022, 0033, 0038-0034, 0042, 0069] teaches device (100) which has modules for performing: (1) montgomerization and (2) encryption of data, using Paillier encryption (homomorphic encryption) schemes; The resulting montgomerized and encrypted data has been converted into the claimed “Montgomery state”; [0272-0284] Persons of ordinary skill in the art would appreciate, from the above descriptions of homomorphic addition and multiplication in FHE/UHE, that plaintext addition maps to cipher text multiplication while plaintext multiplication also maps to cipher text multiplication)
performing a homomorphic encryption operation on the first converted plaintext in the Montgomery state by using a public key to obtain a first converted ciphertext, wherein the homomorphic encryption operation comprises a plurality of modular exponentiation operations; (Zhang [0003-0022, 0033, 0038-0034, 0042, 0069]; [0003] teaches using homomorphic encryption technology such as the Paillier encryption algorithm to encrypt and share local data for federated learning; [0004] teaches using Paillier encryption algorithm based on modular exponentiation operations)
first converted ciphertext in the Montgomery state (Zhang [0012] In accordance with the first aspect of the present disclosure, in a manner of implementation, when the input operator mode is operations related to Paillier encryption algorithm, the controller determines enabling the pre-processing module, the montgomerization module, the confusion calculation module, and the Montgomery reduction module. Therefore, by enabling necessary modules only with respect to the input operator mode that is operations related to Paillier encryption algorithm, it is beneficial to improving the computing performance and system efficiency)
While Zhang discloses creating the first converted ciphertext in the Montgomery state (homomorphically encrypted montgomerizated data), Zhang does not explicitly disclose: instead of converting the first converted ciphertext in the Montgomery state back to the integer ring, sending, by the first device of the first party, the first converted ciphertext in the Montgomery state to a second device of a second party participating in the secure multi-party computation, wherein a first homomorphic operation is performed in the Montgomery state based on the first converted ciphertext in the Montgomery state to obtain a first result ciphertext in the Montgomery state, wherein the first homomorphic operation comprises a modular multiplication operation.
However, in the same field of endeavor Zhang in view of Ahmed discloses: instead of converting the first converted ciphertext in the Montgomery state back to the integer ring, sending, by the first device of the first party, the first converted ciphertext in the Montgomery state to a second device of a second party participating in the secure multi-party computation, wherein a first homomorphic operation is performed in the Montgomery state based on the first converted ciphertext in the Montgomery state to obtain a first result ciphertext in the Montgomery state, wherein the first homomorphic operation comprises a modular multiplication operation. (Ahmed [Fig. 8, 9, 19]; [0010, 0023, 0379-0382, 0440-0446] teaches the multi-party aspects of the invention, specifically [0382] A user requests a search (plaintext) and encrypts a search request (ciphertext) and sends the encrypted search request to a server (2nd party). In response, the server performs a series of FHE/UHE functions on it, including multiplication, to generate a FHE/UHE output that is sent back to the client device, which, in turn, decrypts the FHE/UHE output and displays the result; [0446] In accordance with further aspects of the present specification, the FHE cryptosystem is enabled to be highly efficient by replacing modular exponentiation operations with Montgomery Multiplication arithmetic), and the public key is paired with a private key used to perform a decryption operation based on the first result ciphertext. (Ahmed [0227-0230] With the FHE/UHE system of the present specification, it is possible to implement any key generation scheme with arbitrary key length—such as Public Key, Private Key)
Zhang and Ahmed are analogous art because they are from the same field of endeavor of performing federated homomorphic computations.
Before the effective filing date of the claimed invention, it would have been obvious to one of ordinary skill in the art, having the teachings of Zhang and Ahmed before him or her, to modify the method of Zhang to include the Multi-Party Computing of Ahmed because it will allow for the converted homomorphically encrypted ciphertexts to be processed by separate parties allowing for rapid scalability.
The motivation for doing so would be [“In order to avoid the expensive division operation associated with the modular exponentiation, the FHE scheme uses Montgomery modular arithmetic”] (Paragraph 0010, 0516 by Ahmed)].
Therefore, it would have been obvious to combine Zhang and Ahmed to obtain the invention as specified in the instant claim.
Regarding claim 10,
Zhang discloses: A computer-implemented method for secure multi-party computation, wherein the computer-implemented method is executed by a first device of a first party participating in the secure multi-party computation, and comprises:
converting first plaintext data to a Montgomery state by using a first mapping operation to obtain a first converted plaintext, wherein the first mapping operation converts data from an integer ring to the Montgomery state; (Zhang [0005-0022, 0033, 0038-0034, 0042, 0069] teaches device (100) which has modules for performing: (1) montgomerization and (2) encryption of data, using Paillier encryption (homomorphic encryption) schemes; The resulting montgomerized and encrypted data has been converted into the claimed “Montgomery state”; [0272-0284] Persons of ordinary skill in the art would appreciate, from the above descriptions of homomorphic addition and multiplication in FHE/UHE, that plaintext addition maps to cipher text multiplication while plaintext multiplication also maps to cipher text multiplication)
performing a homomorphic encryption operation on the first converted plaintext in the Montgomery state by using a public key to obtain a first converted ciphertext, wherein the homomorphic encryption operation comprises a plurality of modular exponentiation operations (Zhang [0003-0022, 0033, 0038-0034, 0042, 0069]; [0003] teaches using homomorphic encryption technology such as the Paillier encryption algorithm to encrypt and share local data for federated learning; [0004] teaches using Paillier encryption algorithm based on modular exponentiation operations)
first converted ciphertext in the Montgomery state (Zhang [0012] In accordance with the first aspect of the present disclosure, in a manner of implementation, when the input operator mode is operations related to Paillier encryption algorithm, the controller determines enabling the pre-processing module, the montgomerization module, the confusion calculation module, and the Montgomery reduction module. Therefore, by enabling necessary modules only with respect to the input operator mode that is operations related to Paillier encryption algorithm, it is beneficial to improving the computing performance and system efficiency)
While Zhang discloses creating the first converted ciphertext in the Montgomery state (homomorphically encrypted montgomerizated data), Zhang does not explicitly disclose: : instead of converting the first converted ciphertext in the Montgomery state back to the integer ring sending the first converted ciphertext in the Montgomery state to a second device of a second party participating in the secure multi-party computation; receiving a result ciphertext from a third device of a third party, wherein the result ciphertext is obtained by performing a homomorphic operation in the Montgomery state based on the first converted ciphertext in the Montgomery state, and the homomorphic operation comprises a modular multiplication operation; and performing Montgomery reduction and a decryption operation on the result ciphertext to obtain a result plaintext.
However, in the same field of endeavor Zhang in view of Ahmed discloses: : instead of converting the first converted ciphertext in the Montgomery state back to the integer ring sending the first converted ciphertext in the Montgomery state to a second device of a second party participating in the secure multi-party computation; (Ahmed [Fig. 8, 9, 19]; [0010, 0023, 0379-0382, 0440-0446] teaches the multi-party aspects of the invention, specifically [0382] A user requests a search (plaintext) and encrypts a search request (ciphertext) and sends the encrypted search request to a server (2nd party). In response, the server performs a series of FHE/UHE functions on it, including multiplication, to generate a FHE/UHE output that is sent back to the client device, which, in turn, decrypts the FHE/UHE output and displays the result; [0446] In accordance with further aspects of the present specification, the FHE cryptosystem is enabled to be highly efficient by replacing modular exponentiation operations with Montgomery Multiplication arithmetic)
receiving a result ciphertext from a third device of a third party, wherein the result ciphertext is obtained by performing a homomorphic operation in the Montgomery state based on the first converted ciphertext in the Montgomery state, and the homomorphic operation comprises a modular multiplication operation; and (Ahmed [0378-0384] describes receiving a result ciphertext from third device which has performed operations on the encrypted data to generate an encrypted result, the encrypted results is where is decrypted; [0446] In accordance with further aspects of the present specification, the FHE cryptosystem is enabled to be highly efficient by replacing modular exponentiation operations with Montgomery Multiplication arithmetic)
performing Montgomery reduction and a decryption operation on the result ciphertext to obtain a result plaintext (Ahmed [0376-0384] describes receiving a result ciphertext from third device which has performed operations on the encrypted data to generate an encrypted result, the encrypted results is where is decrypted… the encrypted result of then decrypted), wherein a private key paired with the public key is used to perform the decryption operation based on the result ciphertext. (Ahmed [0227-0230] With the FHE/UHE system of the present specification, it is possible to implement any key generation scheme with arbitrary key length—such as Public Key, Private Key)
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claimed invention to modify with Ahmed for similar reasons as cited in claim 1.
Regarding claim 14,
Zhang discloses: A computer-implemented method for secure multi-party computation, wherein the computer-implemented method is executed by a second device of a second party participating in the secure multi-party computation and comprises:
receiving a first converted ciphertext in a Montgomery state from a first device of a first party participating in the secure multi-party computation, wherein the first converted ciphertext is obtained by (Zhang [0005-0022, 0033, 0038-0034, 0042, 0069] teaches device (100) which has modules for performing: (1) montgomerization and (2) encryption of data, using Paillier encryption (homomorphic encryption) schemes; The resulting montgomerized and encrypted data has been converted into the claimed “Montgomery state”; [0272-0284] Persons of ordinary skill in the art would appreciate, from the above descriptions of homomorphic addition and multiplication in FHE/UHE, that plaintext addition maps to cipher text multiplication while plaintext multiplication also maps to cipher text multiplication)
converting first plaintext data to the Montgomery state by using a first mapping operation to obtain a first converted plaintext, wherein the first mapping operation converts data from an integer ring to the Montgomery state; (Zhang [0005-0022, 0033, 0038-0034, 0042, 0069] teaches device (100) which has modules for performing: (1) montgomerization and (2) encryption of data, using Paillier encryption (homomorphic encryption) schemes; The resulting montgomerized and encrypted data has been converted into the claimed “Montgomery state”; [0272-0284] Persons of ordinary skill in the art would appreciate, from the above descriptions of homomorphic addition and multiplication in FHE/UHE, that plaintext addition maps to cipher text multiplication while plaintext multiplication also maps to cipher text multiplication)
performing a homomorphic encryption operation on the first converted plaintext in the Montgomery state by using a public key to obtain the first converted ciphertext, wherein the homomorphic encryption operation comprises a plurality of modular exponentiation operations; and (Zhang [0003-0022, 0033, 0038-0034, 0042, 0069]; [0003] teaches using homomorphic encryption technology such as the Paillier encryption algorithm to encrypt and share local data for federated learning; [0004] teaches using Paillier encryption algorithm based on modular exponentiation operations)
While Zhang discloses creating the first converted ciphertext (homomorphically encrypted montgomerizated data), Zhang does not explicitly disclose: instead of converting the first converted ciphertext in the Montgomery state back to the integer ring, sending, by the first device of the first party, the first converted ciphertext in the Montgomery state to the second device of the second party; performing a first homomorphic operation in the Montgomery state based on the first converted ciphertext in the Montgomery state to obtain a first result ciphertext in the Montgomery state, wherein the first homomorphic operation comprises a modular multiplication operation; and sending the first result ciphertext.
However, in the same field of endeavor Zhang in view of Ahmed discloses: instead of converting the first converted ciphertext in the Montgomery state back to the integer ring, sending, by the first device of the first party, the first converted ciphertext in the Montgomery state to the second device of the second party; performing a first homomorphic operation in the Montgomery state based on the first converted ciphertext in the Montgomery state to obtain a first result ciphertext in the Montgomery state, wherein the first homomorphic operation comprises a modular multiplication operation; (Ahmed [Fig. 8, 9, 19]; [0010, 0023, 0379-0382, 0440-0446] teaches the multi-party aspects of the invention, specifically [0382] A user requests a search (plaintext) and encrypts a search request (ciphertext) and sends the encrypted search request to a server (2nd party). In response, the server performs a series of FHE/UHE functions on it, including multiplication, to generate a FHE/UHE output that is sent back to the client device, which, in turn, decrypts the FHE/UHE output and displays the result; [0446] In accordance with further aspects of the present specification, the FHE cryptosystem is enabled to be highly efficient by replacing modular exponentiation operations with Montgomery Multiplication arithmetic), and the public key is paired with a private key used to perform a decryption operation based on the first result ciphertext (Ahmed [0227-0230] With the FHE/UHE system of the present specification, it is possible to implement any key generation scheme with arbitrary key length—such as Public Key, Private Key) and sending the first result ciphertext. (Ahmed [Fig. 8, 9, 19]; [0010, 0023, 0379-0382, 0440-0446] a FHE/UHE output that is sent back to the client device, which, in turn, decrypts the FHE/UHE output and displays the result)
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claimed invention to modify with Ahmed for similar reasons as cited in claim 1.
Regarding claims 2 and 15,
Zhang in view of Ahmed discloses: The computer-implemented method according to claim 1, further comprising:
receiving, by the first device of the first party, the first result ciphertext; and
performing, by the first device of the first party, Montgomery reduction and a decryption operation on the first result ciphertext to obtain a first result plaintext. (Ahmed [Fig. 8, 9, 19]; [0010, 0023, 0379-0382, 0440-0446] the server performs a series of FHE/UHE functions on it, including multiplication, to generate a FHE/UHE output that is sent back to the client device, which, in turn, decrypts the FHE/UHE output and displays the result)
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claimed invention to modify with Ahmed for similar reasons as cited in claim 1.
Regarding claims 3 and 16,
Zhang in view of Ahmed discloses: The computer-implemented method according to claim 1, further comprising:
Montgomery state (Zhang [0005-0022, 0033, 0038-0034, 0042, 0069] teaches device (100) which has modules for performing: (1) montgomerization and (2) encryption of data, using Paillier encryption (homomorphic encryption) schemes; The resulting montgomerized and encrypted data has been converted into the claimed “Montgomery state”)
performing, by the second device of the second party, the first homomorphic operation in the Montgomery state based on the first converted ciphertext to obtain the first result ciphertext in the Montgomery state, wherein the first homomorphic operation comprises a modular multiplication operation; and (Ahmed [Fig. 8, 9, 19]; [0010, 0023, 0379-0382, 0440-0446] the server performs a series of FHE/UHE functions on it, including multiplication, to generate a FHE/UHE output that is sent back to the client device, which, in turn, decrypts the FHE/UHE output and displays the result)
sending, by the second device of the second party, the first result ciphertext to a third device of a third party, wherein a second homomorphic operation is performed (Ahmed [0384] in step 1225, which is the output resulting from the application of the at least one string concatenation functions to the FHE or UHE formatted data (modified FHE or UHE formatted data)… in step 1230, the request (which is in a FHE or UHE format) and apply to the request, in step 1235, at least one string concatenation operation. The at least one string concatenation operation is the mathematical equivalent to applying a multiplication and/or addition operation to the plaintext version of the data. As a result of applying the at least one string concatenation operation, the servers generate a second output, still in a FHE or UHE format)
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claimed invention to modify with Ahmed for similar reasons as cited in claim 1.
Regarding claims 6 and 17,
Zhang in view of Ahmed discloses: The computer-implemented method according to claim 1, further comprising:
obtaining, by the second device of the second party, a second converted ciphertext in the Montgomery state; and (Ahmed [0384] in step 1230, the request (which is in a FHE or UHE format) and apply to the request, in step 1235, at least one string concatenation operation. The at least one string concatenation operation is the mathematical equivalent to applying a multiplication and/or addition operation to the plaintext version of the data. As a result of applying the at least one string concatenation operation, the servers generate a second output, still in a FHE or UHE format [0436-0447] teaches obtaining a second ciphertext at a second device of a second party)
the first result ciphertext in the Montgomery state is obtained by operations comprising: performing the first homomorphic operation on the first converted ciphertext and the second converted ciphertext to obtain the first result ciphertext. (Ahmed [0435-0441] teaches obtaining results of a first and second ciphertext by performing homomorphic operations (decrypting) which results in a result ciphertext)
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claimed invention to modify with Ahmed for similar reasons as cited in claim 1.
Regarding claims 7 and 18,
Zhang in view of Ahmed discloses: The computer-implemented method according to claim 6, wherein the obtaining the second converted ciphertext in the Montgomery state comprises:
receiving the second converted ciphertext from the first device of the first party. (Ahmed [0384] in step 1225, which is the output resulting from the application of the at least one string concatenation functions to the FHE or UHE formatted data (modified FHE or UHE formatted data)… in step 1230, the request (which is in a FHE or UHE format) and apply to the request, in step 1235, at least one string concatenation operation. The at least one string concatenation operation is the mathematical equivalent to applying a multiplication and/or addition operation to the plaintext version of the data. As a result of applying the at least one string concatenation operation, the servers generate a second output, still in a FHE or UHE format)
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claimed invention to modify with Ahmed for similar reasons as cited in claim 1.
Regarding claims 8 and 19,
Zhang in view of Ahmed discloses: The computer-implemented method according to claim 6, wherein the obtaining the second converted ciphertext in the Montgomery state comprises:
performing the first mapping operation and homomorphic encryption on local second plaintext data of the second party to obtain the second converted ciphertext. (Zhang [0005-0022, 0033, 0038-0034, 0042, 0069] teaches device (100) which has modules for performing: (1) montgomerization and (2) encryption of data, using Paillier encryption (homomorphic encryption) schemes; The resulting montgomerized and encrypted data has been converted into the claimed “Montgomery state”; [0272-0284] Persons of ordinary skill in the art would appreciate, from the above descriptions of homomorphic addition and multiplication in FHE/UHE, that plaintext addition maps to cipher text multiplication while plaintext multiplication also maps to cipher text multiplication, which describes generating any number of mapped ciphertexts)
Regarding claims 9 and 20,
Zhang in view of Ahmed discloses: The computer-implemented method according to claim 8, wherein the first plaintext data is parameter data of a service prediction model, and the local second plaintext data is characteristic data of a service object. (Ahmed [0368] teaches parameters which are used to as weight in computations that may be performed include without limitation averages, standard deviations, and other statistical functions, such as logistical regressions that can help predict the likelihood of certain events; [0369-0376] teaches second plaintext data, which can be encrypted, that can be considered characteristic(s) of service object(s))
It would have been obvious to a person of ordinary skill in the art before the effective filing date of the claimed invention to modify with Ahmed for similar reasons as cited in claim 1.
Regarding claim 11,
Zhang in view of Ahmed discloses: The computer-implemented method according to claim 10, wherein the second party and the third party are the same party. (Zhang [0005-0022, 0033], [Fig. 1] shows a diagram consisting of separate modules for performing the method which are not explicitly described as separate parties)
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's
disclosure.
Zhang 2021-10-29 (US 11296861) teaches A Paillier decryption system, IC, and method. The IC includes: a modular exponentiation module, for performing modular exponentiation operations related to a first subitem and a second subitem, where a Paillier decryption process of encrypted data is divided into a first subitem and a second subitem according to the Chinese remainder theorem, the first subitem corresponding to a first prime, the second subitem corresponding to a second prime, a public key of the encrypted data being a product of the first prime and the second prime, a bit width of the first prime being the same as a bit width of the second prime; a first module combination corresponding to the first subitem, for determining a computation result of the first subitem; and a second module combination corresponding to the second subitem, for determining a computation result of the second subitem.
Schaffer 2011-05-11 (US 20120288086) teaches Cryptographic systems perform various arithmetic calculations. While many asymmetric cryptosystems are known to be provably secure with respect to mathematical assumptions, such cryptosystems may be vulnerable to implementation attacks such as fault attacks.
Any inquiry concerning this communication or earlier communications from the examiner should be directed to THOMAS A CARNES whose telephone number is (571)272-4378. The examiner can normally be reached Monday-Friday.
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THOMAS A. CARNES
Examiner
Art Unit 2436
/THOMAS A CARNES/Examiner, Art Unit 2436
/MOEEN KHAN/Primary Examiner, Art Unit 2436