DETAILED ACTION
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 .
2. The amendment of claims 1-20, filed on 8/10/2026, is acknowledged and considered. Claims 1-20 are pending.
Claims 1, 12, and 20 are independent claims.
Response to Arguments
4. Applicant’s arguments with respect to claim(s) 1-20 have been considered but are moot because the new ground of rejection does not rely on any reference applied in the prior rejection of record for any teaching or matter specifically challenged in the argument.
The argument is moot as the new limitations are now rejected under Gulak, et al. in view of Stapleton, et al.
Allowable Subject Matter
5. Claims 9 and 19 are objected to as being dependent upon a rejected base claim, but would be allowable if rewritten in independent form including all of the limitations of the base claim and any intervening claims.
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 (i.e., changing from AIA to pre-AIA ) 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.
6. Claim(s) 1-8, 10-18, and 20 is/are rejected under 35 U.S.C. 103 as being unpatentable over Gulak, et al. [US 20220129892] in view of Stapleton, et al. [US 12250299].
As per claim 1: Gulak, et al. teaches a system, comprising:
a memory; and [Gulak: para 0013]
a processor coupled to the memory and configured to: [Gulak: para 0013]
receive from a first computing system, coefficient information [Gulak: para 0039-0040; receiving in terms of the outputs of coefficients in the polynomials] comprising coefficients of a polynomial series determined based on an analytical function, wherein the analytical function represents or uses a cryptographic material; [Gulak: para 0007; homomorphic calculation as a polynomial series and to compute a value of the polynomial series using encrypted data to obtain an encrypted result. Para 0076; analysis includes ciphertext and homomorphic calculations involving the coefficients of the polynomials. See also para 0156-0157]
select the analytical function [Gulak: para 0046; The analytical function may be in terms of encryption or cryptographic related calculation involved. Such as, to implement an Enc(pk, μ) function] **from a plurality of functions by determining a graph kernel using the polynomial series as input to a graph similarity algorithm and optimizing the graph kernel using a phase estimation algorithm; [**Rejected under a secondary reference, discussion below]
determine the cryptographic material using the analytical function; and [Gulak: para 0056; the determination of cryptographic material may be the calculation involved in the encryption such that the correct decryption depends on the ciphertext noise being bounded. Taking C as a fresh ciphertext, it is apparent that homomorphic addition of v ciphertexts increases the noise by a factor of v in the worst case. Since the coefficients of the error polynomials are contemplated to follow a Gaussian distribution, the factor is closer to O(√{square root over (v)}). More examples of analytical function on para 0060, 0069-0072, 0076-0077, 0081]
perform a cryptographic operation using the cryptographic material. [Gulak: para 0080-0081; one example of cryptographic operation using cryptographic material is the encryption scheme and decrypts the most significant bit from all 1 polynomials in the ciphertext. More examples on para 0090, 0103]
Gulak discloses “determine the analytical function”, may be in terms of encryption or cryptographic related calculation involved. Such as, to implement an Enc(pk, μ) function as follows. The message space is R.sub.q. A uniform vector r.sub.N×1 is sampled where each coefficient in the polynomials in r sampled from [0, 1], E.sub.N×2←D.sub.R.sub.q,.sub.σ.sub.c.sup.N×2. The plaintext polynomial μ ∈ R.sub.q is encrypted by calculating the expression [Gulak: para 0046]. However, Gulak did not clearly teach to select from “a plurality of functions by determining a graph kernel using the polynomial series as input to a graph similarity algorithm and optimizing the graph kernel using a phase estimation algorithm”.
Stapleton’s invention discloses an analytic function that uses a quantum graph similarity algorithm to generate a graph kernel, and then uses a quantum phase estimation algorithm to minimize the kernel and identify the analytic function representative of the plaintext message [Stapleton: col.4, line 47-52]. Stapleton obviously suggest “determining a graph kernel using the polynomial series as input to a graph similarity algorithm and optimizing the graph kernel using a phase estimation algorithm”, where one would be motivated to minimizes the kernel and identify the analytic function. Stapleton includes the apparatus includes means, such as function generator for generating an analytic function using the symmetric key and the plaintext message. As part of generating the analytic function, function generator 208 may deploy one or more checks to ensure that the analytic function is differentiable. Upon confirming differentiability of an analytic function candidate, the analytic function candidate may then be selected by the function generator as the analytic function and the procedure may advance to operation [Stapleton: col.10, line 45-60]. An analytic function component may itself be an analytic function. An analytic function component may also comprise an operator or other element that may link together two analytic functions [Stapleton: col.11, line 10-13]. Further, when the function generator defines the initial allocation of analytic function components into the function generation table, the function generator may do this randomly (or pseudorandomly), such as through use of a brute force method (e.g., randomly or pseudorandomly selecting a first analytic function component in the subset, then randomly or pseudorandomly selecting a second analytic function component, and so forth, until all of the analytic functions have been selected, with the order of selection defining the ordering of the analytic function components in the column) [Stapleton: col.12, line 47-52]. As such, Stapleton obviously suggest the selection of an analytic function of analytic functions.
Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine Stapleton with Gulak to teach selecting from “a plurality of functions by determining a graph kernel using the polynomial series as input to a graph similarity algorithm and optimizing the graph kernel using a phase estimation algorithm”, for the reason to minimize the kernel and identify the analytic function, thus, create a new paradigm for securely protecting information [Stapleton: col.1, line 42-44 and col.4, line 47-52].
Claim 2: Gulak: para 0034, 0121 [the different devices and parties involved in data acquisition, storage, and analysis suggest receiving or obtaining from a device, i.e. a first computing system, information such cryptographic that includes coefficient] and Stapleton: para Col.16, line 1-8 [suggesting “to receive the coefficient information from the first computing system”, under the same pretext and motivation as in claim 1]; discussing the system of claim 1, wherein the first computing system comprises at least one of a classical computer or a first quantum computer; and a second computing system is configured to receive the coefficient information from the first computing system, wherein the second computing system comprises a second quantum computer.
Claim 3: Gulak: para 0121; discussing the system of claim 1, wherein each of the first quantum computer or the second quantum computer processes quantum bits or qubits.
Claim 4: Gulak: para 0036, claim 1 [keys involved in encryption, each set of encrypted comparison data using homomorphic operation on the plurality of strings]; discussing the system of claim 1, wherein the cryptographic material comprises a cryptographic key or information used to derive a cryptographic key; and the cryptographic material is expressed using a string.
Claim 5: Gulak: para 0174; discussing the system of claim 1, wherein the polynomial series comprises a Taylor series; and the polynomial series is determined by performing a Taylor series expansion of the analytical function.
Claim 6: Gulak: para 0036, claim 1 [keys involved in encryption, each set of encrypted comparison data using homomorphic operation on the plurality of strings]; discussing the system of claim 1, wherein the coefficient information comprises a string; the string comprises a plurality of strings, each of the plurality of strings is a string of a respective coefficient.
Claim 7: Gulak: para 0174; discussing the system of claim 1, wherein the polynomial series comprises a Taylor series.
Claim 8: Gulak: para 0056, 0076-0081 [determination of cryptographic material may be the calculation involved in the encryption such that the correct decryption depends on the ciphertext. Various examples of analytical functions]; discussing the system of claim 1, wherein determining the analytical function using the coefficient information comprises: determining the polynomial series using the coefficient information; and determining the analytical function using the polynomial series.
Claim 9: Objected
Claim 10: Gulak: para 0137; discussing the system of claim 1, wherein the processor is further configured to receive encrypted data from the first computing system, wherein the cryptographic operation comprises decrypting the encrypted data using the cryptographic material, wherein the cryptographic material comprises a private key.
Claim 11: Gulak: para 0125, 0140-0141 [decryption involves secret or private key, a Hash-based Message Authentication Code (HMAC) appended to the encrypted message for message integrity]; discussing the system of claim 1, wherein the cryptographic operation comprises generate signed data by generating a signature on data using the cryptographic material, wherein the cryptographic material comprises a private key, and wherein the processor is further configured to send the signed data comprising the signature to the first computing system, wherein the first computing system verifies the signature using the private key or a public key corresponding to the private key.
As per claim 12: Gulak, et al. teaches a method, comprising:
receiving, from a first computing system, coefficient information [Gulak: para 0039-0040; receiving in terms of the outputs of coefficients in the polynomials] comprising coefficients of a polynomial series determined based on an analytical function, wherein the analytical function represents or uses a cryptographic material; [Gulak: para 0007; homomorphic calculation as a polynomial series and to compute a value of the polynomial series using encrypted data to obtain an encrypted result. Para 0076; analysis includes ciphertext and homomorphic calculations involving the coefficients of the polynomials. See also para 0156-0157]
selecting the analytical function [Gulak: para 0046; The analytical function may be in terms of encryption or cryptographic related calculation involved. Such as, to implement an Enc(pk, μ) function] **from a plurality of functions by determining a graph kernel using the polynomial series as input to a graph similarity algorithm and optimizing the graph kernel using a phase estimation algorithm; [**Rejected under a secondary reference, discussion below]
determining the cryptographic material using the analytical function; and [Gulak: para 0056; the determination of cryptographic material may be the calculation involved in the encryption such that the correct decryption depends on the ciphertext noise being bounded. Taking C as a fresh ciphertext, it is apparent that homomorphic addition of v ciphertexts increases the noise by a factor of v in the worst case. Since the coefficients of the error polynomials are contemplated to follow a Gaussian distribution, the factor is closer to O(√{square root over (v)}). More examples of analytical function on para 0060, 0069-0072, 0076-0077, 0081]
performing a cryptographic operation using the cryptographic material. [Gulak: para 0080-0081; one example of cryptographic operation using cryptographic material is the encryption scheme and decrypts the most significant bit from all 1 polynomials in the ciphertext. More examples on para 0090, 0103]
Gulak discloses “determine the analytical function”, that may be in terms of encryption or cryptographic related calculation involved. Such as, to implement an Enc(pk, μ) function as follows. The message space is R.sub.q. A uniform vector r.sub.N×1 is sampled where each coefficient in the polynomials in r sampled from [0, 1], E.sub.N×2←D.sub.R.sub.q,.sub.σ.sub.c.sup.N×2. The plaintext polynomial μ ∈ R.sub.q is encrypted by calculating the expression [Gulak: para 0046]. However, Gulak did not clearly teach to select from “a plurality of functions by determining a graph kernel using the polynomial series as input to a graph similarity algorithm and optimizing the graph kernel using a phase estimation algorithm”.
Stapleton’s invention discloses an analytic function that uses a quantum graph similarity algorithm to generate a graph kernel, and then uses a quantum phase estimation algorithm to minimize the kernel and identify the analytic function representative of the plaintext message [Stapleton: col.4, line 47-52]. Stapleton obviously suggest “determining a graph kernel using the polynomial series as input to a graph similarity algorithm and optimizing the graph kernel using a phase estimation algorithm”, where one would be motivated to minimizes the kernel and identify the analytic function. Stapleton includes the apparatus includes means, such as function generator for generating an analytic function using the symmetric key and the plaintext message. As part of generating the analytic function, function generator 208 may deploy one or more checks to ensure that the analytic function is differentiable. Upon confirming differentiability of an analytic function candidate, the analytic function candidate may then be selected by the function generator as the analytic function and the procedure may advance to operation [Stapleton: col.10, line 45-60]. An analytic function component may itself be an analytic function. An analytic function component may also comprise an operator or other element that may link together two analytic functions [Stapleton: col.11, line 10-13]. Further, when the function generator defines the initial allocation of analytic function components into the function generation table, the function generator may do this randomly (or pseudorandomly), such as through use of a brute force method (e.g., randomly or pseudorandomly selecting a first analytic function component in the subset, then randomly or pseudorandomly selecting a second analytic function component, and so forth, until all of the analytic functions have been selected, with the order of selection defining the ordering of the analytic function components in the column) [Stapleton: col.12, line 47-52]. As such, Stapleton obviously suggest the selection of an analytic function of analytic functions.
Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine Stapleton with Gulak to teach selecting from “a plurality of functions by determining a graph kernel using the polynomial series as input to a graph similarity algorithm and optimizing the graph kernel using a phase estimation algorithm”, for the reason to minimize the kernel and identify the analytic function, thus, create a new paradigm for securely protecting information [Stapleton: col.1, line 42-44 and col.4, line 47-52].
Claim 13: Gulak: para 0034, 0121 [the different devices and parties involved in data acquisition, storage, and analysis suggest receiving or obtaining from a device, i.e. a first computing system, information such cryptographic that includes coefficient] and Stapleton: para Col.16, line 1-8 [suggesting “to receive the coefficient information from the first computing system”, under the same pretext and motivation as in claim 12]; discussing the method of claim 12, wherein the first computing system comprises at least one of a classical computer or a first quantum computer; and the second computing system is configured to receive the coefficient information from the first computing system, wherein the second computing system comprises a second quantum computer.
Claim 14: Gulak: para 0036, claim 1 [keys involved in encryption, each set of encrypted comparison data using homomorphic operation on the plurality of strings]; discussing the method of claim 12, wherein the cryptographic material comprises a cryptographic key or information used to derive a cryptographic key; and the cryptographic material is expressed using a string.
Claim 15: Gulak: para 0174; discussing the method of claim 12, wherein the polynomial series comprises a Taylor series; and the polynomial series is determined by performing a Taylor series expansion of the analytical function.
Claim 16: Gulak: para 00; discussing the method of claim 12, wherein the coefficient information comprises a string; the string comprises a plurality of strings, each of the plurality of strings is a string of a respective coefficient.
Claim 17: Gulak: para 0174; discussing the method of claim 12, wherein the polynomial series comprises a Taylor series.
Claim 18: Gulak: para 0056, 0076-0081 [determination of cryptographic material may be the calculation involved in the encryption such that the correct decryption depends on the ciphertext. Various examples of analytical functions]; discussing the method of claim 12, wherein determining the analytical function using the coefficient information comprises: determining the polynomial series using the coefficient information; and determining the analytical function using the polynomial series.
Claim 19: Objected
As per claim 20: Gulak, et al. teaches at least one non-transitory computer-readable medium storing quantum computer readable instructions, such that, when executed, causes at least one quantum processor to perform at least one of:
Receive, from a first computing system, coefficient information [Gulak: para 0039-0040; receiving in terms of the outputs of coefficients in the polynomials] comprising coefficients of a polynomial series determined based on an analytical function, wherein the analytical function represents or uses a cryptographic material; [Gulak: para 0007; homomorphic calculation as a polynomial series and to compute a value of the polynomial series using encrypted data to obtain an encrypted result. Para 0076; analysis includes ciphertext and homomorphic calculations involving the coefficients of the polynomials. See also para 0156-0157]
select the analytical function [Gulak: para 0046; The analytical function may be in terms of encryption or cryptographic related calculation involved. Such as, to implement an Enc(pk, μ) function] **from a plurality of functions by determining a graph kernel using the polynomial series as input to a graph similarity algorithm and optimizing the graph kernel using a phase estimation algorithm [**Rejected under a secondary reference, discussion below]
determining the cryptographic material using the analytical function; and [Gulak: para 0056; the determination of cryptographic material may be the calculation involved in the encryption such that the correct decryption depends on the ciphertext noise being bounded. Taking C as a fresh ciphertext, it is apparent that homomorphic addition of v ciphertexts increases the noise by a factor of v in the worst case. Since the coefficients of the error polynomials are contemplated to follow a Gaussian distribution, the factor is closer to O(√{square root over (v)}). More examples of analytical function on para 0060, 0069-0072, 0076-0077, 0081]
performing a cryptographic operation using the cryptographic material [Gulak: para 0080-0081; one example of cryptographic operation using cryptographic material is the encryption scheme and decrypts the most significant bit from all 1 polynomials in the ciphertext. More examples on para 0090, 0103]
Gulak discloses “determine the analytical function”, that may be in terms of encryption or cryptographic related calculation involved. Such as, to implement an Enc(pk, μ) function as follows. The message space is R.sub.q. A uniform vector r.sub.N×1 is sampled where each coefficient in the polynomials in r sampled from [0, 1], E.sub.N×2←D.sub.R.sub.q,.sub.σ.sub.c.sup.N×2. The plaintext polynomial μ ∈ R.sub.q is encrypted by calculating the expression [Gulak: para 0046]. However, Gulak did not clearly teach to select from “a plurality of functions by determining a graph kernel using the polynomial series as input to a graph similarity algorithm and optimizing the graph kernel using a phase estimation algorithm”.
Stapleton’s invention discloses an analytic function that uses a quantum graph similarity algorithm to generate a graph kernel, and then uses a quantum phase estimation algorithm to minimize the kernel and identify the analytic function representative of the plaintext message [Stapleton: col.4, line 47-52]. Stapleton obviously suggest “determining a graph kernel using the polynomial series as input to a graph similarity algorithm and optimizing the graph kernel using a phase estimation algorithm”, where one would be motivated to minimizes the kernel and identify the analytic function. Stapleton includes the apparatus includes means, such as function generator for generating an analytic function using the symmetric key and the plaintext message. As part of generating the analytic function, function generator 208 may deploy one or more checks to ensure that the analytic function is differentiable. Upon confirming differentiability of an analytic function candidate, the analytic function candidate may then be selected by the function generator as the analytic function and the procedure may advance to operation [Stapleton: col.10, line 45-60]. An analytic function component may itself be an analytic function. An analytic function component may also comprise an operator or other element that may link together two analytic functions [Stapleton: col.11, line 10-13]. Further, when the function generator defines the initial allocation of analytic function components into the function generation table, the function generator may do this randomly (or pseudorandomly), such as through use of a brute force method (e.g., randomly or pseudorandomly selecting a first analytic function component in the subset, then randomly or pseudorandomly selecting a second analytic function component, and so forth, until all of the analytic functions have been selected, with the order of selection defining the ordering of the analytic function components in the column) [Stapleton: col.12, line 47-52]. As such, Stapleton obviously suggest the selection of an analytic function of analytic functions.
Therefore, it would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine Stapleton with Gulak to teach selecting from “a plurality of functions by determining a graph kernel using the polynomial series as input to a graph similarity algorithm and optimizing the graph kernel using a phase estimation algorithm”, for the reason to minimize the kernel and identify the analytic function, thus, create a new paradigm for securely protecting information [Stapleton: col.1, line 42-44 and col.4, line 47-52].
Conclusion
Applicant's amendment necessitated the new ground(s) of rejection presented in this Office action. Accordingly, THIS ACTION IS MADE FINAL. See MPEP § 706.07(a). Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any nonprovisional extension fee (37 CFR 1.17(a)) pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
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Leynna Truvan
Examiner
Art Unit 2435
/L.TT/Examiner, Art Unit 2435
/EDWARD ZEE/Primary Examiner, Art Unit 2435
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