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 regarding claims 1-20, filed on 2/23/2026, are acknowledged and considered.
3. Claims 1-20 are pending. Claims 1, 12, and 20 are independent claims.
Continued Examination Under 37 CFR 1.114
4. 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and the fee set forth in 37 CFR 1.17(e) has been timely paid, the finality of the previous Office action has been withdrawn pursuant to 37 CFR 1.114.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 2/23/2026 has been entered.
Response to Arguments
5. 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. [US 20220129892] in view of Khankin, et al. [US 20230214307].
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) 1-20 is/are rejected under 35 U.S.C. 103 as being unpatentable over Gulak, et al. [US 20220129892] in view of Khankin, et al. [US 20230214307].
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 comparing a plurality of outputs that measure similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of functions; [**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]
Ref1 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, Ref1 did not clearly teach “a plurality of functions by comparing a plurality of outputs that measure similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of functions”.
Khankin obviously suggest using an analytical function of “a plurality of functions by comparing a plurality of outputs that measure similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of functions”, where one would be motivated to a compute graph optimized for efficient execution of the current computation task, in particular the computation of the polynomial-based approximant [Khankin: para 0042]. Khankin teaches computing the approximant may be an iterative process comprising one or more iterations and polynomial-based approximant is selected include a polynomial, a set of polynomials, or in case of a rational approximant, a quotient of two polynomials, and/or the like where an initial set of coefficients is constructed for the selected polynomial, based on the attribute(s) of the certain function and also based on target interval (i.e., range of values) of interest for approximating the certain function. The processing circuitry may then compute the polynomial-based approximant according to the constructed set of coefficients. For example, the polynomial-based approximant may be computed by projecting the compute graph of the polynomial-based approximant on the interconnected computing grid, i.e., mapping the nodes and edges of the approximant's compute graph to the reconfigurable logic elements connectable by the configurable data routing junctions [Khankin: para 0043-0044]. Khankin obviously suggest “a plurality of functions” and output involving to “measure similarity using the coefficient information”. Further, Khankin discloses the processing circuitry compute the polynomial-based approximant by generating a compute graph configured to project the selected polynomial-based approximant with the selected set of coefficients [Khankin: para 0113]. The constraints include an accuracy of the approximation of the polynomial-based approximant. The accuracy may be computed by comparing the result (outcome) of the polynomial-based approximant, over the target interval, to a high accuracy result of the received function which may be received and/or computed using one or more floating-point units [Khankin: para 0119]. As such, obviously suggest “comparing a plurality of outputs” to obtain the “similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of 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 Khankin with Ref1 to teach “a plurality of functions by comparing a plurality of outputs that measure similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of functions”, for the reason to [Khankin: para 0042].
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 Khankin: para 0011, 0043-0044 [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: Gulak: para 0174, 0186-0187 [relational operations includes comparison for similarities. Machine learning may include similarity, estimation, and other forms of data determination for data collection learning and training]; discussing the system of claim 8, wherein determining the analytical function using the polynomial series comprises: determining a graph kernel using the polynomial series as an input to a graph similarity algorithm; and optimizing the graph kernel using a phase estimation algorithm.
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 comparing a plurality of outputs that measure similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of functions; [**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]
Ref1 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, Ref1 did not clearly teach “a plurality of functions by comparing a plurality of outputs that measure similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of functions”.
Khankin obviously suggest using an analytical function of “a plurality of functions by comparing a plurality of outputs that measure similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of functions”, where one would be motivated to a compute graph optimized for efficient execution of the current computation task, in particular the computation of the polynomial-based approximant [Khankin: para 0042]. Khankin teaches computing the approximant may be an iterative process comprising one or more iterations and polynomial-based approximant is selected include a polynomial, a set of polynomials, or in case of a rational approximant, a quotient of two polynomials, and/or the like where an initial set of coefficients is constructed for the selected polynomial, based on the attribute(s) of the certain function and also based on target interval (i.e., range of values) of interest for approximating the certain function. The processing circuitry may then compute the polynomial-based approximant according to the constructed set of coefficients. For example, the polynomial-based approximant may be computed by projecting the compute graph of the polynomial-based approximant on the interconnected computing grid, i.e., mapping the nodes and edges of the approximant's compute graph to the reconfigurable logic elements connectable by the configurable data routing junctions [Khankin: para 0043-0044]. Khankin obviously suggest “a plurality of functions” and output involving to “measure similarity using the coefficient information”. Further, Khankin discloses the processing circuitry compute the polynomial-based approximant by generating a compute graph configured to project the selected polynomial-based approximant with the selected set of coefficients [Khankin: para 0113]. The constraints include an accuracy of the approximation of the polynomial-based approximant. The accuracy may be computed by comparing the result (outcome) of the polynomial-based approximant, over the target interval, to a high accuracy result of the received function which may be received and/or computed using one or more floating-point units [Khankin: para 0119]. As such, obviously suggest “comparing a plurality of outputs” to obtain the “similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of 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 Khankin with Ref1 to teach “a plurality of functions by comparing a plurality of outputs that measure similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of functions”, for the reason to [Khankin: para 0042].
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 Khankin: para 0011, 0043-0044 [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: Gulak: para 0174, 0186-0187 [relational operations includes comparison for similarities. Machine learning may include similarity, estimation, and other forms of data determination for data collection learning and training]; discussing the method of claim 18, wherein determining the analytical function using the polynomial series comprises: determining a graph kernel using the polynomial series as an input to a graph similarity algorithm; and optimizing the graph kernel using a phase estimation algorithm.
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 comparing a plurality of outputs that measure similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of functions; [**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]
Ref1 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, Ref1 did not clearly teach “a plurality of functions by comparing a plurality of outputs that measure similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of functions”.
Khankin obviously suggest using an analytical function of “a plurality of functions by comparing a plurality of outputs that measure similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of functions”, where one would be motivated to a compute graph optimized for efficient execution of the current computation task, in particular the computation of the polynomial-based approximant [Khankin: para 0042]. Khankin teaches computing the approximant may be an iterative process comprising one or more iterations and polynomial-based approximant is selected include a polynomial, a set of polynomials, or in case of a rational approximant, a quotient of two polynomials, and/or the like where an initial set of coefficients is constructed for the selected polynomial, based on the attribute(s) of the certain function and also based on target interval (i.e., range of values) of interest for approximating the certain function. The processing circuitry may then compute the polynomial-based approximant according to the constructed set of coefficients. For example, the polynomial-based approximant may be computed by projecting the compute graph of the polynomial-based approximant on the interconnected computing grid, i.e., mapping the nodes and edges of the approximant's compute graph to the reconfigurable logic elements connectable by the configurable data routing junctions [Khankin: para 0043-0044]. Khankin obviously suggest “a plurality of functions” and output involving to “measure similarity using the coefficient information”. Further, Khankin discloses the processing circuitry compute the polynomial-based approximant by generating a compute graph configured to project the selected polynomial-based approximant with the selected set of coefficients [Khankin: para 0113]. The constraints include an accuracy of the approximation of the polynomial-based approximant. The accuracy may be computed by comparing the result (outcome) of the polynomial-based approximant, over the target interval, to a high accuracy result of the received function which may be received and/or computed using one or more floating-point units [Khankin: para 0119]. As such, obviously suggest “comparing a plurality of outputs” to obtain the “similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of 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 Khankin with Ref1 to teach “a plurality of functions by comparing a plurality of outputs that measure similarity between a graph of the polynomial series generated using the coefficient information and graphs corresponding to the plurality of functions”, for the reason to [Khankin: para 0042].
Conclusion
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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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