DETAILED ACTION
This action is in response to the application filed on March 3, 2025. Claims 1-20 are
pending. Of such, claims 1-14 represent a method, claims 15-20 represent a system directed to polynomial function secret sharing.
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 .
Double Patenting
The nonstatutory double patenting rejection is based on a judicially created doctrine grounded in public policy (a policy reflected in the statute) so as to prevent the unjustified or improper timewise extension of the “right to exclude” granted by a patent and to prevent possible harassment by multiple assignees. A nonstatutory double patenting rejection is appropriate where the conflicting claims are not identical, but at least one examined application claim is not patentably distinct from the reference claim(s) because the examined application claim is either anticipated by, or would have been obvious over, the reference claim(s). See, e.g., In re Berg, 140 F.3d 1428, 46 USPQ2d 1226 (Fed. Cir. 1998); In re Goodman, 11 F.3d 1046, 29 USPQ2d 2010 (Fed. Cir. 1993); In re Longi, 759 F.2d 887, 225 USPQ 645 (Fed. Cir. 1985); In re Van Ornum, 686 F.2d 937, 214 USPQ 761 (CCPA 1982); In re Vogel, 422 F.2d 438, 164 USPQ 619 (CCPA 1970); In re Thorington, 418 F.2d 528, 163 USPQ 644 (CCPA 1969).
A timely filed terminal disclaimer in compliance with 37 CFR 1.321(c) or 1.321(d) may be used to overcome an actual or provisional rejection based on nonstatutory double patenting provided the reference application or patent either is shown to be commonly owned with the examined application, or claims an invention made as a result of activities undertaken within the scope of a joint research agreement. See MPEP § 717.02 for applications subject to examination under the first inventor to file provisions of the AIA as explained in MPEP § 2159. See MPEP § 2146 et seq. for applications not subject to examination under the first inventor to file provisions of the AIA . A terminal disclaimer must be signed in compliance with 37 CFR 1.321(b).
The filing of a terminal disclaimer by itself is not a complete reply to a nonstatutory double patenting (NSDP) rejection. A complete reply requires that the terminal disclaimer be accompanied by a reply requesting reconsideration of the prior Office action. Even where the NSDP rejection is provisional the reply must be complete. See MPEP § 804, subsection I.B.1. For a reply to a non-final Office action, see 37 CFR 1.111(a). For a reply to final Office action, see 37 CFR 1.113(c). A request for reconsideration while not provided for in 37 CFR 1.113(c) may be filed after final for consideration. See MPEP §§ 706.07(e) and 714.13.
The USPTO Internet website contains terminal disclaimer forms which may be used. Please visit www.uspto.gov/patent/patents-forms. The actual filing date of the application in which the form is filed determines what form (e.g., PTO/SB/25, PTO/SB/26, PTO/AIA /25, or PTO/AIA /26) should be used. A web-based eTerminal Disclaimer may be filled out completely online using web-screens. An eTerminal Disclaimer that meets all requirements is auto-processed and approved immediately upon submission. For more information about eTerminal Disclaimers, refer to www.uspto.gov/patents/apply/applying-online/eterminal-disclaimer.
Claims 1-20 are rejected on the ground of nonstatutory double patenting as being unpatentable over claims 1-17 of U.S. Patent No. 12,316,752.
Independent Claims:
Presently presented Claim 1
Claim 1 of ‘752
A computing-processor-implemented method of polynomial function secret sharing by share result computation systems participating in computation of reconstruction share results for a polynomial function evaluated on input data, the computing-processor- implemented method comprising
A computing-processor-implemented method of polynomial function secret sharing by share result computation systems participating in computation of reconstruction share results for a polynomial function evaluated on input data, the computing-processor-implemented method comprising:
receiving an allocatable share of the polynomial function at a first computing system of the share result computation systems, the allocatable share being a member of a set of allocatable shares generated from the polynomial function, each of the allocatable shares being distributed to a unique share result computation system of the share result computation systems
receiving an allocatable share of the polynomial function at a first computing system of the share result computation systems, the allocatable share being a member of a set of allocatable shares generated from the polynomial function, each of the allocatable shares being distributed to a unique share result computation system of the share result computation systems,
generating a reconstruction share result at the first computing system by computing a dot product of the input data and the allocatable share received by the first computing system, wherein a combination of the reconstruction share results generated by the share result computation systems yields a reconstructed result of the polynomial function evaluated on the input data;
generating a reconstruction share result at the first computing system by computing a dot product of the input data and the allocatable share received by the first computing system, wherein a combination of the reconstruction share results generated by the share result computation systems yields a reconstructed result of the polynomial function evaluated on the input data;
and transmitting the reconstruction share result to another computing system for computation of the reconstructed result.
transmitting the reconstruction share result to another computing system for computation of the reconstructed result.
Presently presented Claim 7
Claim 5 of ‘752
A computing-processor-implemented method of polynomial function secret sharing in computation of reconstruction share results for a polynomial function evaluated on input data, the computing-processor-implemented method comprising
A computing-processor-implemented method of polynomial function secret sharing in computation of reconstruction share results for a polynomial function evaluated on input data, the computing-processor-implemented method comprising:
generating an allocatable share of the polynomial function for each share result computation system of a set of share result computation systems, each allocatable share including a share element for each coefficient in the polynomial function;
generating an allocatable share of the polynomial function for each share result computation system of a set of share result computation systems, each allocatable share including a share element for each coefficient in the polynomial function,
and distributing each allocatable share to a unique share result computation system of the share result computation systems to compute a dot product of the input data and the share received by each share result computation system, wherein a combination of the reconstruction share results generated by the share result computation systems yields a reconstructed result of the polynomial function evaluated on the input data.
distributing each allocatable share to a unique share result computation system of the share result computation systems to compute a dot product of the input data and the share received by each share result computation system, wherein a combination of the reconstruction share results generated by the share result computation systems yields a reconstructed result of the polynomial function evaluated on the input data.
Presently presented Claim 15
Claim 12 of ‘752
A system for polynomial function secret sharing by share result computation systems participating in computation of reconstruction share results for a polynomial function evaluated on input data, the system comprising
A system for polynomial function secret sharing by share result computation systems participating in computation of reconstruction share results for a polynomial function evaluated on input data, the system comprising:
one or more hardware processors; a communication interface configured to receive an allocatable share of the polynomial function, the allocatable share being a member of a set of allocatable shares generated from the polynomial function, each of the allocatable being distributed to a unique share result computation system of the share result computation systems
one or more hardware processors; a communication interface configured to receive an allocatable share of the polynomial function, the allocatable share being a member of a set of allocatable shares generated from the polynomial function, each of the allocatable being distributed to a unique share result computation system of the share result computation systems,
and a share result computation system executable by the one or more hardware processors and configured to generate a reconstruction share result by computing a dot product of the input data and the allocatable share received by the communication interface, wherein a combination of the reconstruction share results generated by the share result computation systems yields a reconstructed result of the polynomial function evaluated on the input data, wherein the communication interface is further configured to transmit the reconstruction share result to another computing system for computation of the reconstructed result.
a share result computation system executable by the one or more hardware processors and configured to generate a reconstruction share result by computing a dot product of the input data and the allocatable share received by the communication interface, wherein a combination of the reconstruction share results generated by the share result computation systems yields a reconstructed result of the polynomial function evaluated on the input data, wherein the communications interface is further configured to transmit the reconstruction share result to another computing system for computation of the reconstructed result.
Dependent Claims:
Presently Presented Dependent Claims
Dependent Claims of ‘752
Claims 2, 3
Claim 1
Claim 4
Claim 2
Claim 5
Claim 3
Claim 6
Claim 4
Claim 8
Claim 6
Claim 9
Claim 5
Claim 10
Claim 5
Claim 11
Claim 7
Claim 12
Claim 8
Claim 13
Claim 9
Claim 14
Claim 10
Claim 16
Claim 12
Claim 17
Claims 12 and 16
Claim 18
Claim 13
Claim 19
Claim 14
Claim 20
Claim 15
Claim Objections
Claims 3, 10, 15, and 17 are objected to because of the following informalities:
Claims 3, 10, and 17 are objected due to the following grammatical error “wherein a share elements…”.
Claim 15 is objected to due to the following typographical error “each of the allocatable being distributed” is missing “shares”.
Appropriate correction is required.
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 1-20 are rejected under 35 U.S.C. 101 because the identified claim limitation(s) that recite(s) an abstract idea without significantly more.
Claim 1 recites mathematical calculations intended to “generate a reconstruction share result…by computing a dot product of the input data and the allocatable share”, where “a combination of the reconstruction share results…yields a reconstructed result of the polynomial function evaluated on the input data”. The received shares are numeric vectors, the dot product is a mathematical calculation, and the combination is a mathematical operation reconstructing the function. The limitations as drafted, is a process that, under its broadest reasonable interpretation, that merely covers mathematical calculations using mathematical formulas but for exception of the recitation of generic computer components. That is, other than reciting “computing systems”, “interface”, and “hardware processors” nothing in the claim element precludes the step of performing the mathematical calculations using generic computational methods such as using pen, paper, calculators and other generic computer products.
If a claim limitation, under its broadest reasonable interpretation, covers mathematical concepts but for the recitation of generic computer components, then it falls within the “Mathematical Concepts” grouping of abstract ideas. Accordingly, the claim recites an abstract idea.
This judicial exception is not integrated into a practical application. The method in both steps is recited at a high-level of generality (i.e., as a generic processor performing a sharing and reconstruction of a secret function) such that it amounts no more than mere instructions to apply the exception using a generic computer component. Accordingly, this additional element does not integrate the abstract idea into a practical application because it does not impose any meaningful limits on practicing the abstract idea. Further the claims do not recite an improvement to the functioning of a computer or other technology as the limitations are strictly associated with the mathematical properties of sharing the scheme itself. The claim is directed to an abstract idea.
The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to integration of the abstract idea into a practical application, the additional element of using a system to perform the computation amounts to no more than mere instructions to apply the exception using a generic computer component. Mere instructions to apply an exception using a generic computer component cannot provide an inventive concept. The claim is not patent eligible. Claim 7 and 15 represents a method and system, respectively, of the limitations presented in Claim 1. These are abstract for the same reasons as Claim 1, and do not integrate the abstract ideas into a practical application or add significantly more to the abstract ideas recited in Claim 1.
Claims 2-6, 8-14 and 16-20 are dependent on independent claims 1, 7, and 15 and similarly do not present any additional limitations that would integrate the judicial exception into a practical application. Furthermore, no additional elements are added that impose any meaningful limits on practicing the abstract idea other than generic computer components. For this reason, claims 2-6, 8-14 and 16-20 are also rejected based on their dependency on claims 1, 7, and 15 and not for resolving the deficiencies identified in the rejection of claims 1, 7, and 15 above.
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.
Claims 1, 2, 6-9, 13, 15, 16, and 20 are rejected under 35 U.S.C. 103 as being unpatentable over Raviv et al. (NPL: Private Polynomial Computation from Lagrange Encoding), hereinafter referred to as Raviv, in view of Boyle et al. (NPL: Function Secret Sharing for Mixed-Mode and Fixed-Point Secure Computation), hereinafter referred to as Boyle.
Regarding Claim 1, Raviv discloses:
A computing-processor-implemented method of polynomial function secret sharing by share result computation systems participating in computation of reconstruction share results for a polynomial function evaluated on input data (In the abstract, Raviv discloses “we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data”), the computing-processor-implemented method comprising: receiving an allocatable share of the polynomial function at a first computing system of the share result computation systems (On page 4, Raviv discloses “the user sends S queries pn(1), ….pn(S) Є S to the n’th server”), the allocatable share being a member of a set of allocatable shares generated from the polynomial function, each of the allocatable shares being distributed to a unique share result computation system of the share result computation systems (On page 6, Raviv discloses “Here pn(S) is transmitted to the n’th server during the s’th round, who responds with pn(S) (yn).” Further see Equation 8
PNG
media_image1.png
58
321
media_image1.png
Greyscale
); and transmitting the reconstruction share result to another computing system for computation of the reconstructed result (On page 4, Raviv discloses “the user sends S queries pn(1), ….pn(S) Є S to the n’th server, who responds with the answers pn(1) (yn), ….pn(S) (yn)”)
However, Raviv does not explicitly disclose computing a dot product of a share.
Boyle discloses:
generating a reconstruction share result at the first computing system by computing a dot product of the input data and the allocatable share received by the first computing system (On page 18, Boyle discloses “Once the evaluators P0 and P1 learn the shares of the correct coefficients, they compute an inner product with (xd,...,x0) to learn shares of final output.”), wherein a combination of the reconstruction share results generated by the share result computation systems yields a reconstructed result of the polynomial function evaluated on the input data (On page 11, Boyle discloses “FSS scheme is an efficient algorithm that splits a function f ∈ F into two additive shares f0,f1, such that: (1) each fσ hides f; (2) for every input x, f0(x) + f1(x) = f(x).”);
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Raviv’s approach by utilizing Boyle’s approach of performing a dot product to learn the shares of the final output as the motivation would be to reduce the complexity of interaction and communication between the participants when performing secret sharing (Boyle et al. Page 1).
Regarding Claim 2, the combination of Raviv and Boyle disclose the limitations of Claim 1.
However, Raviv does not explicitly disclose one share element per coefficient.
Boyle discloses:
The computing-processor-implemented method of claim 1, wherein each allocatable share includes a share element for each coefficient in the polynomial function (On page 19, Figure 4, Boyle discloses in steps 1-2 and 7, “Let (fd,...,f0) ∈ UN(d+1) ) N be coefficients of f’ such that f’(x) = f(x−rin)… Set β = (f’d,...,f’0) ∈ UN(d+1) and γ=(N−1)+rin ∈UN…. Sample random β0, β1 ← UN(d+1) s.t. β0+β1 =β.”).
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Raviv’s approach by utilizing Boyle’s approach of performing a dot product to learn the shares of the final output as the motivation would be to reduce the complexity of interaction and communication between the participants when performing secret sharing (Boyle et al. Page 1).
Regarding Claim 6, the combination of Raviv and Boyle disclose:
The computing-processor-implemented method of claim 1, wherein each coefficient is a member of a Galois field (On page 3, Raviv discloses “The symbol Fq is used to denote the finite field of cardinality q.”).
Regarding Claim 7, Raviv discloses:
A computing-processor-implemented method of polynomial function secret sharing in computation of reconstruction share results for a polynomial function evaluated on input data, the computing-processor-implemented method comprising (In the abstract, Raviv discloses “we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data”):
However, Raviv does not explicitly disclose computing a dot product of a share.
Boyle discloses:
generating an allocatable share of the polynomial function for each share result computation system of a set of share result computation systems, each allocatable share including a share element for each coefficient in the polynomial function (On page 19, Figure 4, Boyle discloses in steps 1-2 and 7, “Let (fd,...,f0) ∈ UN(d+1) ) N be coefficients of f’ such that f’(x) = f(x−rin)… Set β = (f’d,...,f’0) ∈ UN(d+1) and γ=(N−1)+rin ∈UN…. Sample random β0, β1 ← UN(d+1) s.t. β0+β1 =β.”); and distributing each allocatable share to a unique share result computation system of the share result computation systems (On page 12, Boyle discloses “the dealer uses the FSS scheme for G to split the function g[rin,rout] into two functions with keys k0,k1, and delivers each key kσ to party Pσ.”) to compute a dot product of the input data and the share received by each share result computation system (On page 18, Boyle discloses “Once the evaluators P0 and P1 learn the shares of the correct coefficients, they compute an inner product with (xd,...,x0) to learn shares of final output.”), wherein a combination of the reconstruction share results generated by the share result computation systems yields a reconstructed result of the polynomial function evaluated on the input data (On page 11, Boyle discloses “FSS scheme is an efficient algorithm that splits a function f ∈ F into two additive shares f0,f1, such that: (1) each fσ hides f; (2) for every input x, f0(x) + f1(x) = f(x).”)
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Raviv’s approach by utilizing Boyle’s approach of performing a dot product to learn the shares of the final output as the motivation would be to reduce the complexity of interaction and communication between the participants when performing secret sharing (Boyle et al. Page 1).
Regarding Claim 8, the combination of Raviv and Boyle disclose:
The computing-processor-implemented method of claim 7, further comprising: combining the reconstruction share results generated by the share result computation systems to yield the reconstructed result of the polynomial function evaluated on the input data. (On page 7, Raviv discloses “The scheme construction will guarantee that the sets A(s) = {a(s) | i = 0,...,H−1} of coefficients decoded during round s each consist of H unique coefficients of the polynomials γb(z). That is, A(s) ∩ A(t) = ∅ for s = t, and since each has size H, the user will have decoded HS = BL unique coefficients of the B polynomials γb(z) at the end of the scheme.”)
Claim 9 is directed to a method having functionality corresponding to the method of Claim 2 and is rejected by a similar rationale, mutatis mutandis.
Claim 13 is directed to a method having functionality corresponding to the method of Claim 6 and is rejected by a similar rationale, mutatis mutandis.
Claims 15 and 16 are directed to a system having functionality corresponding to the method of Claim 1 and 2, respectively, and are rejected by a similar rationale, mutatis mutandis.
Claim 20 is directed to a system having functionality corresponding to the method of Claim 6 and is rejected by a similar rationale, mutatis mutandis.
Claims 3-5, 10-12, 14, 17-19 are rejected under 35 U.S.C. 103 as being unpatentable over Raviv et al. (NPL: Private Polynomial Computation from Lagrange Encoding), hereinafter referred to as Raviv, in view of Boyle et al. (NPL: Function Secret Sharing for Mixed-Mode and Fixed-Point Secure Computation), hereinafter referred to as Boyle, in further view of Luo (NPL: Efficient Threshold Function Secret Sharing With Information-Theoretic Security), hereinafter referred to as Luo.
Regarding Claim 3, the combination of Raviv and Boyle disclose the limitations of Claim 1.
However, Raviv does not explicitly disclose the randomly chosen polynomials to reconstruct the coefficient.
Luo discloses:
The computing-processor-implemented method of claim 1, wherein a share elements for a coefficient of the polynomial function equals evaluations of a randomly chosen polynomial and the share elements for the coefficient across the share result computation systems being reconstructable to the coefficient (On page 6525, Luo discloses “Share generation: Given a secret s ∈ Fq, the dealer chooses uniformly a1,...,at−1 ∈ Fq and defines the polynomial P(X) = s +
∑
i
=
1
t
-
1
a
i
X
i
. This is a random polynomial of degree at most t − 1 with constant term fixed to s.”).
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Raviv’s approach by utilizing Luo’s approach of evaluations of randomly chosen polynomials and secret sharing as the motivation would be to generate a more flexible function secret sharing scheme and allowing for the protocol to compute even when all the function shares are unavailable (Luo et al. Pages 6526, 6523).
Regarding Claim 4, the combination of Raviv and Boyle disclose the limitations of Claim 1.
However, Raviv does not explicitly disclose LaGrange interpolation of a proper subset.
Luo discloses:
The computing-processor-implemented method of claim 1, wherein the combination includes Lagrange interpolation of a proper subset of the reconstruction share results generated by the share result computation systems (On page 6525, Luo discloses “Secret reconstruction: Any t participants Pir , for r = 1,...,t, from the participants set {Pi}i∈[n], work together to recover the secret s by the polynomial interpolation as follows.” Further, see Equation 3).
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Raviv’s approach by utilizing Luo’s approach of evaluations of randomly chosen polynomials and secret sharing as the motivation would be to generate a more flexible function secret sharing scheme and allowing for the protocol to compute even when all the function shares are unavailable (Luo et al. Pages 6526, 6523).
Regarding Claim 5, the combination of Raviv and Boyle disclose the limitations of Claim 1.
However, Raviv does not explicitly disclose fewer than all shares required.
Luo discloses:
The computing-processor-implemented method of claim 1, wherein reconstruction share results from fewer than all of the share result computation systems participating in computation of reconstruction share results for the polynomial function evaluated on the input data are required to generate the reconstructed result of the polynomial function evaluated on the input data (On page 6526, Luo discloses “definition 3 allows the algorithm Dec successful decoding the function value at an evaluation point even if at most n−t inputs cannot given in time.”).
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Raviv’s approach by utilizing Luo’s approach of evaluations of randomly chosen polynomials and secret sharing as the motivation would be to generate a more flexible function secret sharing scheme and allowing for the protocol to compute even when all the function shares are unavailable (Luo et al. Pages 6526, 6523).
Claims 10, 11, and 12 are directed to a method having functionality corresponding to the method of Claim 3, 4, and 5, respectively, and are rejected by a similar rationale, mutatis mutandis.
Regarding Claim 14, the combination of Raviv and Boyle disclose the limitations of Claim 7.
However, Raviv does not explicitly disclose the share elements corresponding to a coefficient.
Luo discloses:
The computing-processor-implemented method of claim 7, wherein each share element of each allocatable share is computed as a Shamir share, each share element corresponding to a coefficient of the polynomial function (On page 6526, Luo discloses “the dealer D chooses N = 2l random polynomials over Fq with degree at most (t − 1), labeled by elements in {0,1}l. Let the constant term of the α-th polynomial be fα,β(α), for all α ∈ {0,1}l. The dealer D generates n function shares of fα,β through the N polynomials evaluating at n publicly known distinct non zero elements λ1,...,λn ∈ Fq”)
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Raviv’s approach by utilizing Luo’s approach of evaluations of randomly chosen polynomials and secret sharing as the motivation would be to generate a more flexible function secret sharing scheme and allowing for the protocol to compute even when all the function shares are unavailable (Luo et al. Pages 6526, 6523).
Claims 17, 18, and 19 are directed to a system having functionality corresponding to the method of Claim 3, 4, and 5, respectively, and are rejected by a similar rationale, mutatis mutandis.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Rindal et al. (US 20240413984 ) discloses a method for using a function for secret sharing and leveraging LaGrange interpolation.
Gama et al. (US 20200304293) discloses a method for secure multiparty computations to produce a shared result of a continuous function.
Any inquiry concerning this communication or earlier communications from the examiner should be directed to SHADI H KOBROSLI whose telephone number is (571)272-1952. The examiner can normally be reached M-F 9am-5pm ET.
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/SHADI H KOBROSLI/Examiner, Art Unit 2492 /RUPAL DHARIA/Supervisory Patent Examiner, Art Unit 2492
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