DETAILED ACTION
This action is in response to the Request for Continued Examination filed on June 29, 2026. Claims 25-27 are new and claims 21-22 have been canceled. Claims 1-20 and 23-27 are pending. Of such, claims 1-7 and 23-27 represent a method and claims 8-14 represent a device and claims 15-20 represent a tangible processor-readable storage media directed to evolving threshold 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 .
Continued Examination Under 37 CFR 1.114
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and the fee set forth in 37 CFR 1.17(e) has been timely paid, the finality of the previous Office action has been withdrawn pursuant to 37 CFR 1.114.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 June 29, 2026 has been entered.
Response to Arguments
Applicant’s arguments with respect to claim(s) 1-20 and 23-24 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.
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 1-4, 8-11, 15-18, 23 and 25 are rejected under 35 U.S.C. 103 as being unpatentable over Koshiba, Takeshi (NPL: Fourier-based Function Secret Sharing with General Access Structure), hereinafter referred to as Koshiba, in view of Csirmaz et al. (NPL: On-line secret sharing), hereinafter referred to as Csirmaz.
Regarding Claim 1, Koshiba discloses:
A computing-processor-implemented method of performing evolving function secret sharing on a given function by multiple share parties (In the Abstract Koshiba discloses “Function secret sharing (FSS) scheme is a mechanism that calculates a function f(x) for x ∈ {0,1}n which is shared among p parties, by using distributed functions fi : {0,1}n → G (1 ≤ i ≤ p), where G is an Abelian group, while the function f : {0,1}n → G is kept secret to the parties.”), the computing-processor- implemented method comprising: and distributing an array of the function shares to each share party (In section 4.1, Koshiba discloses “Each key ki is distributed to the i-th party Pi.” further represented by Algorithm 4), wherein a first function share result resulting from a computation of a first function share on given input data and at least a second function share result resulting from a computation of a second function share on the given input data are combinable to yield a result of the given function executed on the given input data (In Algorithm 5 and 6, Koshiba discloses the evaluation and reconstruction of the function shares and further in Section 2.2, Koshiba discloses “The evaluation algorithm Eval(i,ki,x), on input a party index i, a key ki, and an element x ∈ D, outputs a value yi, corresponding to the i-th party’s share of f(x)”)
However, Koshiba does not explicitly disclose the share parties arriving over time and a random value corresponding to the arrival order of each party.
Csirmaz discloses:
selecting, by a dealing party, a random vector for each share party of a set of multiple share parties, the random vector of each share party corresponding to an arrival order at which each share party arrived to be added to a set of the multiple share parties (In section 3, page 7, Csirmaz discloses “When the participant p arrives, the dealer gives him a new random bit rp (independently from every other bits)” and further in section 2, page 5 “When a participant p shows up, his identity (as a vertex of Γ) is not revealed, only those qualified subsets are shown to the dealer which p is the last member of (i.e., all other members arrived previously).”); generating, by the dealing party, an array of function shares for each share party of the set of the multiple share parties, each array including a function share based on the random vector corresponding to the share party and one or more function shares cryptographically generated based on the random vector corresponding to each previously-arrived share party (In section 3, page 7, Csirmaz discloses “The secret is a uniform random bit s, the access structure is a graph G. When the participant p arrives, the dealer gives him a new random bit rp (independently from every other bits) and do the following for each backward edge (q,p) ∈ G: take the random bit rq assigned to q, and give rq ⊕s to p as well.” And further in Section 3, page 7 “each participant receives a share whose size is only one more than the number of backward edges containing that vertex, i.e., edges which are revealed when the vertex arrives.”), the first function share being selected from an array of a previously-arrived share party and the second function share being selected from an array of a later-arriving share party (In section 3, page 7, Csirmaz discloses “do the following for each backward edge (q,p) ∈ G: take the random bit rq assigned to q, and give rq ⊕s to p as well.”)
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Koshiba’s approach by utilizing Csirmaz’ approach of on-line dealing as the secret sharing scheme within Koshiba as the motivation would be to allow for the creation of additional secret shares to be generated as additional parties arrive without needing to modify the previously distributed shares (See Csirmaz, section 3).
Regarding Claim 2, the combination of Koshiba and Csirmaz disclose the limitations of Claim 1.
However, Koshiba does not explicitly disclose the share parties arriving over time and a random value corresponding to the arrival order of each party.
Csirmaz discloses:
wherein the first function share selected from the array of the previously-arrived share party selected from the array of the previously-arrived share party according to an array index corresponding to the previously-arrived share party (In section 3, page 7, Csirmaz discloses “each participant receives a share whose size is only one more than the number of backward edges containing that vertex, i.e., edges which are revealed when the vertex arrives.” Where each participant’s share is a collection having one component associated with each earlier participant and one component associated with the participant itself.)
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Koshiba’s approach by utilizing Csirmaz’ approach of on-line dealing as the secret sharing scheme within Koshiba as the motivation would be to allow for the creation of additional secret shares to be generated as additional parties arrive without needing to modify the previously distributed shares (See Csirmaz, section 3).
Regarding Claim 3, the combination of Koshiba and Csirmaz disclose the limitations of Claim 1.
However, Koshiba does not explicitly disclose the share parties arriving over time and a random value corresponding to the arrival order of each party.
Csirmaz discloses:
wherein the second function share is selected from the array of the later-arriving share party selected from an array of the later-arriving share party according to an array index corresponding to the previously-arrived share party. (In section 3, page 7, Csirmaz discloses “do the following for each backward edge (q,p) ∈ G: take the random bit rq assigned to q, and give rq ⊕s to p as well.”)
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Koshiba’s approach by utilizing Csirmaz’ approach of on-line dealing as the secret sharing scheme within Koshiba as the motivation would be to allow for the creation of additional secret shares to be generated as additional parties arrive without needing to modify the previously distributed shares (See Csirmaz, section 3).
Regarding Claim 4, the combination of Koshiba and Csirmaz disclose the limitations of Claim 1.
However, Koshiba does not explicitly disclose the share parties arriving over time and a random value corresponding to the arrival order of each party.
Csirmaz discloses:
wherein function shares in each array are ordered in the array according to the arrival order of the multiple share parties. (In section 3, page 7, Csirmaz discloses “each participant receives a share whose size is only one more than the number of backward edges containing that vertex, i.e., edges which are revealed when the vertex arrives.”)
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Koshiba’s approach by utilizing Csirmaz’ approach of on-line dealing as the secret sharing scheme within Koshiba as the motivation would be to allow for the creation of additional secret shares to be generated as additional parties arrive without needing to modify the previously distributed shares (See Csirmaz, section 3).
Claims 8-11 are directed to a device having functionality corresponding to the method of Claims 1-4, and are rejected by a similar rationale, mutatis mutandis.
Claims 15-18 are directed to a tangible processor-readable storage media having functionality corresponding to the method of Claims 1-4, and are rejected by a similar rationale, mutatis mutandis.
Regarding Claim 23, the combination of Koshiba and Csirmaz disclose:
The computing-processor-implemented method of claim 1, wherein distributing the array of the function shares to each share party is performed over a communications interface of a computing system of the dealing party. (In section 3.2, Koshiba discloses “In the sharing phase, the dealer D chooses a random vector r ∈ (Fq)p−1 and sends a share mTi ,(s,r)T to the i-th party.”)
Regarding Claim 25, the combination of Koshiba and Csirmaz disclose the limitations of Claim 1.
However, Koshiba does not explicitly disclose the share parties arriving over time and a random value corresponding to the arrival order of each party.
Csirmaz discloses:
wherein the dealing party stores the random vector corresponding to each share party for use in subsequent function share generation, and wherein generating the array of function shares for a later-arriving share party comprises using each stored random vector corresponding to each previously-arrived share party to generate a corresponding function share in the array of the later-arriving share party, without modifying or reissuing any function shares previously distributed to earlier-arrived share parties. (In section 3, page 7, Csirmaz discloses “do the following for each backward edge (q,p) ∈ G: take the random bit rq assigned to q, and give rq ⊕s to p as well.” And further in section 2.2, page 6 “in fact one can visualize the process as assigning variables to participants, and only after all assignments evaluating the variables according to their joint distribution.”)
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Koshiba’s approach by utilizing Csirmaz’ approach of on-line dealing as the secret sharing scheme within Koshiba as the motivation would be to allow for the creation of additional secret shares to be generated as additional parties arrive without needing to modify the previously distributed shares (See Csirmaz, section 3).
Claims 5-7, 12-14, 19-20, 24, and 27 are rejected under 35 U.S.C. 103 as being unpatentable over Koshiba, Takeshi (NPL: Fourier-based Function Secret Sharing with General Access Structure), hereinafter referred to as Koshiba, in view of Csirmaz et al. (NPL: On-line secret sharing), hereinafter referred to as Csirmaz, in further view of Xing et al. (NPL: Evolving Secret Sharing Schemes Based on Polynomial Evaluations and Algebraic Geometry Codes), hereinafter referred to as Xing.
Regarding Claim 5, the combination of Koshiba and Csirmaz disclose the limitations of Claim 1.
However, Koshiba does not explicitly disclose allocating share parties to generational sets.
Xing discloses:
wherein each share party in the set of the multiple share parties is allocated to a generational set corresponding to the arrival order and receives an intra-generation function share for combining with another share party of a same generational set to yield the result of the given function executed on the given input data. (On page 11, Xing discloses “Assign the share shg t = (shg 1,t ,shg 2,t,...,shg k,t) to the t-th party in the g-th generation.” And further “the cg parties from the g-th generation can recover cg secrets shg−1 1 ,...,shg−1 cg which are shares held by cg virtual parties from the (g − 1)-th generation.”)
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Koshiba’s approach by utilizing Xing’s approach of generational secret sharing scheme within Koshiba as the motivation would be to utilizing the generational secret sharing scheme in conjunction with the dealer sharing would reduce the size of the shares (See Xing, page 12).
Regarding Claim 6, the combination of Koshiba and Csirmaz disclose the limitations of Claim 1.
However, Koshiba does not explicitly disclose allocating share parties to generational sets.
Xing discloses:
wherein each share party in the set of the multiple share parties is allocated to a generational set corresponding to the arrival order and the function share based on the random vector corresponding to the share party corresponds to the generational set of the share party and the one or more function shares cryptographically generated based on the random vector corresponding to each previously- arrived share party correspond to the generational set of each previously-arrived share party. (On page 11, Xing discloses “Assign the share shg t = (shg 1,t ,shg 2,t,...,shg k,t) to the t-th party in the g-th generation.” And further “the cg parties from the g-th generation can recover cg secrets shg−1 1 ,...,shg−1 cg which are shares held by cg virtual parties from the (g − 1)-th generation.”)
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Koshiba’s approach by utilizing Xing’s approach of generational secret sharing scheme within Koshiba as the motivation would be to utilizing the generational secret sharing scheme in conjunction with the dealer sharing would reduce the size of the shares (See Xing, page 12).
Regarding Claim 7, the combination of Koshiba and Csirmaz disclose the limitations of Claim 1.
However, Koshiba does not explicitly disclose allocating share parties to generational sets.
Xing discloses:
wherein each share party in the set of the multiple share parties is allocated to a generational set corresponding to the arrival order and each generational set and each successive generational set includes more share parties than a previous generational set. (On page 14, Xing discloses “Theorem 3. For any sequence of threshold value {k1,k2,...,kt,...} that define a dynamic access structure, there exists an evolving secret sharing scheme for sharing one bit secret in which the share size of the t-th party is at most t4.”)
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Koshiba’s approach by utilizing Xing’s approach of generational secret sharing scheme within Koshiba as the motivation would be to utilizing the generational secret sharing scheme in conjunction with the dealer sharing would reduce the size of the shares (See Xing, page 12).
Claims 12-14 are directed to a device having functionality corresponding to the method of Claims 5-7, and are rejected by a similar rationale, mutatis mutandis.
Claims 19-20 are directed to a tangible processor-readable storage media having functionality corresponding to the method of Claims 5-6, and are rejected by a similar rationale, mutatis mutandis.
Regarding Claim 24, the combination of Koshiba and Csirmaz disclose the limitations of Claim 1.
However, Koshiba does not explicitly disclose allocating share parties to generational sets.
Xing discloses:
wherein each array is stored in computer memory in an arrival-ordered index that corresponds to a generational set associated with an arrival time of each share party, and each function share in the array is cryptographically bound to a generational set corresponding to the share party and to previously-arrived parties. (On page 11, Xing discloses “Assign the share shg t = (shg 1,t ,shg 2,t,...,shg k,t) to the t-th party in the g-th generation.” And further “the cg parties from the g-th generation can recover cg secrets shg−1 1 ,...,shg−1 cg which are shares held by cg virtual parties from the (g − 1)-th generation.”)
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Koshiba’s approach by utilizing Xing’s approach of generational secret sharing scheme within Koshiba as the motivation would be to utilizing the generational secret sharing scheme in conjunction with the dealer sharing would reduce the size of the shares (See Xing, page 12).
Regarding Claim 27, the combination of Koshiba and Csirmaz disclose the limitations of Claim 1.
However, Koshiba does not explicitly disclose allocating share parties to generational sets.
Xing discloses:
wherein each share party in the set of the multiple share parties is allocated to a generational set corresponding to the arrival order, and a size of the array of function shares for each share party grows at most logarithmically with respect to an arrival index of the share party. (On page 14, Xing discloses “Theorem 3. For any sequence of threshold value {k1,k2,...,kt,...} that define a dynamic access structure, there exists an evolving secret sharing scheme for sharing one bit secret in which the share size of the t-th party is at most t4.”)
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Koshiba’s approach by utilizing Xing’s approach of generational secret sharing scheme within Koshiba as the motivation would be to utilizing the generational secret sharing scheme in conjunction with the dealer sharing would reduce the size of the shares (See Xing, page 12).
Claim 26 is rejected under 35 U.S.C. 103 as being unpatentable over Koshiba, Takeshi (NPL: Fourier-based Function Secret Sharing with General Access Structure), hereinafter referred to as Koshiba, in view of Csirmaz et al. (NPL: On-line secret sharing), hereinafter referred to as Csirmaz, in further view of Bonawitz et al. (NPL: Practical Secure Aggregation for Privacy-Preserving Machine Learning), hereinafter referred to as Bonawitz.
Regarding Claim 26, the combination of Koshiba and Csirmaz disclose the limitations of Claim 1.
However, Koshiba does not explicitly disclose determining arrival order prior to computation.
Bonawitz discloses:
wherein, prior to computing the first function share result and the second function share result, two share parties from the set of multiple share parties negotiate to determine which of the two share parties arrived later than the other (In section 4.0.1, Bonawitz discloses “Assume a total order on users, and suppose each pair of users (u,v), u< v agree on some random vectors u,v.” and further in Figure 4 “Broadcast to all users in U1 the list”), and the share party determined to have arrived later selects from its array a function share at an index corresponding to the share party determined to have arrived earlier (In Figure 4, Bonawitz discloses in round 2 computing the masked input vector where different operations occur for the users based on whether u>v or u<v).
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Koshiba’s approach by utilizing Bonawitz’ approach of determining the arrival order as the motivation would be to allow the users to compare their positions to determine their arrival order and correlate the associated random value to determine their function input (See Bonawitz, Figure 4).
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Schnieder, James (US 20100217986) discloses a method for distributed secret sharing and authentication using polynomials to reconstruct a secret.
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.
Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice.
If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Rupal Dharia can be reached at 571-272-3880. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300.
Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000.
/SHADI H KOBROSLI/Examiner, Art Unit 2492 /RUPAL DHARIA/Supervisory Patent Examiner, Art Unit 2492
Prosecution Insights