DETAILED ACTION
This action is in response to the amendments filed on January 30, 2026. Claims 21-24 are new. Claims 1-24 are pending. Of such, claims 1-7 and 21-24 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 .
Claim Rejections - 35 USC § 101
The rejection to the claims has been withdrawn in view of the Remarks submitted on January 30, 2026 as well as the additional new claim limitations.
Response to Arguments
Applicant's arguments filed January 30, 2026 have been fully considered but they are not persuasive.
On page 16 of the Remarks, the applicant argues the combination fails to disclose a share based on the random vector corresponding to the share party and one or more shares cryptographically generated based on the random vector corresponding to each previously-arrived share party. Luo teaches per-party random vectors but does not disclose that later-arriving shares depend on earlier parties’ random vectors. Komargodski discloses an evolving scheme where a new share is generated using the secret and previous shares of the secret – not using random vectors.
This argument is not persuasive.
The applicants argument rests on a narrow reading of Komargodski and misapplies the 103 standard by attacking each reference individually. Komargodski does in fact generate new shares based on random values associated with each previously arrived party. In the evolving 2-threshold construction (Komargodski, Section 1.3), the dealer samples a random bit for each arriving party and distributes to the party an array including a random bit values associated with previously arrived parties. The passage the Applicant quotes from Komargodski on page 13 (“Generate on share using the secret sharing scheme given the secret s and previous share {v_i}”) describes a higher-level recursive composition operating on outputs of the base, which itself generates shares from per-party random values.
Combining this with Luo, which uses random vectors in F{d+1} as the per-party quantity in function secret sharing, yields shares generated from the random vector of each previously arrived party. The only difference from Komargodski is dimensionality which Luo supplies. The Applicant’s specification in ¶ 37 discloses the function st+1,i = a-ri is structurally identical to Komargodski’s s ⊕ bi which vectors substituted for scalars.
On page 16 of the Remarks, the Applicant argues that Komargodski addresses arrival order only conceptually, not as the claimed cryptographic construction requiring both a share based on the share party’s own random vector and shares based on prior parties’ random vectors.
This argument is not persuasive.
Komargodski’s construction is an explicit cryptographic algorithm, not conceptual. Party t’s share array contains both (a) a component based on party t’s own random value bt (b) components {s⊕ b1 …s⊕ b(t-1) } generated from the random values of each previously arrived party. This is the dual structure the claim recites. Applied to Luo’s vector-valued Function Secret Sharing, the scalar bi becomes a random vector ri and XOR becomes vector subtraction over a finite field. The arrival-order indexing, the dependency on prior parties’ random values and the share structure are all expressly disclosed.
On page 17 of the Remarks, the Applicant argues it would not have been obvious to combine the references to yield the claimed dependency structure. The motivation does not supply a reason to construct function shares that depend on the random vectors of previously arrived parties; Luo provides no linking mechanism; Komargodski depends on prior shares, not random vectors; and the references rely on incompatible structures.
This argument is not persuasive.
The motivation to combine is outlined by the problem identified in the applicant’s specification (¶ 16) where a function secret sharing scheme requires refreshing all the existing shares to add one. A person in ordinary skill in the art would naturally look at Komargodski, describing evolving secret sharing, as the solution. The claimed dependency is the result of the combination, not an additional limitation needing separate motivation. Komargodski inherently generates new shares from prior parties’ random values (see argument 1); Luo inherently uses random vectors in function secret sharing. The combination yields the claimed structure without hindsight. With respect to the applicant’s argument on incompatibility, the applicant does not identify a specific obstacle to the incompatibility. Both references are linear secret sharing schemes over a finite field. Both address Shamir threshold secret sharing in which Luo addresses function splitting and Komargodski addresses dynamic party participation which are complementary and share the same foundation.
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 1-24 are rejected under 35 U.S.C. 103 as being unpatentable over Luo et al. (NPL: Efficient Threshold Function Secret Sharing With Information-Theoretic Security), hereinafter referred to as Luo, in view of Komargodski et al. (NPL: How to Share a Secret, Infinitely), hereinafter referred to as Komargodski.
Regarding Claim 1, Luo discloses:
A computing-processor-implemented method of performing evolving function secret sharing on a given function by multiple share parties (In the abstract, Luo discloses “an n-party FSS scheme splits a function f into n functions f1,...,fn such that f = f1 +...+ fn and every strict subset of the function shares hide f .”), the computing-processor-implemented method comprising: selecting, by a dealing party, a random vector for each share party of a set of multiple share parties (On page 6526, Luo discloses “in the algorithm of Gen , the dealer D chooses N=2l random polynomials over Fq with degree at most (t−1), labeled by elements in {0,1}l .” further on page 6527, Luo discloses “We note that A is a random matrix of size (t − 1) × N and 3 is a nonsingular matrix of order (t − 1). As a result, K = A + A0 ∈
F
q
N
is a random vector.”), 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 (On page 6526, Luo discloses “The dealer D generates n function shares of fα,β through the N polynomials evaluating at n publicly known distinct nonzero elements λ1, . . . , λn ∈ Fq.” Further, Figure 2-4 displaying the shares as an array), and distributing an array of the function shares to each share party (On page 6525, Luo discloses “Each share si is distributed to the corresponding participant Pi independently and privately through a secure channel.”), 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 (On page 6525, Luo discloses “Eval(i, ki, x): This is the evaluation algorithm run by each participants Pi , for i = 1, . . . , n. It takes the share ki , an evaluation point x ∈ Df as inputs and outputs a value yi , corresponding to the participant’s share of f (x).”), 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 (On page 6526, Luo discloses “In the algorithm of Eval, the participant Pi, upon receiving α 0 ∈ {0, 1} l , outputs the evaluation of the α 0th polynomial at the point λi ∈ Fq.”, wherein the examiner interprets a participant number of two, one participant can be interpreted as the previously arrived party and the second as the later arriving party. ),
However, Luo does not explicitly disclose the evolving participants.
Komargodski discloses:
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 (On page 3, Komargodski discloses “would simulate the dealer for Shamir’s scheme, sample a random polynomial of degree k − 1 and increase the field size from which we compute shares as more parties arrive.”); and one or more function shares cryptographically generated based on the random vector corresponding to each previously-arrived share party (On page 13, Komargodski discloses “Generate one share using the secret sharing scheme Π given the secret s and previous shares
{
v
(
i
)
}
i
∈
0
,
…
,
g
-
1
.
Denote the resulting share by
v
(
g
)
.”)
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Luo’s approach by utilizing Komargodski’s approach of the use the concept of evolving participants when performing secret sharing 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 Komargodski, Page 1).
Regarding Claim 2, the combination of Luo and Komargodski disclose:
The computing-processor-implemented method of claim 1, 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 (On page 6528, Luo disclsoes “We split the truth table of fα,β : {0, 1} l → Fq to a tensor products of l vectors V1, . . . , Vl of length 2. We share V1, . . . , Vl, using 2l (t, n)-Shamir’s schemes. The function share for the participant Pi is obtained by packing the i-th shares of the 2l (t, n)-Shamir’s schemes.”).
Regarding Claim 3, the combination of Luo and Komargodski disclose:
The computing-processor-implemented method of claim 1, 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 (On page 6528, Luo disclsoes “We split the truth table of fα,β : {0, 1} l → Fq to a tensor products of l vectors V1, . . . , Vl of length 2. We share V1, . . . , Vl, using 2l (t, n)-Shamir’s schemes. The function share for the participant Pi is obtained by packing the i-th shares of the 2l (t, n)-Shamir’s schemes.”).
Regarding Claim 4, the combination of Luo and Komargodski disclose the limitations of Claim 1.
However Luo does not disclose maintaining an order of participants.
Komargodski discloses:
The computing-processor-implemented method of claim 1, wherein function shares in each array are ordered in the array according to the arrival order of the multiple share parties (On page 4, Komargodski discloses “. Let A be any evolving access structure and let At = A∩[t] be the qualified sets at time t. Note that the dealer does not know A in advance but is only given At when the tth party 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 Luo’s approach by utilizing Komargodski’s approach of the use the concept of evolving participants when performing secret sharing 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 Komargodski, Page 1).
Regarding Claim 5, the combination of Luo and Komargodski disclose the limitations of Claim 1.
However Luo does not disclose the evolving participants.
Komargodski discloses:
The computing-processor-implemented method of claim 1, 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 5, Komargodski disclsoes “For each generation we generate k − 1 shares s1, . . . , sk−1 for the evolving scheme and share each si using a standard i-out-of-size(g) secret sharing scheme. Thus, if w ≤ k − 1 parties from some generation come together, they can reconstruct s1, . . . , sw which are w shares for the evolving scheme.”).
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Luo’s approach by utilizing Komargodski’s approach of the use the concept of evolving participants when performing secret sharing 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 Komargodski, Page 1).
Regarding Claim 6, the combination of Luo and Komargodski disclose the limitations of Claim 1.
However Luo does not disclose the evolving participants.
Komargodski discloses:
The computing-processor-implemented method of claim 1, 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 4, Komargodski discloses “The dealer maintains an infinitely (random) growing string w and gives the tth party arriving either the string w[1 : σ(t)] (if the secret to share is 0), or w[1 : σ(t)] ⊕ Σ(t), where w[1 : σ(t)] is the σ(t)-bit length prefix of w and Σ(t) is the encoding of the number t using the prefix code”).
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Luo’s approach by utilizing Komargodski’s approach of the use the concept of evolving participants when performing secret sharing 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 Komargodski, Page 1).
Regarding Claim 7, the combination of Luo and Komargodski disclose the limitations of Claim 1.
However Luo does not disclose the evolving participants.
Komargodski discloses:
The computing-processor-implemented method of claim 1, 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 13, Komargodski discloses “The generations are growing in size: For g = 0, 1, 2 . . . the gth generation begins when the (2g )-th party arrives” further, see Figure 1 as the generations double in size as they grow).
One in ordinary skill in the art of cryptography would have been motivated, before the effective filing date of the claimed invention to modify Luo’s approach by utilizing Komargodski’s approach of the use the concept of evolving participants when performing secret sharing 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 Komargodski, Page 1).
Claims 8-14 are directed to a device having functionality corresponding to the method of Claims 1-7, and are rejected by a similar rationale, mutatis mutandis.
Claims 15-20 are directed to a tangible processor-readable storage media having functionality corresponding to the method of Claims 1-6, and are rejected by a similar rationale, mutatis mutandis.
Regarding Claim 21, the combination of Luo and Komargodski disclose:
The computing-processor-implemented method of claim 1, wherein a dealing party includes a computing system (On page 6525, Luo discloses “Gen(1λ,f): This is the share generation algorithm run by the dealer. It takes the security parameter 1λ and function description f as inputs, and outputs n shares k1, . ..,kn.”).
Regarding Claim 22, the combination of Luo and Komargodski disclose:
The computing-processor-implemented method of claim 1, wherein the each share party is a share result computation system (On page 6525, Luo discloses “Eval(i,ki,x): This is the evaluation algorithm run by each participants Pi, for i = 1,...,n. It takes the share ki, an evaluation point x ∈ Df as inputs and outputs a value yi, corresponding to the participant’s share of f (x).”)
Regarding Claim 23, the combination of Luo and Komargodski 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. (On page 6523, Luo discloses “A function f : {0,1}∗ → G, with arbitrary input length and range G, which is generally assumed to be a group, is divided into n function shares fi : {0,1}∗ → G for i = 1,...,n, which are sent to each participant independently and privately over some communication channels.”)
Regarding Claim 24, the combination of Luo and Komargodski disclose the limitations of Claim 1.
However, Luo does not explicitly disclose evolving secret sharing.
Komargodski discloses:
The computing-processor-implemented method of claim 1, 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 5-6, section 1.3, Komargodski discloses “generations are of geometrically increasing size). Within each generation we execute a standard 4 secret sharing scheme for 2-threshold…. For each generation we generate one share for the evolving scheme and give it to each party in that 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 Luo’s approach by utilizing Komargodski’s approach of the use the concept of evolving participants when performing secret sharing 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 Komargodski, Page 1).
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Matsuo; Masakatsu (US 9331984) discloses a secret sharing process based on an improved threshold scheme, secret data is shared as shared data parts equal to or greater than a threshold value in number such that the secret data cannot be reconstructed from shared data parts less than the threshold value in number.
THIS ACTION IS MADE FINAL. 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.
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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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.
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/SHADI H KOBROSLI/Examiner, Art Unit 2492 /RUPAL DHARIA/Supervisory Patent Examiner, Art Unit 2492
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