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 .
Response to Arguments
Remarks
The Examiner acknowledges no claims have been cancelled, no claims have been amended, and no new claims have been added.
Specification
The Examiner acknowledges the amendments to the applicant’s specification regarding the applicant’s Abstract, and paragraph [0019]. The objection is withdrawn regarding paragraph [0019] due to the amendment, however, the objection regarding the abstract remains due to the amended abstract still being over the 150 word count.
35 U.S.C. 101
The Examiner acknowledges and has fully considered the applicant’s arguments.
The applicant seemingly argues (Remarks page 9 paragraph 5 – page 10 paragraphs 1-2) that claim 1 is directed towards a technical solution for a technical problem, and is not merely an abstract mathematical problem. The Examiner respectfully disagrees for at least the reasons given in the Non-Final Rejection Office Action mailed on 04/14/2026. Furthermore, the Examiner respectfully notes that "it is important to keep in mind that an improvement in the abstract idea itself (e.g. a recited fundamental economic concept) is not an improvement in technology", MPEP 2106.05(a)(II).
The applicant continues, (Remarks page 10 paragraph 3), seemingly arguing that a claim reciting a judicial exception is not directed to that exception if the exception is integrated into a practical application, and that a claim proves integration when it reflects an improvement in the functioning of a computer, or an improvement to other technology or technical field. The Examiner respectfully notes that, "it is important to keep in mind that an improvement in the abstract idea itself (e.g. a recited fundamental economic concept) is not an improvement in technology", MPEP 2106.05(a)(II).
The applicant continues, (Remarks page 10 paragraph 4 – page 11 paragraphs 1-3), seemingly arguing that claim 1 does not merely apply mathematics on a generic computer, that with the limitations taken as a whole are an ordered set of operations that is a technical solution to a technical problem. The Examiner respectfully disagrees for at least the reasons given in the Non-Final Rejection Office Action mailed on 04/14/2026. Furthermore, the Examiner respectfully notes that "it is important to keep in mind that an improvement in the abstract idea itself (e.g. a recited fundamental economic concept) is not an improvement in technology", MPEP 2106.05(a)(II).
The applicant continues, (Remarks page 11 paragraph 4), seemingly arguing that claim 1 describes a particular technical manner of secure computation and not merely the use of a mathematical formula to calculate a number. The Examiner respectfully disagrees for at least the reasons given in the Non-Final Rejection Office Action mailed on 04/14/2026. Claim 1 recites mathematical concepts which include, “using masked compressing of coefficients of a polynomial having ns arithmetic shares, comprising: shifting a first arithmetic share of the ns arithmetic shares by an input mask λ1; scaling the shifted first arithmetic share by a value based on a first compression factor δ and a masking scaling factor Ψ1; shifting the scaled first arithmetic share by a value based on the masking scaling factor Ψ1; scaling a second to ns shares of the ns arithmetic shares by a value based on the first compression factor δ and the masking scaling factor Ψ1; converting the ns scaled arithmetic shares to ns Boolean shares; right shifting the ns Boolean shares based upon the masking scaling factor Ψ1 and a second compression factor Ψ2; XORing an output mask λ2 with the shifted first Boolean share to produce ns compressed Boolean shares; and carrying out using the ns arithmetic shares when the ns compressed Boolean shares indicates that the coefficients of the polynomial are within boundary values”. As referenced in the Non-Final Rejection Office Action mailed on 04/14/2026 (page 4), claim 1 is neither integrated into a practical application nor amounts to significantly more than the abstract idea.
The applicant continues, (Remarks page 11 paragraph 5 – page 12 paragraphs 1-3), seemingly arguing that the specification describes the recited claim 1 as an improvement to technology, seemingly arguing that the improvement is not merely an improvement to a mathematical formula but an improvement to the practical implementation of side-channel-protected cryptographic processing on computer devices with limited processing and randomness resources. The Examiner respectfully disagrees. The applicant seemingly is arguing for unclaimed elements regarding side-channel-protected processing on computer devices. As referenced in the Non-Final Rejection Office Action mailed on 04/14/2026 (pages 3-4), recited additional elements are generically recited as merely a generic computing device upon which the abstract idea is applied, and further additional elements are generally recited as merely generally linking to a particular field of use. The applicant continues, seemingly arguing that claim 1 improves computer security using a specific technique including an ordered combination of masked arithmetic and Boolean share operations, and provides a particular masked compressed comparison technique that improves efficiency of side-channel-protected cryptographic implementation. The Examiner respectfully notes that the improvements the applicant seemingly argues, is directed towards the mathematical concepts rather than technology itself. The Examiner further notes, "it is important to keep in mind that an improvement in the abstract idea itself (e.g. a recited fundamental economic concept) is not an improvement in technology", MPEP 2106.05(a)(II).
The applicant continues, (Remarks page 12 paragraph 4 – page 13 paragraphs 1-2), seemingly arguing that the cited additional elements of “cryptographic operation” and “lattice-based cryptography” are not generically recited as a field of use. The applicant seemingly argues that the ordered combination of operations defines a particular technical manner of performing masked polynomial rejection in a lattice-based cryptographic implementation, not a generic instruction to apply mathematics in a cryptographic field. The applicant further seemingly argues that claim 1 does not rely on the mere presence of a processor, memory, or non-transitory medium for eligibility of claim 1, but rather the eligibility arises from the claimed ordered combination which changes how secret-dependent polynomial coefficient data is processed during masked rejection/compression in a lattice-based cryptographic implementation. The Examiner respectfully disagrees for at least the reasons given in the Non-Final Rejection Office Action mailed on 04/14/2026 (pages 3-4). Claim 1 is directed towards instructions comprising mathematical concepts, an algorithm, it is generically linked to the field of use of “the instructions for a cryptographic operation”, “for lattice-based cryptography in a processor”, and merely generically recites a generic computer “A data processing system comprising instructions embodied in a non-transitory computer readable medium” upon which the abstract idea is applied.
The applicant continues, (Remarks page 13 paragraph 3) , seemingly arguing that the limitations of claim 1 cannot be practically performed in the human mind, thus is not a mental process. The Examiner respectfully disagrees, and notes that mental processes are not limited strictly to being performed in the human mind, a mental process may also be performed by using a computer as a tool, MPEP 2106.04(a)(2)(III)(C).
The applicant continues, (Remarks page 13 paragraph 4), seemingly arguing that USPTO example 41 recites mathematical formulas for cryptographic encoding and was held eligible at Step 2A, Prong 2 because the mathematical concepts were integrated into a process for securing communications, and that the applicant’s claim 1 is analogous and thus should be eligible due to the recited operations (arithmetic or Boolean) being integrated into a concrete security process. The Examiner respectfully disagrees for at least the reasons given in the Non-Final Rejection Office Action mailed on 04/14/2026. The analysis given for USPTO example 41 describes the claim as being eligible due to the combination of additional elements using the mathematical formulas and calculations in a specific manner that sufficiently limits the mathematical concepts to a practical application, not merely because the mathematical concepts are directed towards securing communications. Furthermore, the Examiner respectfully notes that in USPTO example 41, the mathematical concepts are not generically recited in a manner that generally links to a particular field of use or technology.
The applicant continues, (Remarks page 14 paragraph 2), seemingly arguing that claims 2-8 are eligible for at least the same reasons as claim 1 due to dependence. The Examiner respectfully disagrees for at least the reasons above. The applicant continues, seemingly arguing that claims 2-3 tie the claim to a practical application by reciting a masked comparison function on the ns compressed Boolean shares and by reciting that compressed polynomial coefficients corresponding to values in a valid range have a value of 0 and are compared to 0. The Examiner respectfully disagrees and notes that the operations the applicant describes regarding claims 2-3 are merely further mathematical concepts. The applicant continues, seemingly arguing that claims 4-8 specify particular calculations for the masked arithmetic-share shifting, scaling, Boolean-share right shifting, and output-mask XORing operations, which further define the particular technical implementation of the masked compression/rejection countermeasure. The Examiner respectfully notes that the described operations of claims 4-8 are merely further mathematical concepts, and that, "it is important to keep in mind that an improvement in the abstract idea itself (e.g. a recited fundamental economic concept) is not an improvement in technology", MPEP 2106.05(a)(II).
The applicant continues, (Remarks page 14 paragraph 3), seemingly arguing that claim 9 is independently eligible for the same reasons as given with claim 1. The Examiner respectfully disagrees for at least the same reasons given above regarding claim 1, and for at least the same reasons given in the Non-Final Rejection Office Action mailed on 04/14/2026.
The applicant continues, (Remarks page 15 paragraph 2), seemingly arguing that dependent claims 10 and 11 are eligible for at least the same reasons as claim 9 due to dependence. The Examiner respectfully disagrees for at least the same reasons given above regarding claim 9, and for at least the same reasons given in the Non-Final Rejection Office Action mailed on 04/14/2026. The applicant continues, seemingly arguing that claim 10 further specifies that the predetermined value is 0, and claim 11 further specifies particular calculations for the masked arithmetic-shar shifting, scaling, Boolean-share right shifting, and output-mask XORing operations which further define the particular technical implementation of the masked rejection countermeasure. The Examiner respectfully notes that the described further operations of claims 10 and 11 are merely further mathematical concepts, and that, "it is important to keep in mind that an improvement in the abstract idea itself (e.g. a recited fundamental economic concept) is not an improvement in technology", MPEP 2106.05(a)(II).
The applicant continues, (Remarks page 15 paragraph 3), seemingly arguing that claim 12 recites the same ordered combination of masked share operations as claim 1 in method form, and that claim 12’s ordered combination reflect the same specific technical implementation as with claim 1, and thus is integrated into a practical application by its own merits. The Examiner respectfully disagrees for at least the same reasons as with claim 1, and for at least the same reasons given in the Non-Final Rejection Office Action mailed on 04/14/2026. As referenced above, the recited ordered combination is merely the mathematical concepts, and the claim as a whole is not integrated into a practical application nor amount to significantly more than the abstract idea.
The applicant continues, (Remarks page 16 paragraph 1), seemingly arguing that claims 13-19 are integrated into a practical application for at least the same reasons as with claim 12. The Examiner respectfully disagrees for at least the same reasons as referenced above regarding claim 12. The applicant continues, seemingly arguing that claims 13-14 further recite the masked comparison function and the comparison of compressed Boolean shares to 0 for values in a valid range. The Examiner respectfully notes that the described operations of claims 13-14 are merely further mathematical concepts. The applicant continues, seemingly arguing that claims 15-19 further specify particular calculations for the masked arithmetic-share shifting, scaling, Boolean-share right shifting, and output-mask XORing operations, thus the dependent claims further define the particular technical implementation of the masked compression/rejection countermeasure. The Examiner respectfully disagrees and notes that the described further operations of claims 15-19 are merely further mathematical concepts, and that "it is important to keep in mind that an improvement in the abstract idea itself (e.g. a recited fundamental economic concept) is not an improvement in technology", MPEP 2106.05(a)(II).
The applicant continues, (Remarks page 16 paragraph 2), seemingly arguing that the ordered combinations recited by the independent claims and the dependent claims amount to significantly more than any abstract idea. The Examiner respectfully disagrees for at least the reasons given above, and for at least the reasons given in the Non-Final Rejection Office Action mailed on 04/14/2026. The applicant continues, seemingly arguing that the Examiner’s lack of applying prior at rejections confirms that the claimed ordered combinations are specific implementations of a masked compression/rejection countermeasures rather than a well-understood, routine, conventional applications of mathematical concepts to cryptography. The Examiner respectfully disagrees, prior art analysis is not considered when applying the Alice Framework Step 2 prong 2 or Step 2B analysis.
The applicant continues, (Remarks page 16 paragraph 3 – page 17 paragraphs 1-2), seemingly restating arguments regarding why the claims should be eligible under Step 2A Prong 2 and 2B. The Examiner respectfully disagrees for at least the reasons referenced above, and for at least the reasons given in the Non-Final Rejection Office Action mailed on 04/14/2026.
Conclusion
The Examiner acknowledges the applicant’s conclusion statements.
Specification
The abstract of the disclosure is objected to because the abstract is over the maximum word count of 150 words, see MPEP 608.01(b). A corrected abstract of the disclosure is required and must be presented on a separate sheet, apart from any other text. See MPEP § 608.01(b).
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 1-19 are rejected under 35 U.S.C. 101 because the claimed invention is directed to a judicial exception (i.e., a law of nature, a natural phenomenon, or an abstract idea) without significantly more.
Regarding claim 1, under the Alice Framework Step 1, claim 1 falls within the four statutory categories of patentable subject matter identified by 35 USC 101: a process, machine, manufacture, or a composition of matter.
Under the Alice Framework Step 2A prong 1, claim 1 recites an abstract idea, including both a mental process and mathematical concept. Specifically, claim 1 recites the following mathematical formulas:
“using masked compressing of coefficients of a polynomial having ns arithmetic shares, comprising: shifting a first arithmetic share of the ns arithmetic shares by an input mask λ1; scaling the shifted first arithmetic share by a value based on a first compression factor δ and a masking scaling factor Ψ1; shifting the scaled first arithmetic share by a value based on the masking scaling factor Ψ1; scaling a second to ns shares of the ns arithmetic shares by a value based on the first compression factor δ and the masking scaling factor Ψ1; converting the ns scaled arithmetic shares to ns Boolean shares; right shifting the ns Boolean shares based upon the masking scaling factor Ψ1 and a second compression factor Ψ2; XORing an output mask λ2 with the shifted first Boolean share to produce ns compressed Boolean shares; and carrying out using the ns arithmetic shares when the ns compressed Boolean shares indicates that the coefficients of the polynomial are within boundary values”
Under the Alice Framework Step 2A prong 2, and Step 2B analysis, claim 1 recites additional elements of, “data processing system comprising instructions”, “non-transitory computer readable medium”, “cryptographic operation”, “lattice-based cryptography”, “instructions”, and “processor”. The recited additional elements are describing merely a generic computing device upon which the abstract idea is applied, see MPEP 2106.04(d)(I), and 2106.05(f). Furthermore, the recited additional elements are merely a generic computing device performing generic functions, see MPEP 2106.05(A)(ii), and MPEP 2106.05(A)(i) regarding mere instructions to implement an abstract idea on a computer. Furthermore, the recited additional elements of “cryptographic operation”, and “lattice-based cryptography”, are merely generally linking to a particular field of use, see MPEP 2106.04(d), 2106.05(h), 2106.05(A)(iv). For these reasons, claim 1 is neither integrated into a practical application nor amounting to significantly more than the abstract idea.
Claim 2 is rejected for at least the reasons set forth with respect to claim 1. Claim 2 merely further limits the mental process and mathematical concept set forth in claim 1. Under the Alice Framework Step 2A prong 1, claim 2 recites an abstract idea, mathematical formulas. Specifically, claim 2 recites the following mathematical formulas:
“further comprising performing a masked comparison function on the ns compressed Boolean shares configured to indicate that the coefficients of the polynomial are within boundary values.”
Claim 2 recites no further additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Claim 3 is rejected for at least the reasons set forth with respect to claim 2. Claim 3 merely further limits the mental process and mathematical concept set forth in claim 2. Under the Alice Framework Step 2A prong 1, claim 3 recites an abstract idea, mathematical formulas. Specifically, claim 3 recites the following mathematical formulas:
“wherein the compressed polynomial coefficients corresponding to the n s compressed Boolean shares having a value in a valid range of values have a value of 0, and the masked comparison function compares the ns compressed Boolean shares to 0.”
Claim 3 recites no further additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Claim 4 is rejected for at least the reasons set forth with respect to claim 1. Claim 4 merely further limits the mental process and mathematical concept set forth in claim 1. Under the Alice Framework Step 2A prong 1, claim 4 recites an abstract idea, mathematical formulas. Specifically, claim 4 recites the following mathematical formulas:
“wherein shifting a first arithmetic share of the ns arithmetic shares by an input mask 1 includes calculating a(0)A = a(0)A + λ1 mod q, where a(0)A is the first arithmetic share of the ns arithmetic shares and q is a prime modulus.”
Claim 4 recites no further additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Claim 5 is rejected for at least the reasons set forth with respect to claim 4. Claim 5 merely further limits the mental process and mathematical concept set forth in claim 4. Under the Alice Framework Step 2A prong 1, claim 5 recites an abstract idea, mathematical formulas. Specifically, claim 5 recites the following mathematical formulas:
“wherein scaling the shifted first arithmetic share by a value based on a first compression factor δ and a masking scaling factor Ψ1 and shifting the scaled first arithmetic share by a value based on a masking scaling factor Ψ1 includes calculating 𝐚(𝟎)𝑨 = (⌊
2
Ψ
1
*
δ
q
*
a
(
0
)
A
⌋+
2
Ψ
1
-
1
)mod
2
Ψ
1
-
1
δ.”
Claim 5 recites no further additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Claim 6 is rejected for at least the reasons set forth with respect to claim 5. Claim 6 merely further limits the mental process and mathematical concept set forth in claim 5. Under the Alice Framework Step 2A prong 1, claim 6 recites an abstract idea, mathematical formulas. Specifically, claim 6 recites the following mathematical formulas:
“wherein scaling second to ns shares of the ns shares by a value based on the first compression factor δ and the masking scaling factor Ψ1 includes calculating 𝐚(𝒊)𝑨 = (⌊
2
Ψ
1
*
δ
q
*
a
(
i
)
A
⌋)mod
2
Ψ
1
δ
where 𝐚(𝒊)𝑨 is the ith arithmetic share of the ns arithmetic shares.”
Claim 6 recites no further additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Claim 7 is rejected for at least the reasons set forth with respect to claim 6. Claim 7 merely further limits the mental process and mathematical concept set forth in claim 6. Under the Alice Framework Step 2A prong 1, claim 7 recites an abstract idea, mathematical formulas. Specifically, claim 7 recites the following mathematical formulas:
“wherein right shifting the ns Boolean shares based upon the masking scaling factor Ψ1 and a second compression factor Ψ2 includes calculating: 𝒂̅(∗)𝑩 = 𝒂̅(∗)𝑩 ≫ (Ψ𝟏+Ψ𝟐), where 𝒂̅(∗)𝑩 is the ns Boolean shares.”
Claim 7 recites no further additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Claim 8 is rejected for at least the reasons set forth with respect to claim 7. Claim 8 merely further limits the mental process and mathematical concept set forth in claim 7. Under the Alice Framework Step 2A prong 1, claim 8 recites an abstract idea, mathematical formulas. Specifically, claim 8 recites the following mathematical formulas:
“wherein XORing an output mask λ2 to the shifted first Boolean share to produce ns compressed Boolean shares includes calculating: 𝒂̅(0)𝑩 = 𝒂̅(0)𝑩 Ꚛ λ𝟐.”
Claim 8 recites no further additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Regarding claim 9, under the Alice Framework Step 1, claim 9 falls within the four statutory categories of patentable subject matter identified by 35 USC 101: a process, machine, manufacture, or a composition of matter.
Under the Alice Framework Step 2A prong 1, claim 9 recites an abstract idea, including both a mental process and mathematical concept. Specifically, claim 9 recites the following mathematical formulas:
“using a masked rejection of a polynomial with coefficients having ns arithmetic shares for lattice-based cryptography, comprising: generating a ns arithmetic shares for each coefficient of the polynomial; performing a masked compression of each coefficient of the polynomial using the ns arithmetic shares for each coefficient of the polynomial, including: shifting a first arithmetic share of the ns arithmetic shares by an input mask λ1; scaling the shifted first arithmetic share by a value based on a first compression factor δ and a masking scaling factor Ψ1; shifting the scaled first arithmetic share by a value based on the masking scaling factor Ψ1; scaling the second to ns shares of the ns arithmetic shares by a value based on the first compression factor δ and the masking scaling factor Ψ1; converting the ns scaled arithmetic shares to Boolean shares; right shifting the ns Boolean shares based upon the masking scaling factor Ψ1 and a second compression factor Ψ2; and XORing an output mask λ2 to the shifted first Boolean share to produce ns compressed Boolean shares, wherein the compressed ns Boolean shares indicate compressed polynomial coefficients having a predetermined value when the polynomial coefficients are within boundary values; comparing the polynomial coefficients represented by the ns compressed Boolean shares to the predetermined value; and carrying out using the ns arithmetic shares when the polynomial coefficients represented by the ns compressed shares are equal to the predetermined value.”
Under the Alice Framework Step 2A prong 2, and Step 2B analysis, claim 9 recites additional elements of, “data processing system comprising instructions”, “non-transitory computer readable medium”, “cryptographic operation”, “instructions”, and “processor”. The recited additional elements are describing merely a generic computing device upon which the abstract idea is applied, see MPEP 2106.04(d)(I), and 2106.05(f). Furthermore, the recited additional elements are merely a generic computing device performing generic functions, see MPEP 2106.05(A)(ii), and MPEP 2106.05(A)(i) regarding mere instructions to implement an abstract idea on a computer. Furthermore, the recited additional element of “cryptographic operation”, is merely generally linking to a particular field of use, see MPEP 2106.04(d), 2106.05(h), 2106.05(A)(iv). For these reasons, claim 9 is neither integrated into a practical application nor amounting to significantly more than the abstract idea.
Claim 10 is rejected for at least the reasons set forth with respect to claim 9. Claim 10 merely further limits the mental process and mathematical concept set forth in claim 9. Under the Alice Framework Step 2A prong 1, claim 10 recites an abstract idea, mathematical formulas. Specifically, claim 10 recites the following mathematical formulas:
“wherein the predetermined value is 0.”
Claim 10 recites no further additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Claim 11 is rejected for at least the reasons set forth with respect to claim 9. Claim 11 merely further limits the mental process and mathematical concept set forth in claim 9. Under the Alice Framework Step 2A prong 1, claim 11 recites an abstract idea, mathematical formulas. Specifically, claim 11 recites the following mathematical formulas:
“wherein shifting a first arithmetic share of the ns arithmetic shares by an input mask λ1 includes calculating a(0)A = a(0)A + λ1 mod q, wherein a(0)A is the first arithmetic share of the ns shares and q is a prime modulus, scaling the shifted first arithmetic share by a value based on a first compression factor δ and a masking scaling factor Ψ1 and shifting the scaled first arithmetic share by a value based on the masking scaling factor Ψ1 includes calculating 𝐚(𝟎)𝑨 = (⌊
2
Ψ
1
*
δ
q
*
a
(
0
)
A
⌋ + 𝟐Ψ1−𝟏)𝒎𝒐𝒅 𝟐Ψ1𝜹, scaling second to ns shares of the ns arithmetic shares by a value based on the first compression factor δ and the masking scaling factor Ψ1 includes calculating 𝒂(𝒊)𝑨 = ⌊
2
Ψ
1
*
δ
q
*
a
(
i
)
A
⌋ 𝒎𝒐𝒅 𝟐Ψ𝟏𝜹 where 𝒂(𝒊)𝑨 is the ith arithmetic share of the ns arithmetic shares, right shifting the ns Boolean shares based upon the masking scaling factor Ψ1 and a second compression factor Ψ2 includes calculating: 𝒂̅(∗)𝑩 = 𝒂̅(∗)𝑩 ≫ (Ψ𝟏+Ψ𝟐), where 𝒂̅(∗)𝑩 is the ns Boolean shares, and XOring an output mask λ2 to the shifted first Boolean share to produce ns compressed Boolean shares includes calculating: 𝒂̅(𝟎)𝑩 = 𝒂̅(𝟎)𝑩 Ꚛ λ𝟐.”
Claim 11 recites no further additional elements that would require further analysis under Step 2A prong 2 and Step 2B.
Regarding claim 12, under the Alice Framework Step 1, claim 12 falls within the four statutory categories of patentable subject matter identified by 35 USC 101: a process, machine, manufacture, or a composition of matter.
Under the Alice Framework Step 2A prong 1, claim 12 recites an abstract idea, including both a mental process and mathematical concept. Specifically, claim 12 recites the following mathematical formulas:
“A method using masked compressing of coefficients of a polynomial having ns arithmetic shares, comprising: shifting a first arithmetic share of the ns arithmetic shares by an input mask λ1; scaling the shifted first arithmetic share by a value based on a first compression factor δ and a masking scaling factor Ψ1; shifting the scaled first arithmetic share by a value based on the masking scaling factor Ψ1; scaling a second to ns shares of the ns arithmetic shares by a value based on the first compression factor δ and the masking scaling factor Ψ1; converting the ns scaled arithmetic shares to ns Boolean shares; right shifting the ns Boolean shares based upon the masking scaling factor Ψ1 and a second compression factor Ψ2; XORing an output mask λ2 to the shifted first Boolean share to produce ns compressed Boolean shares; and carrying out using the ns arithmetic shares when the ns compressed Boolean shares indicates that the coefficients of the polynomial are within boundary values.”
Under the Alice Framework Step 2A prong 2, and Step 2B analysis, claim 12 recites additional elements of, “cryptographic operation”, and “lattice-based cryptography”. The recited additional elements of “cryptographic operation”, and “lattice-based cryptography” are merely generally linking to a particular field of use, see MPEP 2106.04(d), 2106.05(h), 2106.05(A)(iv). For these reasons, claim 12 is neither integrated into a practical application nor amounting to significantly more than the abstract idea.
Claim 13 is rejected for at least the reasons set forth with respect to claim 12. Claim 13 merely further limits the mental process and mathematical concept set forth in claim 12. Under the Alice Framework Step 2A prong 1, claim 13 recites an abstract idea, mathematical formulas. Specifically, claim 13 recites the following mathematical formulas:
“further comprising performing a masked comparison function on the ns compressed Boolean shares configured to indicate that the coefficients of the polynomial are within boundary values.”
Claim 13 recites no additional elements that would require analysis under Step 2A prong 2 and Step 2B.
Claim 14 is rejected for at least the reasons set forth with respect to claim 13. Claim 14 merely further limits the mental process and mathematical concept set forth in claim 13. Under the Alice Framework Step 2A prong 1, claim 14 recites an abstract idea, mathematical formulas. Specifically, claim 14 recites the following mathematical formulas:
“wherein the compressed polynomial coefficients corresponding to the ns compressed Boolean shares having a value in a valid range of values have a value of 0, and the masked comparison function compares the ns compressed Boolean shares to 0.”
Claim 14 recites no additional elements that would require analysis under Step 2A prong 2 and Step 2B.
Claim 15 is rejected for at least the reasons set forth with respect to claim 12. Claim 15 merely further limits the mental process and mathematical concept set forth in claim 12. Under the Alice Framework Step 2A prong 1, claim 15 recites an abstract idea, mathematical formulas. Specifically, claim 15 recites the following mathematical formulas:
“wherein shifting a first arithmetic share of the ns arithmetic shares by an input mask λ1 includes calculating a(0)A = a(0)A + λ1 mod q, where a(0)A is the first arithmetic share of the ns arithmetic shares and q is a prime modulus.”
Claim 15 recites no additional elements that would require analysis under Step 2A prong 2 and Step 2B.
Claim 16 is rejected for at least the reasons set forth with respect to claim 15. Claim 16 merely further limits the mental process and mathematical concept set forth in claim 15. Under the Alice Framework Step 2A prong 1, claim 16 recites an abstract idea, mathematical formulas. Specifically, claim 16 recites the following mathematical formulas:
“wherein scaling the shifted first arithmetic share by a value based on a first compression factor δ and a masking scaling factor Ψ1 and shifting the scaled first arithmetic share by a value based on the masking scaling factor Ψ1 includes calculating 𝐚(𝟎)𝑨 = (⌊
2
Ψ
1
*
δ
q
*
a
(
0
)
A
⌋+
2
Ψ
1
-
1
)𝒎𝒐𝒅
2
Ψ
1
δ
.”
Claim 16 recites no additional elements that would require analysis under Step 2A prong 2 and Step 2B.
Claim 17 is rejected for at least the reasons set forth with respect to claim 16. Claim 17 merely further limits the mental process and mathematical concept set forth in claim 16. Under the Alice Framework Step 2A prong 1, claim 17 recites an abstract idea, mathematical formulas. Specifically, claim 17 recites the following mathematical formulas:
“wherein scaling second to ns shares of the ns shares by a value based on the first compression factor δ and the masking scaling factor 1 includes calculating 𝒂(𝒊)𝑨 = ⌊
2
Ψ
1
*
δ
q
*
a
(
i
)
A
⌋𝒎𝒐𝒅
2
Ψ
1
δ
where 𝒂(𝒊)𝑨 is the ith arithmetic share of the ns arithmetic shares.”
Claim 17 recites no additional elements that would require analysis under Step 2A prong 2 and Step 2B.
Claim 18 is rejected for at least the reasons set forth with respect to claim 17. Claim 18 merely further limits the mental process and mathematical concept set forth in claim 17. Under the Alice Framework Step 2A prong 1, claim 18 recites an abstract idea, mathematical formulas. Specifically, claim 8 recites the following mathematical formulas:
“wherein right shifting the ns Boolean shares based upon the masking scaling factor Ψ1 and a second compression factor Ψ2 includes calculating: 𝒂̅(∗)𝑩 = 𝒂̅(∗)𝑩 ≫ (Ψ𝟏+Ψ𝟐), where 𝒂̅(∗)𝑩 is the ns Boolean shares.”
Claim 18 recites no additional elements that would require analysis under Step 2A prong 2 and Step 2B.
Claim 19 is rejected for at least the reasons set forth with respect to claim 18. Claim 19 merely further limits the mental process and mathematical concept set forth in claim 18. Under the Alice Framework Step 2A prong 1, claim 19 recites an abstract idea, mathematical formulas. Specifically, claim 19 recites the following mathematical formulas:
“wherein XORing an output mask λ2 to the shifted first Boolean share to produce ns compressed Boolean shares includes calculating: 𝒂̅(𝟎)𝑩 = 𝒂̅(𝟎)𝑩 Ꚛ λ𝟐.”
Claim 19 recites no additional elements that would require analysis under Step 2A prong 2 and Step 2B.
Allowable Subject Matter
Claims 1-19 would be allowable if rewritten to overcome the rejection(s) under 35 U.S.C. 101 rejections, set forth in this Office action and to include all of the limitations of the base claim and any intervening claims.
The following is a statement of reasons for the indication of allowable subject matter:
Claims 1-19 were previously indicated as containing allowable subject matter, if rewritten to overcome the rejections under 35 U.S.C. 101, in the Non-Final Office Action mailed on 04/14/2026. The reasons for indication of allowable subject matter are substantially the same as the reasons given in the Non-Final Office Action mailed on 04/14/2026.
Conclusion
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 JEROME ANTHONY KLOSTERMAN II whose telephone number is (571)272-0541. The examiner can normally be reached Monday - Friday 8:30am-3:30pm ET.
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/J.A.K./ Examiner, Art Unit 2182
/ANDREW CALDWELL/Supervisory Patent Examiner, Art Unit 2182
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