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 .
Information Disclosure Statement
The information disclosure statements (IDS) submitted on 06/24/2022, and 10/07/2024, is in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statements mentioned above, all portions which have not been struck out, are being considered by the examiner.
Drawings
The drawings are objected to under 37 CFR 1.83(a). The drawings must show every feature of the invention specified in the claims. Therefore, the “counter for each of the adjacent intervals” of claim 22 must be shown or the feature(s) canceled from the claim(s). No new matter should be entered.
Corrected drawing sheets in compliance with 37 CFR 1.121(d) are required in reply to the Office action to avoid abandonment of the application. Any amended replacement drawing sheet should include all of the figures appearing on the immediate prior version of the sheet, even if only one figure is being amended. The figure or figure number of an amended drawing should not be labeled as “amended.” If a drawing figure is to be canceled, the appropriate figure must be removed from the replacement sheet, and where necessary, the remaining figures must be renumbered and appropriate changes made to the brief description of the several views of the drawings for consistency. Additional replacement sheets may be necessary to show the renumbering of the remaining figures. Each drawing sheet submitted after the filing date of an application must be labeled in the top margin as either “Replacement Sheet” or “New Sheet” pursuant to 37 CFR 1.121(d). If the changes are not accepted by the examiner, the applicant will be notified and informed of any required corrective action in the next Office action. The objection to the drawings will not be held in abeyance.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claims 1-25 are rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention.
Regarding claims 1, 13, and 25, claims 1, 13, and 25 recite the limitation of: “and defining a sub-interval closely around a boundary between the selected adjacent intervals”. It is unclear how a sub-interval can be between adjacent intervals. Paragraph [0120] of the applicant’s specification, in referring to the applicant’s drawings figure 6, discusses an example of two adjacent intervals, being [2, 2Q] and [2Q, 3Q] with the sub-interval around the boundary of 2Q. The two intervals in the example are adjacent, and thus do not have any space between one and the other. Thus, the sub-interval is not and could not be between these adjacent intervals. Paragraph [0127] – [0128] of the applicant’s specification, in referring to the applicant’s drawings figure 10b, discusses an example of chosen intervals min(-2P) to max(-2P) and min(-3P) to max(-3P). These paragraphs and the applicant’s figure 10b show overlap between the two intervals, with the overlap being between min(-3P) to max(-2P). It is unclear how these two intervals are adjacent if they overlap one another. Furthermore, these paragraphs and fig. 10b describe choosing a sub-interval that not only is within the overlapping section, but which extends past the overlapping section of each of the intervals. For these reasons it is not clear how a sub-interval is supposed to be “closely around a boundary between the selected adjacent intervals”.
Furthermore, claims 1, 13, and 25 recite the limitation of: “two adjacent intervals of an intermediate result”. It is unclear if it is meant to be understood as the intervals are adjacent to one another or if it is meant to be understood as the intervals are each adjacent to the intermediate result. In the applicant’s specification, paragraphs [0118] - [0120] and regarding figure 6 of the applicant’s drawings, there seemingly is no description as to where in the range the intermediate result is located, but it does talk about in paragraph [0120] a pair of intervals with a sub-interval, intervals [2, 2Q] and [2Q, 3Q]. Since these intervals are adjacent to one another, both including the value 2Q, either interpretation may be gathered from this example, the intervals may be considered adjacent to one another, or, if the intermediate result is 2Q, it may be understood that each interval is adjacent to the intermediate result. However, looking at paragraphs [0127] – [0128] and figure 10b of the applicant’s specification and drawings, the mention of the intermediate result seemingly points to its location at either -2P or -3P, but as shown in the applicant’s drawings figure 10b, it is shown that there is a max and min for each the -2P and -3P respectively. The applicant’s specification, paragraphs [0127] – [0128] describe the min to max of -2P and the min to max of the -3P as an interval pair. However, there is an overlap between the Max(-2P) and Min(-3P), so in this instance, the intermediate result seemingly would not make sense to be located at Max(-2P) or Min(-3P) because it would be included in at least one of the interval pairs with at least one of the interval pairs not being considered adjacent. However, due to the two intervals overlapping one another, they also wouldn’t be considered adjacent to one another either. Therefore it is unclear if the limitation is meant to be understood as the intervals are adjacent to one another, or if they are each adjacent to an intermediate result.
Furthermore, the term “closely” in claims 1, 13, and 25 is a relative term which renders the claim indefinite. The term “closely” is not defined by the claim, the specification does not provide a standard for ascertaining the requisite degree, and one of ordinary skill in the art would not be reasonably apprised of the scope of the invention.
Furthermore, claims 1, and 13 recite the limitation of: “repeatedly determining”, and claim 25 recites the limitation of: “repeatedly determine”. It is unclear if these limitations of claims 1, 13, and 25 are meant to be understood as this determining is done repeatedly without end, and thus indefinite, or if there is ever an end to this repetition.
Furthermore, claims 1, 3, 6, 7, 10, 11 and 25 recite the limitations of: “selecting, by the one or more processors”. There is insufficient antecedent basis for this limitation in the claim.
Claims 2-12 inherit the same deficiencies as claim 1 based on dependence. Claims 14-24 inherit the same deficiencies as claim 13 based on dependence.
Regarding claims 5, 6, 17 and 18, The term “small” in claims 6 and 18 is a relative term which renders the claim indefinite. The term “as small as possible” is not defined by the claim, the specification does not provide a standard for ascertaining the requisite degree, and one of ordinary skill in the art would not be reasonably apprised of the scope of the invention.
Regarding claims 6 and 18, The term “closest” in claims 6 and 18 is a relative term which renders the claim indefinite. The term “closest” is not defined by the claim, the specification does not provide a standard for ascertaining the requisite degree, and one of ordinary skill in the art would not be reasonably apprised of the scope of the invention.
Regarding claim 7, claims 7 recites the limitation of: “using a sub-unit of the multiplier”. There is insufficient antecedent basis for this limitation in the claim.
Furthermore, claim 7 recites the limitation of: “wherein the intervals comply with at least one of: determining, by the one or more processors, using a sub-unit of the multiplier, a correction value X for each intermediate result, thereby building a group of correction values SCV; and determining, by the one or more processors, from a specification of the sub-unit a minimal value min(X) and a maximum value max(X) for which the sub-unit determines a correction value X, such that the range CR gets thus partitioned into a plurality of intervals of [min(X), max(X)].” It is unclear if the intervals [min(X), max(X)] are meant to be understood as the adjacent intervals of claim 1 or some other intervals.
Claim 8 inherits the same deficiency as claim 7 based on dependence.
Regarding claim 8, claim 8 recites the limitation of: “wherein at least two of the intervals [min(x1), max(x1)] and [min(x2), max(x2)] overlap, and wherein for such an interval pair, a subinterval is chosen such that it completely includes an intersection of the intervals [min(x1), max(x1)] and [min(x2), max(x2)].” It is unclear if the intervals of the claim are meant to be understood as the adjacent intervals of claim 1 or some other intervals.
Regarding claim 19, claim 19 recites the limitation of: “wherein the intervals comply with at least one of: determining, by the one or more processors, using a sub-unit of a multiplier, a correction value X for each intermediate result, thereby building a group of correction values SCV; and determining, by the one or more processors, from a specification of the sub-unit a minimal value min(X) and a maximum value max(X) for which the sub-unit determines a correction value X, such that range CR gets thus partitioned into a plurality of intervals of [min(X), max(X)].” It is unclear if the intervals [min(X), max(X)] are meant to be understood as the adjacent intervals of claim 13 or some other intervals.
Regarding claim 20, claim 20 recites the limitation of: “wherein at least two of the intervals [min(x1), max(x1)] and [min(x2), max(x2)] overlap, and wherein for such an interval pair, the subinterval is chosen such that it completely includes an intersection of the intervals [min(x1), max(x1)] and [min(x2), max(x2)].” It is unclear if the intervals of the claim are meant to be understood as the adjacent intervals of claim 13 or some other intervals.
Regarding claim 22, the bounds of the claim are unclear because the claim does not provide a discernable boundary on what structure in the claimed processor performs the claimed function of performing counting as recited the claim: “using, by the one or more processors, a counter for each of the adjacent intervals; counting, by the one or more processors, using the counter”. The functions which the processor is claimed do not follow from the structure recited in the claim, so it is unclear whether the function requires some other structure or is simply a result of operating the counter in a certain manner. Therefore, one of ordinary skill in the art would not be able to draw a clear boundary between what is and is not covered by the claims. See MPEP 2173.05(g) for more information.
Furthermore, regarding claim 22, claim 22 recites the limitation of: “using, by the one or more processors, a counter for each of the adjacent intervals; counting, by the one or more processors, using the counter”. The counter is being inferentially claimed, which renders the bounds of the claim unclear. It is unclear whether the structure of the counter is being claimed or merely steps performed in operating the counter are being claimed. See MPEP 2173.
Claim 23 inherits the deficiency of claim 22 based on dependence.
Regarding claim 23, the bounds of the claim are unclear because the claim does not provide a discernable boundary on what structure in the claimed processor performs the claimed function of performing counting as recited the claim: “incrementing, by the one or more processors, the counters when their data patterns hit a corresponding sub-interval”. The functions which the processor is claimed do not follow from the structure recited in the claim, so it is unclear whether the function requires some other structure or is simply a result of operating the counter in a certain manner. Therefore, one of ordinary skill in the art would not be able to draw a clear boundary between what is and is not covered by the claims. See MPEP 2173.05(g) for more information.
Furthermore, regarding claim 23, claim 23 recites the limitation of: “incrementing, by the one or more processors, the counters when their data patterns hit a corresponding sub-interval”. The counter is being inferentially claimed, which renders the bounds of the claim unclear. It is unclear whether the structure of the counter is being claimed or merely steps performed in operating the processor are being claimed. See MPEP 2173.
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 1-25 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 U.S.C 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 mental process, mathematical relationships, and mathematical formulas:
A method for generating test data for verifying a modular correction of a modular multiplication, the method comprising: selecting, two adjacent intervals of an intermediate result obtained from a coarse-grained modular correction on a binary multiplication of two operands A, B and defining a sub-interval closely around a boundary between the selected adjacent intervals, wherein the intermediate result is within a range CR smaller than P^2, with P being a prime number used as modulus for the modular multiplication; selecting, a value V in the sub-interval; using, a first factorization algorithm for the value V for determining operands A', B', wherein the modular multiplication result R' of the operands A' and B' corrected by the coarse-grained correction is in the sub-interval; repeatedly determining, A' plus varying [Symbol font/0x65]-values as A" values; and determining, B" values so that the modular multiplication corrected by the coarse-grained correction is in the sub-interval, thereby generating a test operand data A" and B".
Under the Alice Framework Step 2A prong 2, and Step 2B analysis, claim 1 recites additional
elements of, “computer-implemented” and, “one or more processors”. These additional elements merely recite a generic computer system performing generic computer functions upon which the abstract idea is applied to and thus are not integrated into a practical application, see MPEP 2106.05(I)(A)(ii), and MPEP 2106.05(f)(2)(i). For these reasons these additional elements are neither integrated into a practical solution nor amount 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 mathematical concept set forth in claim 1.
Under the Alice Framework Step 2A prong 1, claim 2 recites an abstract idea, including a
mathematical concept. Specifically, claim 2 recites the following mathematical concept:
wherein the varying [Symbol font/0x65]-values are generated randomly or based on a preselected algorithm.
Claim 2 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 2 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 3 is rejected for at least the reasons set forth with respect to claim 1. Claim 3 merely further limits the mathematical concept set forth in claim 1.
Under the Alice Framework Step 2A prong 1, claim 3 recites an abstract idea, including a
mathematical concept. Specifically, claim 3 recites the following mathematical concept:
wherein the first factorization is performed by: determining, n1 as ⌊sqrt(V)⌋; determining, n2 as ⌈sqrt( V - (n1)^2 )⌉; determining, by the one or more processors, A' as (n1 + n2); and determining, B' as (n1 - n2).
Claim 3 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 3 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 4 is rejected for at least the reasons set forth with respect to claim 1. Claim 4 merely further limits the mathematical concept set forth in claim 1.
Under the Alice Framework Step 2A prong 1, claim 4 recites an abstract idea, including a
mathematical concept. Specifically, claim 4 recites the following mathematical concept:
wherein A and B is each an integer value having a number of bits between 255 to 2^13.
Claim 4 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 4 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 5 is rejected for at least the reasons set forth with respect to claim 1. Claim 5 merely further limits the mathematical concept set forth in claim 1.
Under the Alice Framework Step 2A prong 1, claim 5 recites an abstract idea, including a
mathematical concept. Specifically, claim 5 recites the following mathematical concept:
wherein the intervals comply with [s*P, t*P], a range CR is within the intervals, and wherein s, t are integer values, and s and t are as small as possible, such that the range CR is partitioned into a plurality of intervals [j*P, (j+1)*P] for all integers j in s<j< (t-1).
Claim 5 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 5 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 6 is rejected for at least the reasons set forth with respect to claim 1. Claim 6 merely further limits the mathematical concept set forth in claim 1.
Under the Alice Framework Step 2A prong 1, claim 6 recites an abstract idea, including a
mathematical concept. Specifically, claim 6 recites the following mathematical concept:
wherein the intervals comply with at least one of: determining, a value q such that 2^q is closest to a prime number P, wherein the range CR is part of an interval [s*2^q, t*2^q], where s, t, are integer values, and s, and t are as small as possible, such that the range CR is partitioned into a plurality of intervals [j*2^q, (j+1)*2^q] for all integers j in s<j< (t-1).
Claim 6 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 6 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 7 is rejected for at least the reasons set forth with respect to claim 1. Claim 7 merely further limits the mathematical concept set forth in claim 1.
Under the Alice Framework Step 2A prong 1, claim 7 recites an abstract idea, including a
mathematical concept. Specifically, claim 7 recites the following mathematical concept:
wherein the intervals comply with at least one of: determining, a correction value X for each intermediate result, thereby building a group of correction values SCV; and determining, from a specification of the sub-unit a minimal value min(X) and a maximum value max(X) for which the sub-unit determines a correction value X, such that the range CR gets thus partitioned into a plurality of intervals of [min(X), max(X)].
Under the Alice Framework Step 2A prong 2, and Step 2B analysis, claim 7 recites additional
elements of, “sub-unit of a multiplier”. This additional element merely recites a part of a generic computer system performing generic computer functions upon which the abstract idea is applied to and thus are not integrated into a practical application, see MPEP 2106.05(I)(A)(ii), and MPEP 2106.05(f)(2)(i). For these reasons these additional elements are neither integrated into a practical solution nor amount to significantly more than the abstract idea.
Claim 8 is rejected for at least the reasons set forth with respect to claim 7. Claim 8 merely further limits the mathematical concept set forth in claim 7.
Under the Alice Framework Step 2A prong 1, claim 8 recites an abstract idea, including a
mathematical concept. Specifically, claim 8 recites the following mathematical concept:
wherein at least two of the intervals [min(x1), max(x1)] and [min(x2), max(x2)] overlap, and wherein for such an interval pair, a subinterval is chosen such that it completely includes an intersection of the intervals [min(x1), max(x1)] and [min(x2), max(x2)].
Claim 8 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 8 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 9 is rejected for at least the reasons set forth with respect to claim 1. Claim 9 merely further limits the mathematical concept set forth in claim 1.
Under the Alice Framework Step 2A prong 1, claim 9 recites an abstract idea, including a
mathematical concept. Specifically, claim 9 recites the following mathematical concept:
wherein a selection of two adjacent intervals comprises a looping sub-method and a selection sub-method, wherein in each loop of the looping sub-method a pair of adjacent intervals is selected, and for that interval pair test operand data A" and B" are generated.
Claim 9 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. 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 mathematical concept set forth in claim 9.
Under the Alice Framework Step 2A prong 1, claim 10 recites an abstract idea, including a
mathematical concept. Specifically, claim 10 recites the following mathematical concept:
wherein the selection sub-method comprises: using, for each of the adjacent intervals; counting, for an adjacent interval pair of intervals how often their sub-interval was hit by a test operand data pattern; and selecting, using the selection sub-method, a next interval pair based on values, by selecting a next interval having a lowest counter value.
Under the Alice Framework Step 2A prong 2, and Step 2B analysis, claim 10 recites additional
elements of, “counter”. This additional element merely recites a generic computer system performing generic computer functions upon which the abstract idea is applied to and thus are not integrated into a practical application, see MPEP 2106.05(I)(A)(ii), and MPEP 2106.05(f)(2)(i). For these reasons these additional elements are neither integrated into a practical solution nor amount to significantly more than the abstract idea.
Claim 11 is rejected for at least the reasons set forth with respect to claim 10. Claim 11 merely further limits the mathematical concept set forth in claim 10.
Under the Alice Framework Step 2A prong 1, claim 11 recites an abstract idea, including a
mathematical concept. Specifically, claim 11 recites the following mathematical concept:
further comprising: incrementing, when their data patterns hit a corresponding sub-interval.
Claim 11 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 11 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 12 is rejected for at least the reasons set forth with respect to claim 1. Claim 12 merely further limits the mathematical concept set forth in claim 1.
Under the Alice Framework Step 2A prong 1, claim 12 recites an abstract idea, including a
mathematical concept. Specifically, claim 12 recites the following mathematical concept:
wherein a prime number P used for applied modular arithmetic is selected from at least one of NIST primes, Edwards primes, and generalized Mersenne primes.
Claim 12 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 12 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Regarding claim 13, under the Alice Framework Step 1, claim 13 falls within the four statutory categories of patentable subject matter identified by 35 U.S.C 101: a process, machine, manufacture, or a composition of matter.
Under the Alice Framework Step 2A prong 1, claim 13 recites an abstract idea, including both a mental process and mathematical concept. Specifically, claim 13 recites the following mental process, mathematical relationships, and mathematical formulas:
for generating test data for verifying a modular correction of a modular multiplication, comprising: is capable of performing a method comprising: selecting, two adjacent intervals of an intermediate result obtained from a coarse-grained modular correction on a binary multiplication of two operands A, B and defining a sub-interval closely around a boundary between the selected adjacent intervals, wherein the intermediate result is within a range CR smaller than P^2, with P being a prime number used as modulus for the modular multiplication; selecting, a value V in the sub-interval; using, a first factorization algorithm for the value V for determining operands A', B', wherein the modular multiplication result R' of the operands A' and B' corrected by the coarse-grained correction is in the sub-interval; repeatedly determining, A' plus varying g-values as A" values; and determining, B" values so that the modular multiplication corrected by the coarse-grained correction is in the sub-interval, thereby generating a test operand data A" and B".
Under the Alice Framework Step 2A prong 2, and Step 2B analysis, claim 13 recites additional
elements of, “computer system”, “one or more processors”, “one or more computer-readable memories”, “one or more computer-readable tangible storage devices”, and “program instructions stored on at least one of the one or more storage devices for execution by at least one of the one or more processors via at least one of the one or more memories”. These additional elements merely recite a generic computer system performing generic computer functions upon which the abstract idea is applied to and thus are not integrated into a practical application, see MPEP 2106.05(I)(A)(ii), and MPEP 2106.05(f)(2)(i). For these reasons these additional elements are neither integrated into a practical solution nor amount to significantly more than the abstract idea.
Claim 14 is rejected for at least the reasons set forth with respect to claim 13. Claim 14 merely further limits the mathematical concept set forth in claim 13.
Under the Alice Framework Step 2A prong 1, claim 14 recites an abstract idea, including a
mathematical concept. Specifically, claim 14 recites the following mathematical concept:
wherein the varying [Symbol font/0x65]-values are generated randomly or based on a preselected algorithm.
Claim 14 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 14 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 15 is rejected for at least the reasons set forth with respect to claim 13. Claim 15 merely further limits the mathematical concept set forth in claim 13.
Under the Alice Framework Step 2A prong 1, claim 15 recites an abstract idea, including a
mathematical concept. Specifically, claim 15 recites the following mathematical concept:
wherein the first factorization is performed by: determining, by the one or more processors, n1 as ⌊sqrt(V)⌋; determining, by the one or more processors, n2 as ⌈sqrt( V - (n1)^2 )⌉; determining, by the one or more processors, A' as (n1 + n2); and determining, by the one or more processors, B' as (n1 - n2).
Claim 15 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 15 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 16 is rejected for at least the reasons set forth with respect to claim 13. Claim 16 merely further limits the mathematical concept set forth in claim 13.
Under the Alice Framework Step 2A prong 1, claim 16 recites an abstract idea, including a
mathematical concept. Specifically, claim 16 recites the following mathematical concept:
wherein A and B is each an integer value having a number of bits between 255 to 2^13.
Claim 16 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 16 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 17 is rejected for at least the reasons set forth with respect to claim 13. Claim 17 merely further limits the mathematical concept set forth in claim 13.
Under the Alice Framework Step 2A prong 1, claim 17 recites an abstract idea, including a
mathematical concept. Specifically, claim 17 recites the following mathematical concept:
wherein the intervals comply with [s*P, t*P], a range CR is within the intervals, and wherein s, t are integer values, and s and t are as small as possible, such that the range CR is partitioned into a plurality of intervals [j*P, (j+1)*P] for all integers j in s<j< (t-1).
Claim 17 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 17 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 18 is rejected for at least the reasons set forth with respect to claim 13. Claim 18 merely further limits the mathematical concept set forth in claim 13.
Under the Alice Framework Step 2A prong 1, claim 18 recites an abstract idea, including a
mathematical concept. Specifically, claim 18 recites the following mathematical concept:
wherein the intervals comply with at least one of: determining, a value q such that 2^q is closest to a prime number P, wherein the range CR be part of an interval [s*2^q, t*2^q], where s, t, are integer values, and s, and t are as small as possible, such that the range CR is partitioned into a plurality of intervals [j*2^q, (j+1)*2^q] for all integers j in s<j< (t-1).
Claim 18 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 18 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 19 is rejected for at least the reasons set forth with respect to claim 13. Claim 19 merely further limits the mathematical concept set forth in claim 13.
Under the Alice Framework Step 2A prong 1, claim 19 recites an abstract idea, including a
mathematical concept. Specifically, claim 19 recites the following mathematical concept:
wherein the intervals comply with at least one of: determining, a correction value X for each intermediate result, thereby building a group of correction values SCV; and determining, from a specification of the sub-unit a minimal value min(X) and a maximum value max(X) for which the sub-unit determines a correction value X, such that range CR gets thus partitioned into a plurality of intervals of [min(X), max(X)].
Under the Alice Framework Step 2A prong 2, and Step 2B analysis, claim 19 recites additional elements of, “sub-unit of a multiplier”. This additional element merely recites a part of a generic computer system performing generic computer functions upon which the abstract idea is applied to and thus are not integrated into a practical application, see MPEP 2106.05(I)(A)(ii), and MPEP 2106.05(f)(2)(i). For these reasons these additional elements are neither integrated into a practical solution nor amount to significantly more than the abstract idea.
Claim 20 is rejected for at least the reasons set forth with respect to claim 19. Claim 20 merely further limits the mathematical concept set forth in claim 19.
Under the Alice Framework Step 2A prong 1, claim 20 recites an abstract idea, including a
mathematical concept. Specifically, claim 20 recites the following mathematical concept:
wherein at least two of the intervals [min(x1), max(x1)] and [min(x2), max(x2)] overlap, and wherein for such an interval pair, the subinterval is chosen such that it completely includes an intersection of the intervals [min(x1), max(x1)] and [min(x2), max(x2)].
Claim 20 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 20 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 21 is rejected for at least the reasons set forth with respect to claim 13. Claim 21 merely further limits the mathematical concept set forth in claim 13.
Under the Alice Framework Step 2A prong 1, claim 21 recites an abstract idea, including a
mathematical concept. Specifically, claim 21 recites the following mathematical concept:
wherein a selection of two adjacent intervals comprises a looping sub-method and a selection sub-method, wherein in each loop of the looping sub-method a pair of adjacent intervals is selected, and for that interval pair test operand data A" and B" are generated.
Claim 21 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 21 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 22 is rejected for at least the reasons set forth with respect to claim 21. Claim 22 merely further limits the mathematical concept set forth in claim 21.
Under the Alice Framework Step 2A prong 1, claim 22 recites an abstract idea, including a
mathematical concept. Specifically, claim 22 recites the following mathematical concept:
wherein the selection sub-method comprises: counting, by the one or more processors, using the counter, for an adjacent interval pair of intervals how often their sub-interval was hit by a test operand data pattern; and selecting, by the one or more processors, using the selection sub-method, a next interval pair based on counter values, by selecting a next interval having a lowest counter value.
Under the Alice Framework Step 2A prong 2, and Step 2B analysis, claim 22 recites additional elements of, “counter”. This additional element merely recites a generic computer system performing generic computer functions upon which the abstract idea is applied to and thus are not integrated into a practical application, see MPEP 2106.05(I)(A)(ii), and MPEP 2106.05(f)(2)(i). For these reasons these additional elements are neither integrated into a practical solution nor amount to significantly more than the abstract idea.
Claim 23 is rejected for at least the reasons set forth with respect to claim 21. Claim 23 merely further limits the mathematical concept set forth in claim 21.
Under the Alice Framework Step 2A prong 1, claim 23 recites an abstract idea, including a
mathematical concept. Specifically, claim 23 recites the following mathematical concept:
further comprising: incrementing, when their data patterns hit a corresponding sub-interval.
Claim 23 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 23 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Claim 24 is rejected for at least the reasons set forth with respect to claim 13. Claim 24 merely further limits the mathematical concept set forth in claim 13.
Under the Alice Framework Step 2A prong 1, claim 24 recites an abstract idea, including a
mathematical concept. Specifically, claim 24 recites the following mathematical concept:
wherein a prime number P used for applied modular arithmetic is selected from at least one of NIST primes, Edwards primes, and generalized Mersenne primes.
Claim 24 recites no additional elements in the claim limitations which require a Step 2A prong 2
or Step 2B analysis. For these reasons, claim 24 is neither integrated into a practical application nor
amounting to significantly more than the abstract idea.
Regarding claim 25, under the Alice Framework Step 1, claim 25 falls within the four statutory categories of patentable subject matter identified by 35 U.S.C 101: a process, machine, manufacture, or a composition of matter.
Under the Alice Framework Step 2A prong 1, claim 25 recites an abstract idea, including both a mental process and mathematical concept. Specifically, claim 25 recites the following mental process, mathematical relationships, and mathematical formulas:
A product for generating test data for verifying a modular correction of a modular multiplication, comprising: two adjacent intervals of an intermediate result obtained from a coarse-grained modular correction on a binary multiplication of two operands A, B and defining a sub-interval closely around a boundary between the selected adjacent intervals, wherein the intermediate result is within a range CR smaller than P^2, with P being a prime number used as modulus for the modular multiplication; select, a value V in the sub- interval; a first factorization algorithm for the value V for determining operands A', B', wherein the modular multiplication result R' of the operands A' and B' corrected by the coarse-grained correction is in the sub- interval; to repeatedly determine, A' plus varying g-values as A" values; and to determine, B" values so that the modular multiplication corrected by the coarse-grained correction is in the sub-interval, thereby generating a test operand data A" and B".
Under the Alice Framework Step 2A prong 2, and Step 2B analysis, claim 25 recites additional
elements of, “computer program”, “one or more computer readable storage media”, “one or more computer readable storage media”, “program instructions”, and “one or more processors”. These additional elements merely recite a generic computer system upon which the abstract idea is applied to and thus are not integrated into a practical application, see MPEP 2106.05(I)(A)(ii), and MPEP 2106.05(f)(2)(i). Furthermore, these additional elements which merely recite a generic computer system performing generic computer functions are considered well-understood, routine, and conventional activities, see MPEP 2106.05 (I)(A)(ii), and 2106.05(d)(II). For these reasons these additional elements are neither integrated into a practical solution nor amount to significantly more than the abstract idea.
Deferring of Indication of Allowable Subject Matter
The Examiner is deferring indication of allowable subject matter over the prior art cited pending resolution of the 35 U.S.C. 112(b), and 101 rejections made against claims 1-25.
Conclusion
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/J.A.K./Examiner, Art Unit 2182 /EMILY E LAROCQUE/ Primary Examiner, Art Unit 2182