CTNF 17/990,355 CTNF 100120 DETAILED ACTION Notice of Pre-AIA or AIA Status 07-03-aia AIA 15-10-aia The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA. Claim Objections Claim 14 objected to as failing to comply with 37 CFR 1.75(a) because of the following informalities: In claim 14, ll.3, “the paring computation” should read as “the pairing computation”. Appropriate correction is required Claim Rejections - 35 USC § 112 07-30-02 AIA 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. 07-34-01 Claims 1-18 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. Claim 1 is rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA), second paragraph, as being indefinite in that it fails to point out what is included or excluded by the claim language. The claim is unclear because it uses the term “deg”, however there are no details on what is “deg” is, it could be a function or it could be something else. As such it is unclear. Claims 2-18 effectively depends on claim 1, and are rejected for the reasons given above. Claim 18 is rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA), second paragraph, as being indefinite in that it fails to point out what is included or excluded by the claim language. The claim is unclear because it uses “performs” as the transitional phrase, this transitional phrase is unclear if it makes the claim open-ended or closed-ended. For examination purposes the claim will be treated as open-ended, the examiner suggests using the transitional phrase of comprising. See MPEP 2111.03 for transitional phrases. Claim Rejections - 35 USC § 101 07-04-01 AIA 07-04 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 1-18 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more. Under the Alice Framework Step 1, claims 1-16 recites a device and, therefore, is a machine. Claim 17 recite a method and, therefore, is a process. Claim 18 recites a CRM and, therefore, is an article of manufacture. Under the Alice Framework Step 2A prong 1, claim 1 recites: A final exponentiation computation device comprising processing circuitry to decompose an exponent portion of a final exponentiation computation portion of pairing computation in an elliptic curve into an easy part and a hard part with using a polynomial Φ k p x , the elliptic curve being expressed by a polynomial r(x), a polynomial p(x), a polynomial t(x), and an embedding degree k, and to factorize the hard part obtained by decomposition, with using a homogeneous cyclotomic polynomial Ψ k x , p indicated by Formula 1, [Formula 1] Ψ k x , p = p x d Φ k ( x / p x ) 1 w h e n k > 1 w h e n k = 1 where d = deg Φ k x . The above underlined limitations are related to decomposing an exponent into two parts and factorizing one of the parts, which amount to mathematical calculations, relationship, and formulas, and falls within the “mathematical concepts” groupings of abstracts ideas. Accordingly, the claim recites an abstract idea. Under the Alice Framework Step 2A prong 2, the claim recites the following additional elements: processing circuitry. However, the additional element of the processing circuitry is recited at a high-level of generality (i.e., as a generic computer component for performing mathematical operations) such that they amount to no more than mere instructions using a generic computer component or merely as tools to implement the abstract idea. The additional element do not, individually or in combination, integrate the exception into a practical application. Accordingly, the claim is not integrated into a practical application. Under the Alice Framework Step 2B, the claim does not include additional elements that individually or in combination, are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to integration of the abstract idea into a practical application, the additional element of the processing circuitry is recited at a high-level of generality (i.e., as a generic computer component for performing mathematical operations) such that they amount to no more than mere instructions using a generic computer component or merely as tools to implement the abstract idea. The claim does not recite additional elements that alone or in combination amount to an inventive concept. Accordingly, the claim does not amount to significantly more than the abstract idea. Under the Alice Framework Step 2A prong 1, Claims 2-16 recite further steps and details to decomposing an exponent into two parts and factorizing one of the parts and falls within the “mathematical Concepts” grouping of abstract ideas. Claims 2-4 recites further mathematical relationships and factorization of the hard part with respect to a formula. The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B. Accordingly, the claims recites an abstract idea. Claim 5 and 6 recites further mathematical relationships and formula of the polynomial t(x). The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B. Accordingly, the claims recites an abstract idea. Claims 7-12 recites further mathematical formula/calculation of the polynomial t(x), r(x) and p(x). The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B. Accordingly, the claims recites an abstract idea. Claim 13 recites further mathematical relation of the easy part and the hard part with respect to p(x) and x, respectively. The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B. Accordingly, the claims recites an abstract idea. Claim 14 recites further mathematical operation of a Miller function. The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B. Accordingly, the claims recites an abstract idea. Claim 15 recites further performing mathematical operations on the result of the Miller function. The claim does not include additional elements that would require further analysis under Step 2A prong 2 and Step 2B. Accordingly, the claims recites an abstract idea. Claim 16 merely recites a cryptographic processing device to perform a cryptographic process using the result of the pairing computation. Accordingly, the claims recites an abstract idea. Under the Alice Framework Step 2A prong 2, the claim recites the following additional elements: “a cryptographic processing device to perform a cryptographic process using the result of the pairing computation…”. However, the additional element of the cryptographic processing device is recited at a high-level of generality (i.e., as a generic computer component for performing mathematical operations on a result) such that they amount to no more than mere instructions using a generic computer component or merely as tools to implement the abstract idea. The additional element of “perform a cryptographic process using the result of the pairing computation…” is merely generally linking the use of a judicial exception to a particular technological environment or field of use in a cryptographic process. The additional element do not, individually or in combination, integrate the exception into a practical application. Accordingly, the claim is not integrated into a practical application. Under the Alice Framework Step 2B, the claim does not include additional elements that individually or in combination, are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to integration of the abstract idea into a practical application, the additional element of the cryptographic processing device is recited at a high-level of generality (i.e., as a generic computer component for performing mathematical operations on a result) such that they amount to no more than mere instructions using a generic computer component or merely as tools to implement the abstract idea. The additional element of “perform a cryptographic process using the result of the pairing computation…” is merely generally linking the use of a judicial exception to a particular technological environment or field of use in a cryptographic process. The claim does not recite additional elements that alone or in combination amount to an inventive concept. Accordingly, the claim does not amount to significantly more than the abstract idea. Regarding claim 17, it is directed to a method practiced by the device of claim 1. A change in statutory class is obvious. As such, claim 17 is rejected for the reasons given in claim 1. Regarding claim 18, it is directed to a non-transitory computer readable medium performed by a computer to function as the final exponentiation computation device of claim 1. A change in statutory class is obvious. As such, claim 18 is rejected for the reasons given in claim 1. Allowable Subject Matter Claims 1-18 would be allowable if rewritten to overcome the related rejections under 35 USC 101, 35 USC 112(b), and objections to the claims. 13-03-01 AIA The following is a statement of reasons for the indication of allowable subject matter: Regarding claim 1, Yutaro et al. (JP 2018-205511 A, See IDS filed 01/19/2023) discloses Final Exponentiation of a pairing operation including cyclotomic polynomials with various polynomials and embedding degrees; Miller algorithm; easy and hard part decomposition; phi/Euler function; and a Deg function, See Translation par.1-16, 74, and see pages 5-6 and 14 of the Japanese application. However, Yutaro does not explicitly disclose factorizing the hard part using a homogeneous cyclotomic polynomial as indicated by formula 1 (and related 5/6). Yonemura et al. (US 2015/0023496 A1, See IDS filed 01/19/2023) discloses Miller function used as the input into the Final Exponentiation; cyclotomic polynomial decomposed into hard and easy parts; BN curves, See Figure 1, par. 18, and 53-58. However, Yonemura does not explicitly disclose factorizing the hard part using a homogeneous cyclotomic polynomial as indicated by formula 1 (and related 5/6). Bach et al. (NPL: “Factoring with Cyclotomic Polynomials”) discloses factorizing the Cyclotomic Polynomials by P + 1, while also discloses alterative reference for P – 1. See p.203-205. However, Bach does not explicitly disclose decomposing into easy and hard parts nor factorizing the hard part using a homogeneous cyclotomic polynomial as indicated by formula 1 (and related 5/6). Sharifi (NPL: “On Cyclotomic Polynomials, Power Residues, and Reciprocity Laws”) discloses Homogeneous Cyclotomic Polynomials. See pages 2-3 and 7-13. However, Sharifi does not explicitly disclose decomposing into easy and hard parts nor factorizing the hard part using a homogeneous cyclotomic polynomial as indicated by formula 1 (and related 5/6). Surowski et al. (NPL: “Homogeneous Polynomial and the minimal Polynomial of Cos(2 π /n)”) discloses Homogeneous Cyclotomic Polynomials. See pages 5-8. However, Surowski does not explicitly disclose decomposing into easy and hard parts nor factorizing the hard part using a homogeneous cyclotomic polynomial as indicated by formula 1 (and related 5/6). The prior art above alone or in combination with any other reference fails to disclose or provide motivation for the following limitation in combination with the rest of the claim limitations: “…to factorize the hard part obtained by decomposition, with using a homogeneous cyclotomic polynomial Ψ k x , p indicated by Formula 1, [Formula 1] Ψ k x , p = p x d Φ k ( x / p x ) 1 w h e n k > 1 w h e n k = 1 where d = deg Φ k x . ”. Regarding claims 17 and 18, the claims are merely a method and a non-transitory computer readable medium that performs or performed by claim 1. As such, the reasons for indication of allowable subject matter follows the reasons given above for claim 1 . Conclusion Any inquiry concerning this communication or earlier communications from the examiner should be directed to Kenny K. Bui whose telephone number is (571)270-0604. The examiner can normally be reached 8:00 am to 3:00 pm on Monday, 8:00 am to 4:00 pm on Tuesday to Friday ET. 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Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000. /KENNY K. BUI/Patent Examiner, Art Unit 2182 (571)270-0604 /ANDREW CALDWELL/Supervisory Patent Examiner, Art Unit 2182 Application/Control Number: 17/990,355 Page 2 Art Unit: 2182 Application/Control Number: 17/990,355 Page 3 Art Unit: 2182 Application/Control Number: 17/990,355 Page 4 Art Unit: 2182 Application/Control Number: 17/990,355 Page 5 Art Unit: 2182 Application/Control Number: 17/990,355 Page 6 Art Unit: 2182 Application/Control Number: 17/990,355 Page 7 Art Unit: 2182 Application/Control Number: 17/990,355 Page 8 Art Unit: 2182 Application/Control Number: 17/990,355 Page 9 Art Unit: 2182 Application/Control Number: 17/990,355 Page 10 Art Unit: 2182 Application/Control Number: 17/990,355 Page 11 Art Unit: 2182
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