DETAILED ACTION
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 .
Priority
The present application, 17735190, filed 05/03/2022 is a Continuation of PCT/JP2019/051109, filed 12/26/2019.
Information Disclosure Statement
The information disclosure statement (IDS) submitted on 05/03/2022, 12/15/2022, 01/31/2023 and 11/20/2023 are in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statement is being considered by the examiner.
Drawings
Figure 10 should be designated by a legend such as --Prior Art-- because only that which is old is illustrated. See paragraph [0049] which discloses Fig. 10 is a conventional method decomposing the exponent part using the cyclotomic polynomial
Φ
21
. See MPEP § 608.02(g). Corrected drawings in compliance with 37 CFR 1.121(d) are required in reply to the Office action to avoid abandonment of the application. The replacement sheet(s) should be labeled “Replacement Sheet” in the page header (as per 37 CFR 1.84(c)) so as not to obstruct any portion of the drawing figures. 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.
Specification
The disclosure is objected to because of the following informalities: Some paragraphs do not include a paragraph number. For example, the paragraph in the cross reference to related application section and the paragraph(s) between paragraphs [0004-0005], [0005-0006], [0006-0007], [0049-0050] do not include paragraph numbers. See US 20220269486 A1 for comparison which includes 154 paragraph numbers while the current specification only includes 66 paragraphs numbers.
Appropriate correction is required.
The specification is objected to under 37 C.F.R. 1.74, which requires the detailed description to refer to the different parts of the figures by use of reference letters or reference numerals. Implicit in this rule is that the detailed description correctly reference the figures. In this application the figures and detailed description are inconsistent as explained below.
A. In paragraph [0049] line 5, “pard part” should read “hard part” instead.
Claim Objections
Claim 6 is objected to under 37 C.F.R. 1.71(a) which requires “full, clear, concise, and exact terms” as to enable any person skilled in the art or science to which the invention or discovery appertains, or with which it is most nearly connected, to make and use the same. The following should be corrected.
A. In claim 6 line 2, “a result of the pairing operation” should read “the result of the pairing operation” instead because a result of the pairing operation is already introduced in clam 4 from which the claim depends.
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 1-8 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 recites “
Φ
21
(
q
u
)
r
(
u
)
” in formula 2. It is unclear what
Φ
represents. For purposes of examination
Φ
is interpreted as the cyclotomic polynomial. Claims 7-8 recite the same limitation and are rejected for the same reason. Claims 2-6 inherit the same deficiency as claim 1 by reason of dependence.
Claim 3 recites “wherein the processing circuitry calculates a Miller function of the pairing operation by repeating doubling steps four times, performing one addition step, repeating doubling steps twice, performing one addition step, repeating doubling steps 31 times, performing one addition step, and repeating doubling steps six times”. It is unclear whether the doubling steps are different or not. It is unclear whether the repeating doubling steps twice is included in the doubling steps four times and/or six times and whether the doubling steps four times and/or six times are included in the doubling steps 31 times or these are different doubling steps. Claims 4-6 inherit the same deficiency as claim 3 by reason of dependence.
Further, it is unclear whether the one addition step is the same addition step or three different addition steps. For purposes of examination, this is interpreted as “wherein the processing circuitry calculates a Miller function of the pairing operation by performing a first doubling step four times, performing one first addition step, performing a second doubling step twice, performing one second addition step, performing a third doubling step 31 times, performing one third addition step, and performing a fourth doubling step six times consistent with Fig. 4. Claims 4-6 inherit the same deficiency as claim 3 by reason of dependence.
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 1-8 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Under Step 1, claims 1-6 recite a device and, therefore, is a machine. Claim 7 recites a series of steps and, therefore, is a process. Claim 8 recites a non-transitory computer readable medium and, therefore, is an article of manufacture.
Under Step 2A prong 1, claim 1 recites
A final exponentiation calculation device comprising:
processing circuitry to: decompose an exponent part into an easy part indicated in Formula 1 and a hard part indicated in Formula 2, using a cyclotomic polynomial, the exponent part being in a final exponentiation calculation part of a pairing operation on an elliptic curve that is represented by a polynomial r(u), a polynomial q(u), a polynomial t(u), an embedding degree k, and a parameter u, and is a Barreto-Lynn-Scott (BLS) 21 curve with the embedding degree k of 21, and
transform the hard part obtained as a result of decomposition into a linear sum of the polynomial q(u) indicated in Formula 3
[Formula 1]
(
q
(
u
)
7
-
1
)
∙
(
q
u
2
+
q
u
+
1
[Formula 2]
Φ
21
(
q
u
)
r
(
u
)
[Formula 3]
∑
i
=
1
11
λ
i
u
q
(
u
)
i
where
λ
11
u
=
u
4
-
u
3
-
u
+
1
,
λ
10
u
=
u
-
1
λ
11
u
,
λ
9
u
=
u
λ
10
u
,
λ
8
u
=
u
λ
9
u
+
λ
11
u
,
λ
7
u
=
λ
8
u
-
λ
11
u
,
λ
6
u
=
u
λ
7
u
,
λ
5
u
=
u
λ
6
u
+
λ
11
u
,
λ
4
u
=
u
λ
5
u
,
λ
3
u
=
u
λ
4
u
-
λ
11
u
,
λ
2
u
=
u
λ
3
u
+
λ
11
u
,
λ
1
u
=
u
λ
2
u
,
λ
0
u
=
u
λ
1
u
-
λ
11
u
+
3
.
The above italicized limitations of decomposing an exponent into two parts defined by formulas 1 and 2 and transforming formula 2 into formula 3 amounts to processing mathematical relationships/calculations and falls within the “Mathematical Concepts” grouping of abstract ideas. Accordingly, the claim is directed to recite an abstract idea.
Under step 2A prong 2, the claim recites the following additional elements: a final exponentiation calculation device comprising: processing circuitry. However, the additional elements of “a final exponentiation calculation device comprising: processing circuitry” is recited at a high-level of generality (i.e., as a generic calculation device that includes a generic computer component for performing a series of mathematical operations) such that it amounts to no more than mere instructions using a generic computer component or merely as tools to implement the abstract idea or merely reciting the words “apply it” (or an equivalent) with the judicial exception. The additional elements do not, individually or in combination, integrate the exception into a practical application. Accordingly, the claim is not integrated into a practical application.
Under step 2B, claim 1 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 elements of “a final exponentiation calculation device comprising: processing circuitry” is recited at a high-level of generality (i.e., as a generic calculation device that includes a generic computer component for performing a series of mathematical operations) such that it amounts to no more than mere instructions using a generic computer component or merely as tools to implement the abstract idea or merely reciting the words “apply it” (or an equivalent) with the judicial exception. 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 step 2A prong 1, claims 2-6 recite the same abstract idea as claim 1 by reason of dependence. Further, claim 2 recites further details of the abstract idea of the parameter u “wherein the parameter u is “
2
43
+
2
39
+
2
37
+
2
6
”; claim 3 recites further abstract idea of “calculates a Miller function of the pairing operation by repeating doubling steps four times, performing one addition step, repeating doubling steps twice, performing one addition step, repeating doubling steps 31 times, performing one addition step, and repeating doubling steps six times”; claim 4 recites further abstract idea of “calculates, for a function value, which is a result of calculating the Miller function, an exponentiation of the easy part and an exponentiation of the hard part that has been transformed into the linear sum, so as to calculate a result of the pairing operation” which falls within the “Mathematical Concepts” and “Mental Processes” grouping of abstract ideas. In particular, claims 2 and 4 do not include additional elements that would require further analysis under step 2A prong 2 and step 2B. Accordingly, the claims are directed to recite an abstract idea.
Under step 2A prong 2, claim 3 recites the following additional elements: a pairing operation device. Claims 5-6 recite the following additional elements: perform a cryptographic process, using a result of the pairing operation calculated by the pairing operation device. However, the additional elements of “a pairing operation device” in claims 3 and 5-6 are recited at a high-level of generality (i.e., as a generic pairing operation device for performing a series of mathematical operations) such that it amounts to no more than mere instructions using a generic computer component or merely as tools to implement the abstract idea or merely reciting the words “apply it” (or an equivalent) with the judicial exception. The additional elements of “perform a cryptographic process, using a result of the pairing operation calculated by the pairing operation device” in claims 5-6 are merely generally linking the use of a judicial exception to a particular technological environment or field of use in a cryptographic process. The additional elements do not, individually or in combination, integrate the exception into a practical application. Accordingly, the claims are not integrated into a practical application.
Under step 2B, claims 3 and 5-6 do 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 elements of “a pairing operation device” in claims 3 and 5-6 are recited at a high-level of generality (i.e., as a generic pairing operation device for performing a series of mathematical operations) such that it amounts to no more than mere instructions using a generic computer component or merely as tools to implement the abstract idea or merely reciting the words “apply it” (or an equivalent) with the judicial exception. The additional elements of “perform a cryptographic process, using a result of the pairing operation calculated by the pairing operation device” in claims 5-6 are merely generally linking the use of a judicial exception to a particular technological environment or field of use in a cryptographic process. The claims do not recite additional elements that alone or in combination amount to an inventive concept. Accordingly, the claims do not amount to significantly more than the abstract idea.
Regarding claim 7, it is directed to a method practiced by the device of claim 1. All steps performed by the method of claim 7 would be practiced by the device of claim 1. Claim 1 analysis applies equally to claim 7.
Regarding claim 8, it is directed to a non-transitory computer readable medium storing a final exponentiation calculation program that causes a computer to function as the final exponentiation of claim 1. All steps stored in the non-transitory computer-readable medium of claim 8 would be practiced by the device of claim 1. Claim 1 analysis applies equally to claim 8.
Allowable Subject Matter
Claims 1-8 would be allowable if rewritten to overcome the 35 U.S.C. 101 and 35 U.S.C. 112(b) rejections discussed above.
The following is a statement of reasons for the indication of allowable subject matter:
Claim 1 directed to a final exponentiation calculation device comprising: processing circuitry to: decompose an exponent part into an easy part indicated in Formula 1 and a hard part indicated in Formula 2, using a cyclotomic polynomial, the exponent part being in a final exponentiation calculation part of a pairing operation on an elliptic curve that is represented by a polynomial r(u), a polynomial q(u), a polynomial t(u), an embedding degree k, and a parameter u, and is a Barreto-Lynn-Scott (BLS) 21 curve with the embedding degree k of 21, and transform the hard part obtained as a result of decomposition into a linear sum of the polynomial q(u) indicated in Formula 3
[Formula 1]
(
q
(
u
)
7
-
1
)
∙
(
q
u
2
+
q
u
+
1
[Formula 2]
Φ
21
(
q
u
)
r
(
u
)
[Formula 3]
∑
i
=
1
11
λ
i
u
q
(
u
)
i
where
λ
11
u
=
u
4
-
u
3
-
u
+
1
,
λ
10
u
=
u
-
1
λ
11
u
,
λ
9
u
=
u
λ
10
u
,
λ
8
u
=
u
λ
9
u
+
λ
11
u
,
λ
7
u
=
λ
8
u
-
λ
11
u
,
λ
6
u
=
u
λ
7
u
,
λ
5
u
=
u
λ
6
u
+
λ
11
u
,
λ
4
u
=
u
λ
5
u
,
λ
3
u
=
u
λ
4
u
-
λ
11
u
,
λ
2
u
=
u
λ
3
u
+
λ
11
u
,
λ
1
u
=
u
λ
2
u
,
λ
0
u
=
u
λ
1
u
-
λ
11
u
+
3
.
Toure et al. (NPL – “Optimal Ate Pairing on Elliptic Curves with Embedding Degree 21”) is the closest prior art found. Toure discloses decomposing an exponent part
q
k
-
1
r
into an easy part
q
k
-
1
Φ
k
(
q
)
and a hard part
Φ
k
(
q
)
r
, where
Φ
k
(
x
)
is the k-th cyclotomic polynomial, the exponent part being in a final exponentiation calculation part of a pairing operation on an elliptic curve that is represented by a polynomial r, a polynomial q, a polynomial t, an embedding degree k, and is a Barreto-Lynn-Scott (BLS) 21 curve with the embedding degree k of 21, such that the final exponentiation is computed as
f
q
21
-
1
r
=
(
f
q
7
-
1
)
q
14
q
7
+
1
r
. Further,
q
14
q
7
+
1
r
is transformed into d which is a linear sum of polynomials
γ