Abstract: Provided are a pairing computation device, a pairing computation method, and a pairing computation program all of which enable fast pairing computation.

Abstract: There is provided a pairing computation device provided with a CPU which computes pairing e(S,Q) with S?G1, Q?G2, ? being a given integer variable, and F being a rational function calculated using Miller's algorithm with respect to multi-pairing (MMA). An order r, a trace t of the Frobenius endomorphism ?p are specified preliminarily using the integer variable ? according to an embedding degree k. The CPU performs pairing computation by means of: an input unit which inputs the integer variable ?, the rational point S, and the rational point Q into respective predetermined registers; a computation unit which computes F; a computation unit which computes a value at a rational point Q(xQ, yQ) of a straight line passing through given rational points; a computation unit which computes f? ?,S(Q) using the aforementioned F and the value; and a computation unit which computes the pairing e(S,Q) using aforementioned f? ?,S(Q) as [F83]. [F83] e(S,Q)=f??,S(Q)(pk?1)/r.

Abstract: Provided are a scalar multiplier and a scalar multiplication program for performing a scalar multiplication at a high speed. In computing a scalar multiplication [s]P of a rational point P of an additive group E(Fp) including rational points on an elliptic curve where a characteristic p, an order r, and a trace t of a Frobenius endomorphism at an embedding degree k=12 using an integer variable ? are given by: p(?)=36?4?36?3+24?2?6?+1, r(?)=36?4?36?3+18?2?6?+1=p(?)+1?t(?), t(?)=6?2+1, the scalar multiplication [s]P is computed as: [s]P=([A]??2+[B])P, using a Frobenius map ??2 given by: [p2]P=??2(P) assuming that a twist degree d is 6 and a positive integer e is 2 where k=d×e.

Abstract: In an arithmetic operation method and an arithmetic operation device arithmetic operations such as exponentiation or scalar multiplication can be performed at high speed. In the case where there exists a plurality of different elements Y and each element Y is represented by tuples in which a plurality of different elements X are combined with an operator, an arithmetic operation method for calculating each element Y by using an electronic computer, associates each element Y with the element X by setting each element X, sets temporary data having an index indicating whether or not each element Y has an identical element X for each element X, and represents each element Y by the temporary data combined with the operator. When there is a combination of temporary data which is common in plurality of elements Y in temporary data contained in each element Y, new temporary data is set by combining the common temporary data and each element Y consisting of each tuple is calculated using the new temporary data.

Abstract: There is provided a pairing computation device, a pairing computation method and a recording medium recording a pairing computation program all enabling a pairing computation at high speed. In the case where the Ate pairing e(Q,P) is defined as in equation (1) and k is any one of even, a multiple of 3, a multiple of 4, and a multiple of 6, arithmetic operations of a rational function which is required to derive the Miller function fs,Q(P) are performed on the proper subfield specified by a twist curve using a quadratic and cubic non-residue v which becomes 1 when an exponentiation of this fs,Q(P) to the power of (qk?1)/r is performed.

Abstract: The invention relates to a planar heat generating element for use on steering wheels of automotive vehicles and motorboats, and a problem of the invention is to adjust a temperature portion of a planar heat generating element which is attached to a steering wheel, so as to enhance the sensation of using the steering wheel by the user when he or she grips thereon.

Abstract: There is provided a pairing computation device provided with a CPU which computes pairing e (S, Q) with S?G1, Q?G2, ? being a given integer variable, and F being a rational function calculated using Miller's algorithm with respect to multi-pairing (MMA). An order r, a trace t of the Frobenius endomorphism ?p are specified preliminarily using the integer variable ? according to an embedding degree k. The CPU performs pairing computation by means of: an input unit which inputs the integer variable ?, the rational point S, and the rational point Q into respective predetermined registers; a computation unit which computes F; a computation unit which computes a value at a rational point Q(xQ, yQ) of a straight line passing through given rational points; a computation unit which computes f? ?,S(Q) using the aforementioned F and the value; and a computation unit which computes the pairing e(S, Q) using aforementioned f? ?,S(Q) as [F83]. [F83] e(S, Q)=f? ?,S(Q)(pk?1)/r.

Abstract: There is provided a computer-readable recording medium recording a program for encryption/decryption, an apparatus for encryption/decryption, an apparatus for multiplication in an extension field, that enable to perform high speed multiplication processing, while allowing the selection of arbitrary key lengths. In multiplying two elements A={a0, a1, a2, . . . , am?1} and B={b0, b1, b2, . . . , bm?1} in an extension field Fpm of extension degree m with a prime number p as characteristic, firstly, a positive integer k is determined such that km+1 is a prime number and p is a primitive element in Fkm+1. Next, two elements A and B are multiplied as two elements in extension field Fpkm of extension degree km with a prime number p as characteristic using the positive integer k. Lastly, using the result of such multiplication, a result of multiplication in an element in the extension field Fpm of extension degree m which is a subfield of Fpkm is obtained.

Abstract: Provided are a scalar multiplier and a scalar multiplication program for performing a scalar multiplication at a high speed. In computing a scalar multiplication [s]P of a rational point P of an additive group E(Fp) including rational points on an elliptic curve where a characteristic p, an order r, and a trace t of a Frobenius endomorphism at an embedding degree k=12 using an integer variable ? are given by: p(?)=36?4?36?3+24?2?6?+1, r(?)=36?4?36?3+18?2?6?+1=p(?)+1?t(?), t(?)=6?2+1, the scalar multiplication [s]P is computed as: [s]P=([A]??2+[B])P, using a Frobenius map ??2 given by: [p2]P=??2(P) assuming that a twist degree d is 6 and a positive integer e is 2 where k=d×e.

Abstract: In an arithmetic operation method and an arithmetic operation device arithmetic operations such as exponentiation or scalar multiplication can be performed at high speed. In the case where there exists a plurality of different elements Y and each element Y is represented by tuples in which a plurality of different elements X are combined with an operator, an arithmetic operation method for calculating each element Y by using an electronic computer, associates each element Y with the element X by setting each element X, sets temporary data having an index indicating whether or not each element Y has an identical element X for each element X, and represents each element Y by the temporary data combined with the operator. When there is a combination of temporary data which is common in plurality of elements Y in temporary data contained in each element Y, new temporary data is set by combining the common temporary data and each element Y consisting of each tuple is calculated using the new temporary data.

Abstract: There are provided a computation method for scalar multiplication or exponentiation and a scalar multiplication program or an exponentiation program which can compute at high speed. In the computation method for scalar multiplication and the scalar multiplication program for computing scalar multiplication by n of a rational point Q in G with respect to a non-negative integer n using an electronic computer, since ?q(Q)=[q]Q=[t?1]Q holds true with respect to the rational point Q in G, (t?1)-adic expansion of a scalar n is performed and a Frobenius endomorphism ?q with respect to a rational point is used in place of t?1.

Abstract: Provided are a pairing computation device, a pairing computation method, and a pairing computation program all of which enable fast pairing computation.

Abstract: There is provided a pairing computation device, a pairing computation method and a recording medium recording a pairing computation program all enabling a pairing computation at high speed. In the case where the Ate pairing e(Q,P) is defined as in equation (1) and k is any one of even, a multiple of 3, a multiple of 4, and a multiple of 6, arithmetic operations of a rational function which is required to derive the Miller function fs,Q(P) are performed on the proper subfield specified by a twist curve using a quadratic and cubic non-residue v which becomes 1 when an exponentiation of this fs,Q(P) to the power of (qk?1)/r is performed.

Abstract: There is provided a computer-readable recording medium recording a program for encryption/decryption, an apparatus for encryption/decryption, an apparatus for multiplication in an extension field, that enable to perform high speed multiplication processing, while allowing the selection of arbitrary key lengths. In multiplying two elements A={a0, a1, a2, . . . , am?1} and B={b0, b1, b2, . . . , bm?1} in an extension field Fpm of extension degree m with a prime number p as characteristic, firstly, a positive integer k is determined such that km+1 is a prime number and p is a primitive element in Fkm+1. Next, two elements A and B are multiplied as two elements in extension field Fpkm of extension degree km with a prime number p as characteristic using the positive integer k. Lastly, using the result of such multiplication, a result of multiplication in an element in the extension field Fpm of extension degree m which is a subfield of Fpkm is obtained.

Abstract: The invention relates to a planar heat generating element for use on steering wheels of automotive vehicles and motorboats, and a problem of the invention is to adjust a temperature portion of a planar heat generating element which is attached to a steering wheel, so as to enhance the sensation of using the steering wheel by the user when he or she grips thereon.

Abstract: A picture encoding system which performs a prediction of picture element values within a block having a plurality of picture elements into which an original picture is divided, a discrete sine transform with respect to prediction error signals for obtaining a transform coefficient, a quantization of the transform coefficient for encoding quantized indexes, an inverse quantization of the quantized indexes for reproduction of the transform coefficient, an inverse discrete sine transform of the reproduced coefficient to reproduce the prediction error signal, and an addition thereto of the predicted picture element value for reproducing the picture element values within the block to employ them in predicting a next stage block to be encoded, whereby the block can be minimized in size while simplifying required transform operation.

Abstract: An apparatus for detecting the flow amount of a fluid passing through a passage. The apparatus comprises a scroll chamber having a circular horizontal cross section and having an inlet opening defined in a tangential direction of the scroll chamber and an outlet opening defined at a substantial center portion of a bottom surface of the scroll chamber. The fluid is introduced through the inlet opening and discharged from the outlet opening. In the scroll chamber, a conically protruding member is provided on a substantial center portion of the top surface of the scroll chamber so as to be protruded vertically and downwardly along the axis of the scroll chamber. A spheral member encased in the scroll chamber is turned about the protruding member and along a wall of the scroll chamber in response to introduction of the fluid through the inlet opening. The flow amount of fluid is measured by detecting the number of turns of the spheral member.

Abstract: A washing apparatus body mounted on a toilet bowl is provided with a hot-water tank supplied with water by a feed water supply device, such as a pump, a function changeover valve connected to the hot-water tank, a plurality of nozzles connected to the function changeover valve, at least a part of the nozzles being provided within the washing apparatus body, and a vacuum releasing valve positioned in the water path between the hot-water tank and the function changeover valve for discharging water in the water path downstream therefrom after use of the apparatus so that no water remains in the downstream water path in a standby state. Hot-water paths leading from the hot-water tank to the nozzles are made as short as possible so as to permit hot water from the hot-water tank to jet out from the respective nozzles toward a user in a short period of time upon the starting of washing and to minimize heat losses in the lines.

Abstract: This invention relates to a sanitary cleaning equipment which includes a flushing portion adapted to direct a jet of cleaning water against a selected area, a deodorizing portion for withdrawing odoriferous air from the neighborhood of the selected area and deodorizing the same, and a dryer portion adapted to direct a jet of warm air against the area. The above deodorizing portion has a first wind tunnel including a deodorant and the above dryer portion has a second wind tunnel including a heater, the first and second wind tunnels being constructed so that they are selectively communicated with a single fan by switching operation of a damper device, thereby providing a sanitary cleaning equipment which is compact and has a high warm air blowing efficiency and a high deodorization efficiency.