Apparatus for generating elliptic curve cryptographic parameter, apparatus for processing elliptic curve cryptograph, program for generating elliptic curve cryptographic parameter, and program for processing elliptic cyptograph

An apparatus for processing elliptic curve cryptograph comprising:

• an input device for inputting information;
• a storage device for storing information;
• a processing device for performing computation;
• a finite field order input unit for inputting an order q of a finite field K=GF(q) in elliptic curve cryptographic processing by using the input device, and for storing the order q input, in the storage device;
• a group order input unit for inputting a group order r by using the input device and for storing the group order r input, in the storage device, the group order r being a group order of an additive group E(K) composed of points on an elliptic curve E over a finite field K=GF(q) in elliptic curve cryptographic processing and having a specific form;
• and an elliptic curve pairing processing unit for reading the order q input by the finite field order input unit and the group order r input by the group order input unit from the storage device, and for performing elliptic curve pairing computation, the elliptic curve pairing computation being performed at a speed higher than a predetermined value by being specialized in the group order having the specific form, based on the order q and the group order r input by the group order input unit, by using the processing device.

An apparatus for processing elliptic curve cryptograph comprising:

• an input device for inputting information;
• a storage device for storing information;
• a processing device for performing computation;
• a finite field order input unit for inputting an order q of a finite field K=GF(q) in elliptic curve cryptographic processing by using the input device, and for storing the order q input, in the storage device;
• and
• an elliptic curve pairing processing unit for reading the order q input by the finite field order input unit from the storage device, and for performing elliptic curve pairing computation by using the processing device, based on the order q and a specific group order r determined in advance as a group order of an additive group E(K) composed of points on an elliptic curve E over the finite pair K=GF(q) in elliptic curve cryptographic processing, the elliptic curve pairing computation being performed at a speed higher than a predetermined value by being specialized in the specific group order.

A nontransitory computer readable medium having stored thereon computer executable program, said program [A program for generating an elliptic curve cryptographic parameter, ] comprising a function for causing a computer including a storage device to store information, an output device to output information, and a processing device to perform computation, to operate as an apparatus for generating an elliptic curve cryptographic parameter, wherein the apparatus includes:

• a prime number generation unit for generating a prime number r by using the processing device, and for storing the prime number r generated, in the storage device;
• a group order suitability judgment unit for reading the prime number r generated by the prime number generation unit from the storage device, and for judging whether the prime number r is suitable as a group order of an additive group E(K) composed of points on an elliptic curve E over a finite field K=GF(q) in elliptic curve cryptographic processing, by using the processing device;
• and
• a group order candidate output unit, when the group order suitability judgment unit judges that the prime number r is suitable as the group order of the additive group E(K) composed of points on the elliptic curve E over the finite field K in elliptic curve cryptographic processing, for reading the prime number r generated by the prime number generation unit from the storage device, and for outputting the prime number r as a group order candidate by using the output device.

A nontransitory computer readable medium having stored thereon computer executable program, said program [A program for processing an elliptic curve cryptographic, ] comprising a function for causing a computer including an input device to input information, a storage device to store information, and a processing device to perform computation, to operate as an apparatus for processing elliptic curve cryptograph, wherein the apparatus includes:

• a finite field order input unit for inputting an order q of a finite field K=GF(q) in elliptic curve cryptographic processing by using the input device, and for storing the order q input, in the storage device;
• a group order input unit for inputting a group order r by using the input device and for storing the group order r input, in the storage device, the group order r being a group order of an additive group E(K) composed of points on an elliptic curve E over a finite field K=GF(q) in elliptic curve cryptographic processing and having a specific form;
• and an elliptic curve pairing processing unit for reading the order q input by the finite field order input unit and the group order r input by the group order input unit from the storage device, and for performing elliptic curve pairing computation, the elliptic curve pairing computation being performed at a speed higher than a predetermined value by being specialized in the group order having the specific form, based on the order q and the group order r by using the processing device.

An apparatus for generating an elliptic curve cryptographic parameter comprising:

• a processing device for performing computation;
• a prime number generation unit for generating a prime number r by using the processing device;
• a group order suitability judgment unit for judging, by using the processing device and based on the prime number r generated by the prime number generation unit, with respect to 2 or more natural numbers k selected from natural numbers each equal to or greater than 2 and less than or equal to a predetermined integer, whether or not each of the natural numbers k is a divisor of a natural number r−1 obtained by subtracting 1 from the prime number r, and when judging that all of the natural numbers k are divisors of the natural number r−1, for judging that the prime number r is suitable as a group order of an additive group E(K) composed of points on an elliptic curve E over a finite field K=GF(q) in elliptic curve cryptographic processing;
• and
• a finite field order determination unit for determining, based on the prime number r judged by the group order suitability judgment unit as being suitable as the group order of the additive group E(K), an order q of the finite field K such that the group order of the additive group E(K) becomes the prime number r, by using the processing device.