A prime number generation unit 110 generates an integer r having a form suitable for fast elliptic curve pairing computation, by using a processing device (S302 to S303). The prime number generation unit 110 judges whether the integer r is a prime number or not, by using the processing device (S304). When the integer r is a prime number, the prime number generation unit 110 judges whether the prime number r is a group order capable of easily changing the level of security or not, by using the processing device (S305). Thereby, it is possible to generate an elliptic curve parameter which is settable to an elliptic curve cryptographic processor that performs elliptic curve pairing computation using an algorithm capable of performing fast computation even by using a processing device with low computational capacity and which is capable of easily changing the level of security.