Patent ID: 7023990

Claim:
A secure parameter generating device in an algebraic curve cryptography having the definition expression of αY a +βX b +1=0, comprising: an input means for receiving two different prime numbers (a, b) specifying degree of complexity of a curve and size (n) of an encryption key to be used; a Stickelberger element computing devices for computing a Stickelberger element (ω) in an ab cyclotomic, based on the prime number (a) and the prime number (b); a Jacobian addition candidate value computing device for computing Jacobian addition candidate value j corresponding to the two different prime numbers a and b, and a prime number p corresponding to the Jacobian addition candidate value j, based on the prime number (a), the prime number (b), the size (n) of an encryption key, and the Stickelberger element (ω); an order candidate value computing device for computing a class H consisting of a plurality of candidate values for order of a Jacobian group of an algebraic curve specified by the prime number a and the prime number b, based on the prime number a, the prime number b, and the Jacobian addition candidate value j; a security judging device for searching for a candidate value h meeting a security condition such as almost prime number characteristic from the class H, according to the class H; a parameter deciding device for computing a parameter of an algebraic curve whose order of the Jacobian group is in accord with the candidate value h, of the algebraic curves specified by the prime number a, the prime number b, and the prime number p, based on the prime number a, the prime number b, the prime number p, and the candidate value h; and an output device for supplying the parameter of the algebraic curve computed by said parameter deciding device to an algebraic curve cryptographic public key system.