SIGNATURE BY ELLIPTIC CURVE, AUTHENTICATION, AND SECRET COMMUNICATION SYSTEM

摘要

PROBLEM TO BE SOLVED: To provide a safe and secure signature, authentication, and secret communication system using an elliptic curve.;SOLUTION: In the elliptic curve, (1) a finite field GF(p) as the field of definition of the elliptic curve is made so that a positive integer d such that the class number of an imaginary quadratic field Q[(-d)^1/2] is small is taken, and that a prime number p is expressed by 2^t-α (where α is a small number), in which p+1-a or p+1+a can be divided by a large prime number and 4p-a²=d×b² is expressed for an integer a. On the finite field GF(p), the elliptic curve and an element, having a j-invariant of the root of a class polynomial H_d(x)=0, are used. (2) En such as the elliptic curves E₁, E₂, and so forth, having a finite field GF(p^r) as the field of definition, are constituted so that the number of elements is the same, although they are not isomorphic each other, and the elliptic curve to be used is properly changed.;COPYRIGHT: (C)2004,JPO