SIGNATURE, AUTHENTICATION AND SECRET COMMUNICATION SYSTEM USING ELLIPTIC CURVE

摘要

PURPOSE: To provide a safe and sure signature, authentication and secret communication system using an elliptic curve. ;CONSTITUTION: An elliptic curve is as follows. (1) A finite body GF (p) being a definition body of an elliptic curve is set so that a class number of an imaginary second order body Q{(-d)^1/2} of a positive integer (d) is made small, a prime number (p) expressed as (2ⁱ-α) (where, α is a small number) is set so that (p+1-a) or (p+1+a) can be divided by a large prime number and it is expressed as (p-a²)=(d.b²) for the integer o. An elliptic curve and an element in which a root of a class polynomial H_d(x)=0 is a (j) constant are used on this finite body GF (p). (2) Elliptic curves E₁, E₂,... E_n of which the definition body is the definite body GF(p^r) are constituted so that they are not the same type but the original numbers are equal, an used elliptic curve is properly changed.;COPYRIGHT: (C)1995,JPO