DEVICE AND METHOD FOR CALCULATING ELLIPTICAL CURVE, AND RECORDING MEDIUM WHERE PROGRAM FOR EXECUTING SAID METHOD IS RECORDED

摘要

PROBLEM TO BE SOLVED: To operate high-speed m-multiplication by the base ϕ-numbering expansion method irrespectively of an amount of a prime number q. ;SOLUTION: This device for performing an arithmetic operation of m- multiplication of a rational point in an elliptic curve form defined on a finite field obtains c0, c1,..., cr-1 satisfying the formula I by the base ϕ-numbering expansion part to inputted integers k, m, an amount q of a defining body q, a point P of GF (qk), and Frobenius map ϕ, and obtains P0, P1,..., Pr-1 from a Pi generation part PiϕiP. And, the device obtains mP by calculating the formula II by a power-of-number table addition part.;COPYRIGHT: (C)2000,JPO