DEVICE AND METHOD FOR OPERATING GROUP CALCULATIONS OF JACOBI VARIETY OF HYPERELLIPTIC CURVE DEFINED ON GALOIS FIELD WITH TWO CHARACTERISTICS

摘要

PROBLEM TO BE SOLVED: To realize a group calculation on a Jacobi variety by a small amount of operations. ;SOLUTION: This device for operating group calculations to the factors of a Jacobi variety of a hyperelliptic curve y2+y=f(x) defined on GF(2n)D1=g.c. d. (a1(x), y-b1(x)) and D2=g.c.d.(a2(x), y-b2(x)) has a means for storing a1(x), a2(x), b1(x), and b2(x), and a means for calculating q(x)={s1(b1(x)+b2(x))) mod a2(x) by using s1(x) satisfying s1(x) a1(x)+s2(x)a2(x)=1 in the case of GCD(a1(x), a2(x))=1 (GCD is a greatest common polynomial). Thus, the calculations are decreased in the amount by arranging the new function q(x), and can also be operated by a reduced quantity of hardware. Moreover, in the case of D1=D2, this device is provided with a means for storing a1(x) and b1(x), and a means for calculating q(x)=Q(b12(x)+f(x) mod a12(x), a1) {Q(A, B) is a quotient of A divided by B}.;COPYRIGHT: (C)2000,JPO