| 摘要 |
PROBLEM TO BE SOLVED: To perform adding and doubling operations on an elliptic curve fast by providing plural multipliers. SOLUTION: For example, input points P(x1, y1, z1, z12) and Q(x2, y2, z2, z22) represented as modified Jacob's coordinates are added and four multipliers are used. The four multipliers calculate u2=z12x2, u1=z22x1, and z13=(z22)z2 respectively (Step 1) to find h2u1-u2, calculate s2=z13y2, s1=z23y1, h2 and z1z2 (Step 2) to find r=s1-s2, and calculate u1(h2), h3=(h2)h, r2, and z3=z1z2 (step 3) to find x3=-h3-2u1h2+r2 and three multipliers calculate r(u1h2-x3), s1h3, and z32 respectively (Step 4) to find y3=-s1h3+r(u1h2-x3), thereby outputting x3, y3, z3, and z32.
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