| 摘要 |
PROBLEM TO BE SOLVED: To enable addition processing without executing inverse number computation and to enable high-speed processing without adding additive coordinates by using the Jacobian coordinates obtained by three-dimensionally projecting the points on an elliptic curve on an element assembly. SOLUTION: In the method of executing the computation by combining the double calculation processing and addition processing in accordance with the multiplier converted to a binary digit system expressed, the points (x, y) on the elliptic curve on the element assembly are converted to the Jacobian coordinate expression of attaining (x, y)=(X/Z2, Y/Z3) and in the case of continuous execution of the double calculation processing, the computation results (Xt+1, Yt+1, Zt+1) at the point of the time (t+1) of the continuous double calculation processing is subjected to the arithmetic processing with the calculation equation shown by the equation using the present Jacobian coordinates (Xt, Yt, Zt). In such a case, the value of Y' which is the value of twice the Y coordinate is first calculated and the number of times of the addition system in the double calculation at the point of the Jacobian coordinates is decreased by using the value of Y'.
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