| 摘要 |
<p num="1"><br/><br/><br/>In computing point multiples in elliptic curve schemes (e.g. kP and sQ) <br/>separately using, for example, Montgomery''s method for the purpose of <br/>combining kP+sQ, several operations are repeated in computing kP and sQ <br/>individually, that could be executed at the same time. A simultaneous scalar <br/>multiplication method is provided that reduces the overall number of doubling <br/>and addition operations thereby providing an efficient method for multiple <br/>scalar multiplication. The elements in the pairs for P and Q method are <br/>combined into a single pair, and the bits in k and s are evaluated at each <br/>step as bit pairs. When the bits in k and s are equal, only one doubling <br/>operation and one addition operation are needed to compute the current pair, <br/>and when the bits in k and s are not equal, only one doubling operation is <br/>needed and two addition operations.<br/> |
