Non-Adjacent Form Recursive Algorithm on Elliptic Curves Cryptograph

Multiplication of a point is the main operation in elliptic curves cryptography system. It is well-known this operation be expensive in time-consuming. we try to improve the computing efficiency of multiple point which will increase the efficiency of elliptic curves cryptography. In order to reach this goal, on the basis of addition-subtraction method, we adopt recursive formula of double point to improve the efficiency of multiple points algorithm. By the improved algorithm, the efficiency of computing multiple point be improved greatly. The improved algorithm be more effective than addition-subtraction method.