Patent ID: 8666076

Claim:
A method of elliptic curve cryptography (ECC) using enhanced window-based mutual opposite form (EW-MOF) on scalar multiplication, comprising the steps of: using an enhanced window-based algorithm to compute essential pre-computed points by a sensing node device arranged in a wireless sensing network according to a selected window size; and saving the essential pre-computed points by the sensing node device when the essential pre-computed points are computed; wherein the essential pre-computed points are saved into the sensing node device, so as to reduce the average time required for randomly generating a private key, and using the elliptic curve to derive a public key can be shortened effectively; wherein the enhanced window-based algorithm generates the essential pre-computed points by the following formula: {2 P, 4 P, 6 P . . . ,(3+2 S ) P , (5+6 S ) P , (7+10 S ) P , . . . }; wherein S is the number of even essential pre-computed points S≧1, and {the largest essential pre-computed point plus (2S)P}≧(2 w−1 )P (the largest pre-computed point).