Method of Elliptic Curve Cryptography Using EW-MOF on Scalar Multiplication

Abstract

A method of elliptic curve cryptography (ECC) using the enhanced window-based mutual opposite form (EW-MOF) on scalar multiplication. First, an elliptic curve and a base point on the elliptic curve are selected. Next, essential pre-computed points for a selected window size are calculated. Then, a private key is randomly generated and the mutual opposite form (MOF) is used to convert the private key's binary representation into a signed binary representation. Finally, a public key is calculated by using the enhanced window (EW) method. By greatly reducing the number of essential pre-computed points, the EW-MOF reduces average key generation time (including pre-computation time).