The increased importance of information security has brought many proposals for encryption. Diffie-Hellman (DH) encryption and Elliptic Curve Cryptography (ECC) are examples of encryption methods proposed for more effective information security.
The Diffie-Hellman (DH) encryption involves exponential operations in the process of encryption. There are also many other different methods for encryption which involve exponential operation.
For more stable information security, a length of key to be an exponent in exponential operation has to be sufficiently long. However, if the key to be an exponent is lengthened, more exponential computations are required such that an operation pace is slowed. A lowered operation pace is more severe in mobile devices which have slower processors.
ECC involves scalar multiplication in the process of encryption.
In the case of ECC, the length of the key as a coefficient being multiplied on a coordinate in scalar multiplication has to be long enough for more stable information security. However, if the key is lengthened, more scalar multiplication computations are required, such that the operation is slowed. The falling-off in operating pace is more severe in the mobile devices which have slower processors.
Accordingly, there is a need for an improved method for generating a key which increases encryption pace by reducing the computational complexity accompanying the encryption.