The key management is an important area of research in internet applications, because protecting secret messages during transmission becomes an essential issue for the Internet. Elliptic Curve Cryptography (ECC) has attracted the attention of researchers and product developers due to its robust mathematical structure and highest security compared to other existing algorithms. This paper produces a new cryptographic key generation approach that investigate from metaheuristic algorithms (Greedy Randomized Adaptive Search Procedure (GRASP) and Variable Neighborhood Search(VNS)) in order generate symmetric mask key that consist of more the one EC points with minimum correlation among points. The proposed approach aims to combine between the features of elliptic curve arithmetic, Discrete Logarithm and metaheuristic algorithms (GRASP and VNS) to produce robust symmetric cryptography key (mask key). The proposed approach tested and gives efficient results when compared with other previous approach in term of secrecy and privacy .