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A computer network is any set of computing nodes which has the ability of exchanging data by interacting with each other meaningfully, allowing resource sharing in a proper manner. The collection of computers is interconnected by communication channels, which need to be secure for better information exchange. This field of networking consists of specialist area of network security adopted by network administrator to prevent and monitor unauthorized access, modification and denial of computer network. To combat the growing problem, security professionals are in search of better protection. Security Attacks compromises the security and hence various Symmetric and Asymmetric cryptographic algorithms have been proposed to achieve the security service in the proper manner, such as Authentication, Confidentiality, Integrity, Non-Repudiation and Availability. These algorithms are required to provide data security and users authenticity. To improve the strength of these security algorithms, a new security algorithm can be designed using combination of both symmetric and asymmetric cryptographic techniques. This algorithm provides three cryptographic primitives such as integrity, confidentiality and authentication. This can be achieved by the combinatorial effect of Elliptic Curve Cryptography implemented by ECDH and ECDSA, Dual RSA and Hash algorithm implemented by Message Digest 5. This new security algorithm has been designed for better security with integrity using a combination of both symmetric and asymmetric cryptographic techniques.