In this Research paper, a novel and strong symmetric cryptographic algorithm is proposed. NASSCA is based on several symmetric cryptographic algorithms. NASSCA is very simple that uses character Converting algorithm, Fibonacci Number Series, Lucas Number series and bitwise XOR. In NASSCA, shared secret files play a vital role in this Proposed Algorithm. The Sub-keys generation depends on shared-secret files which are useful in different rounds of Encryption and Decryption Process. The most important feature is the calculation of the final key from the Sub-Keys in each Round. Key Generation, encryption/decryption schemes of NASSCA are fast and difficult to predict by Cryptanalysts. The feature of the proposed system is Avalanche Effect is more than some of the existing algorithms.