Information Security has become an essential concern in the modern world. Encryption is an effective way to prevent an unofficial person from viewing the digital information with the secret key. RSA encryption is often used for digital signatures which can prove the authenticity and reliability of a message. As RSA encryption is less competent and resource -heavy, it is not used to encrypt the entire message. If a message is encrypted with a symmetric -key RSA encryption it will be more efficient. Under this process, only the RSA private key will be able to decrypt the symmetric key. The Euclidean algorithm is attainably one of the most extensively known algorithms. The Euclidean algorithm is used for finding the greatest common divisor of two numbers. The algorithm can also be defined for more general rings than just the integers. This work is very useful to improve the data security in Smart card and Aadhaar card. In this paper, the RSA algorithm is modified using the Euclidean technique to improve its performance. The proposed algorithm shows its better performance in terms of speed, throughput, power consumption, and the avalanche effect. Experimental results and mathematical justification supporting the proposed method are reported.