Cryptography is used for secretly sending information. The information or given data is protected by cryptographic technique. The technique is used in Text and images. The technique is supported by a lot of algorithms. RSA is a better encryption technique for smart cards. In this paper, an image in the Aadhaar card is encrypted using the RK-RSA algorithm for better protection and confidentiality. The proposed RK-RSA algorithm is very secure for smart cards and Aadhaar cards. The better performance of the RK-RSA is evaluated based on the Avalanche Effect, Speed, Throughput, and Power Consumption. The improved performance of the RK-RSA algorithm’s experimental results is reported. The mathematical justification supporting the RK-RSA algorithm is also detailed.