As each year passes, the digital transformation of data within the computing world increases exponentially. To address these situations, leading enterprises employ a hybrid IT model to provide customers with a reliable, standardized delivery from multiple independent sources. A genetic cryptosystem is employed within a hybrid IT framework to experimentally design a model that can efficiently store and retrieve cloud space data in real time. This cryptosystem generates robust asymmetric keys for Big Data Security. This paper use public key encryption scheme that offers a number of advantages over traditional encryption algorithms. It uses a unique combination of mathematical concepts, including modular arithmetic and prime factorization, to provide secure encryption and decryption of messages. The system is based on the Paillier cryptosystem but has been modified to enhance its security and performance. The scheme involves two keys, a public key used for encryption and a private key used for decryption. The encryption and decryption process in this cryptosystem is relatively fast, making it suitable for use in large-scale encryption applications. Additionally, the system supports homomorphic encryption, which allows for computations to be performed on ciphertext, without the need for decryption. This cryptosystem provides a flexible and secure solution for data privacy and protection in various applications.