This document proposes a method for securely storing and accessing data in cloud storage using elliptic curve cryptography and the Elgamal encryption algorithm. The method aims to protect user data on cloud servers without overburdening server resources. It involves using a user's private key combined with the cloud provider's public key to encrypt data before uploading it to cloud storage. Only authenticated users can decrypt the data when downloading it from the cloud. The method is evaluated against the RSA algorithm, finding that Elgamal encryption takes less time than RSA encryption, while Elgamal decryption is faster than RSA decryption. The proposed approach provides encrypted cloud data storage that is both secure and efficient.