This document proposes a method to improve data storage security in cloud computing using Identity-Based Cryptography (IBC) and Elliptic Curve Cryptography (ECC). IBC reduces key management complexity and eliminates the need for certificates by using a user's identity as their public key. ECC provides data confidentiality through encryption and data integrity is provided by Elliptic Curve Digital Signature Algorithm (ECDS). The proposed method involves a Private Key Generator (PKG) that generates user keys, a Trusted Cloud (TC) that stores encrypted user data, and users who encrypt data using IBC and ECC before storing it on the TC. This is intended to provide secure and flexible data storage in cloud computing.