Cloud computing is a technology which allows the users to share the data and the applications over the internet. An efficient sharing of secure cloud storage services (ESC) scheme allows the users to share the messages in hierarchical order. If a receiver wants to retrieve a message when he is using a system with limited bandwidth, CPU and memory, then the ESC scheme may not work well. The computational cost for decryption is too high, because the receiver does not perform any partial decipherment. Based on the RSA signature, a Trapdoor Commitment scheme is proposed to improve the security level. This scheme allows the receiver to create a short trapdoor and send it to the Cloud Service Provider (CSP) before retrieving files or messages for finding out part of the cipher text. This scheme allows the sender to participate in the partial signature, so as to reduce the computational cost.