One of the most cost-effective services in cloud computing is storage, used by businesses and individuals to outsource their massive data to untrusted servers. Efforts have studied problems around this application scenario in different fronts: efficiency, flexibility, reliability, and security. In this paper we address the security concerns of cloud storage under the scenario where users encrypt-then-outsource data, share their outsourced data with other users, and the service provider can be queried for searching and retrieval of encrypted data. As main distinctive, we propose a security approach for storage, sharing and retrieval of encrypted data in the cloud fully constructed on the basis of attribute-based encryption (ABE) thus enabling access control mechanisms over both the encrypted data and also for the information retrieval task through search access control. Compared to related works, our approach considers efficient encryption at three different levels: i) bulk encryption of data outsourced to the cloud, ii) keys management for access control over encrypted data by means of digital envelopes from attribute based encryption, and for ABSE are provided over the asymmetric setting (Type-III pairings) to support security levels of 128-bits or greater. Experimental results on benchmark data sets demonstrate the viability of our approach for practical realizations using Barreto-Naehrig curves