Several existing access control solutions mainly focus on preserving confidentiality of stored data from unauthorized access and the storage provider. Moreover, to keep sensitive user data confidential against untrusted servers, existing solutions usually apply cryptographic methods by disclosing data decryption keys only to authorized users. However, these solutions inevitably introduce a heavy computation overhead on the data owner for key distribution and data management when fine-grained data access control is desired. In addition, access control policies as well as users' access patterns are also considered as sensitive information that should be protected from the cloud. In this paper, we propose PAbAC, a novel privacy preserving Attribute-based framework, that combines attribute-based encryption and attribute-based signature mechanisms for securely sharing outsourced data via the public cloud. Our proposal is multifold. First, it ensures fine-grained cryptographic access control enforced at the data owner's side, while providing the desired expressiveness of the access control policies. Second, PAbAC preserves users' privacy, while hiding any identifying information used to satisfy the access control. Third, PAbAC is proven to be highly scalable and efficient for sharing outsourced data in remote servers, at both the client and the cloud provider side