Existing Byzantine fault tolerant (BFT) storage solutions that achieve strong consistency and high availability, are costly compared to solutions that tolerate simple crashes. This cost is one of the main obstacles in deploying BFT storage in practice. In this paper, we present PoWerStore, a robust and efficient data storage protocol. PoWerStore's robustness comprises tolerating network outages, maximum number of Byzantine storage servers, any number of Byzantine readers and crash-faulty writers, and guaranteeing high availability (wait-freedom) and strong consistency (linearizability) of read/write operations. PoWerStore's efficiency stems from combining lightweight cryptography, erasure coding and metadata write-backs, where readers write-back only metadata to achieve strong consistency. Central to PoWerStore is the concept of Proofs of Writing (PoW), a novel data storage technique inspired by commitment schemes. PoW rely on a 2-round write procedure, in which the first round writes the actual data and the second round only serves to prove the occurrence of the first round. PoW enable efficient implementations of strongly consistent BFT storage through metadata write-backs and low latency reads. We implemented PoWerStore and show its improved performance when compared to state of the art robust storage protocols, including protocols that tolerate only crash faults.