AbstractCiphertext‐policy attribute‐based encryption (CP‐ABE) is a novel cryptographic primitive for access controlling. However, the existing CP‐ABE schemes are very inefficient as the decryptions involve many expensive pairing operations. Another drawback is that the access policy itself may disclose some privacies of the users. In certain applications, access structures also should be protected. In this work, we propose a notion of CP‐ABE with outsourced decryption and directionally hidden policy, which allows a semi‐trusted proxy in the cloud to help a user decrypt a ciphertext, but the proxy cannot learn the plaintext and the access policy. We construct a concrete scheme from Waters' CP‐ABE and prove its security, verifiability, and directionally hidden policy. Copyright © 2016 John Wiley & Sons, Ltd.