Abstract: Attribute-based encryption (ABE) is a promising version of public key encryption, since it enables fine-grained access control on the encrypted data. In a key-policy ABE (KP-ABE) scheme, every ciphertext is related to attributes set and each secret key is associated with an access structure. Therefore, the decryption overhead is usually proportional to the number of attributes used in decryption process in most existing KP-ABE schemes. Inspired by Hohenberger and Waters’ KP-ABE scheme with fast decryption, we propose a large universe KP-ABE with fast decryption supporting non-monotonic access structure, which is proven selective chosen attribute set secure and chosen plaintext secure in the random oracle model. Moreover, observing Lai et.al expressive KP-ABE with fast decryption and applying with Chameleon Hash technique used to give a direct chosen ciphertext secure KP-ABE construction, we also give a direct chosen plaintext secure KP-ABE construction in the random oracle model, which still achieves the following features: non-monotonic access structure, large-universe and fast decryption. Compared with the related work, both two expressive large universe KP-ABE schemes enjoy comparable time efficiency in decryption process.