Attribute Based Broadcast Encryption (ABBE) is a combination of Attribute Based Encryption (ABE) and Broadcast Encryption (BE). It allows a broadcaster (or encrypter) to broadcast an encrypted message that can only be decrypted by the receivers who are within a predefined
user set and satisfy the access policy specified by the broadcaster. Compared with normal ABE, ABBE allows direct revocation, which is important in many real-time broadcasting applications such as Pay TV. In this paper, we propose two novel ABBE schemes that have distinguishing features: the first scheme is key-policy based and has short ciphertext and constant size decryption key; and the second one is ciphertext-policy based and has constant size ciphertext and short decryption key. Both of our schemes allow access policies to be expressed using AND-gate with positive, negative, and wildcard symbols, and are proven secure under the Decision n-BDHE assumption without random oracles.