Distributed randomness is very useful for many applications, such as smart contract, proof-of-stake-based blockchain, elliptic curve generation and lottery. Randomness beacon protocols are proposed, which are aimed at continuously distributed randomness generation. However, a reliable source of distributed randomness is gained with difficulty because of Byzantine behavior, which may lead to bias for distributed randomness. These Byzantine behaviors include, but not limited to, the “last actor” problem, DoS attack and collusion attack. Various cryptography schemes have been used to generate distributed randomness. Current constructions face challenging obstacles due to high complexity and bias problems. Given these barriers, we propose a new protocol that is the first precept to utilize attribute-based encryption in a commit-and-reveal scheme for distributed randomness (ABERand). Compared to existing public distributed randomness protocols, ABERand possesses distinguished flexibility, security and efficiency. It is primarily because of trading space for time. More specifically, we resolve the “last actor” problem and make ABERand an intensive out- put randomness beacon with communication complexity O(n3), computation complexity O(1), verification complexity O(n) and communication complexity O(n) of nodes adding/removing.