The document describes a construction of a verifiable random function (VRF) that improves upon previous work. It directly constructs a VRF without using Goldreich-Levin hardcore bits, allows inputs of arbitrary size without encoding, and has proofs and keys consisting of a constant number of group elements. The security of the VRF relies on complexity assumptions in bilinear groups and it finds applications like non-interactive lotteries and compact e-cash schemes.