In this paper, a chaos-based cryptographic hash function is proposed for message authentication where a fixed length message digest can be generated from any messages with arbitrary length. The compression function in-use is developed according to the diffusion and confusion properties of a novel high-dimensional discrete chaotic map. A symmetric key structure can also be easily embedded based on the high sensitivity to initial conditions and system parameters of the map. As demonstrated in experiments, the throughput of the proposed scheme is about 1.5 times of that with MD5, and the hash value appears randomly without any correlation with the message or the key.