At present, existing multi-receiver authentication (MRA) schemes can only handle situations where the capabilities of all receivers are the same. However, in reality, different receivers may need to have different storage capabilities. In this paper, inspired by the secret sharing scheme based on the Chinese Remainder Theorem (CRT) for polynomial rings where distinct participants save shares with distinct sizes, we propose a new unconditionally secure MRA scheme for multiple messages by the same technique. As far as we know, our MRA scheme is the first MRA scheme with different storage capacities for different receivers and the first one based on the CRT for polynomial rings supporting general access structures. In contrast to the existing general MRA scheme, although our MRA scheme has more communication complexity, it has less computation complexity.