Multivariate Cryptography is one of the alternatives to guarantee the security of communication in the post-quantum world. One major drawback of such schemes is the huge size of their keys. In [PB10] Petzoldt et al. proposed a way how to reduce the public key size of the UOV scheme by a large factor. In this paper we extend this idea to the Rainbow signature scheme of Ding and Schmidt [DS05]. By our construction it is possible to reduce he size of the public key by up to 62 %.