Considered the cross-domain authentication of mobile devices in the Internet of things,a certificate based anonymous cross-domain authentication scheme was proposed.First,combined with the characteristics of PKI and IBS,a certificate based signature (CBS) algorithm was proposed，and the security of the proposed CBS scheme was proved.The verification result of the signature in the algorithm was constant,which ensured the anonymity of the authentication entities in the cross-domain process.The algorithm does not contain pairing,and avoids complex certificate management in traditional PKI and the key escrow and distribution of IBS.Then a cross-domain authentication scheme for mobile devices was constructed by combining the proposed signature algorithm.The scheme ensures the anonymity of authentication at the same time.Finally,compared with other schemes,the scheme proposed is more secure and has less computation cost and communication cost.Moreover,the scheme is simple and efficient,and could be applied to the cross-domain authentication of mobile devices.