Attribute-based signature scheme (ABS) is a functional variant of digital signature scheme proposed in 2008 by Maji et al. The two basic requirements of ABS (and a hard task to achieve) is collusion resistance and attribute privacy. In this paper, we employ the two-tier signature (TTS) technique to achieve the collusion resistance. Here TTS was proposed in 2007 by Bellare et al., where a signer receives two tier secret keys sequentially. The secondary secret key is served as a onetime key at the timing of signing. First, we propose a definition of an attribute-based two-tier signature scheme (ABTTS). Then we provide ABTTS concretely that enjoys existential unforgeability against chosenmessage attacks, collusion resistance and attribute privacy, in the standard model. For the construction, enhancing the Camenisch-Lysyanskaya signature, we construct signature bundle schemes that are secure under the Strong RSA assumption and the Strong Diffie-Hellman assumption, respectively. These signature bundle schemes enable ABTTS to achieve attribute privacy. Then, using the signature bundle as a witness in the Σ-protocol of the boolean proof, we obtain attribute-based identification schemes (ABIDs). Finally, by applying the TTS technique to ABIDs, we achieve ABTTSs. A feature of our construction is that ABTTS in the RSA setting is pairing-free.