Dynamic k-times anonymous authentication (k-TAA) schemes allow members of a group to be authenticated anonymously by application providers for a bounded number of times, where application providers can independently and dynamically grant or revoke access right to members in their own group. In this paper, we construct a dynamic k-TAA scheme with space and time complexities of O(log(k)) and a variant, in which the authentication protocol only requires constant time and space complexities at the cost of O(k) -sized public key. We also describe some tradeoff issues between different system characteristics. We detail all the zero-knowledge proof-of-knowledge protocols involved and show that our construction is secure in the random oracle model under the q-strong Diffie-Hellman assumption and q-decisional Diffie-Hellman inversion assumption. We provide a proof-of-concept implementation, experiment on its performance, and show that our scheme is practical.