Recently, Kang et al. discussed some security flaws of Wu et al.'s and Wei et al.'s authentication schemes that guarantee user anonymity in wireless communications and showed how to overcome the problems regarding anonymity and the forged login messages. However, we will show that Kang et al.'s improved scheme still did not provide user anonymity as they claimed.

The key escrow problem and high computational cost are the two major problems that hinder the wider adoption of hierarchical identity-based signature (HIBS) scheme. HIBS schemes with either escrow-free (EF) or online/offline (OO) model have been proved secure in our previous work. However, there is no much EF or OO scheme that has been evaluated experimentally. In this letter, several EF/OO HIBS schemes are considered. We study the algorithmic complexity of the schemes both theoretically and experimentally. Scheme performance and practicability of EF and OO models are discussed.