A chameleon hash scheme is a trapdoor collision-resistant hash scheme, and it provides many interesting features in signature schemes with hash-and-sign construction. In this paper, we introduce the notion of key exposure threshold τ for a chameleon hash scheme for which a key exposure free chameleon hash scheme can be understood as the case with τ = ∞. We propose chameleon hash schemes CHτ with the key exposure threshold τ based on discrete logarithm problem (DLP). For τ < ∞, the proposed scheme is noninteractive and key exposure free as long as k ephemeral trapdoors are disclosed for k < τ. The proposed scheme CH∞ is a key exposure free chameleon hash scheme based on DLP, and it requires a label directory that can be managed by a third party. This improves the only known efficient key exposure free chameleon hash scheme based on DLP, which requires one interaction with the trapdoor holder. Copyright © 2012 John Wiley & Sons, Ltd.