Metered signatures: How to restrict the signing capability

We propose a new notion of metered signatures. Metered signature is an extension of k-times signatures in which a signer can generate only k signatures. However, the restriction of metered signatures can be more elaborate: It can be used k-times every day or to preserve the order of signed messages in some applications. Any violation of this regulation reveals a secret key or the signature on a predetermined message. The applications includes proxy signatures, limited free downloads, and the rating web site. We give two instances of metered signatures: One is based on the computational Diffie-Hellman problem (CDHP) using a bilinear map and the other is based on the RSA problem. In both schemes, the signature and certificate size and the verification cost are constant with respect to k. Further, we show that the proposed metered signatures admit batch verification of many signatures almost at one verification cost with small security loss.