Provably Secure Pairing-Free Identity-Based Partially Blind Signature Scheme and Its Application in Online E-cash System

The blind signature scheme permits the user to acquire a signature from the signer; however, the message and the final signature are unknown to the signer. In any partially blind signature (PBS) scheme, the signer is allowed to explicitly incorporate the common information in the signature based on some agreements with the user, however, without compromising the blindness property. Recently, many PBS schemes have been designed by using either certificate authority-based public infrastructure (CA-PKI) or bilinear pairing along with map-to-point hash function. The CA-PKI-based PBS scheme needs huge computation and storage to keep the public keys and the certificates. Note that the pairing and map-to-point hash function are costly operations. Thus, the ID-PBS scheme without pairing is more appropriate for real environments and this paper has come up with an efficient pairing-free ID-PBS scheme. The designed scheme is rigorously examined in the random oracle model, which substantiated that it is provably secure. We also proposed an online e-cash system using our ID-PBS scheme, in which the bank agreed on a common piece of information with the customer and blindly signed some messages. Note that our e-cash system has the properties of unforgeability, unlinkability, non-deniability and prevention of double-spending of e-cash.