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 a partially blind signature (PBS) scheme,
the signer can explicitly incorporate a common information in the
signature based on some agreement with the user and without
violating the blindness property. Many PBS schemes have been
proposed recently either by using certificate authority-based public
infrastructure (CA-PKI) or pairing along with map-to-point function.
The CA-PKI-based PBS scheme needs huge computation and storage to
keep public keys and certificates. On the other hand, pairing and
map-to-point function are costly operations. Thus, the ID-PBS scheme
without pairing is more appropriate for real environments, and an
efficient pairing-free ID-PBS scheme is proposed in this paper. In
the random oracle model, our scheme is analyzed to be provably
secure. The proposed scheme is used to design an online e-cash
system, in which a bank agrees on a common piece of information with
a customer and can blindly sign some messages. It may be noted that
our e-cash system has the properties of unforgeability,
unlinkability, and non-deniability and can prevent the
double-spending of e-cash.
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