Nearly Optimal Randomized Blind Signature Scheme Based On Modular Multiplicative Group Over Integers

Due to the unforgeability and unlinkability properties, blind signatures are the underlying key techniques of untraceable electronic cash systems and anonymous electronic voting protocols. This manuscript will present an extremely efficient randomized blind signature scheme that is especially suitable for the environments where the computation capabilities of users are limited, like mobile commerce and smart-card transactions. Not only does the signer perform merely one modular exponentiation computation, but also the proposed scheme can be demonstrated as being nearly optimal in the computation and communication cost of each user among the randomized blind signature schemes based on a finite commutative group over integers with modular multiplication as the operator, such as El Gamal-like, Rabin-like or RSA-like randomized blind signature schemes. Furthermore, we formally define the unlinkability, the unforgeability and the randomization properties of the proposed scheme and provide formal proofs for these properties under the random oracle model.