Fast RSA-Based Trapdoor Commitment Scheme with Key Exposure Freeness and Strong Trapdoor Opening

Abstract

Trapdoor commitment scheme (TCS) is one of useful tools for designing value-added schemes such as chameleon signatures and sanitizable signatures that provide stronger privacy. Since the privacy of communicating parties is very important for future computing environments such as ubiquitous computing environment, TCS is a useful tool for the environments. In this paper, we propose a RSA-based key exposure free trapdoor commitment scheme which provides strong trapdoor opening. TCS-based value-added signatures are constructed by using a trapdoor commitment scheme instead of an ordinary hash function. Hence, it is desirable to provide efficient commitment evaluation for designing efficient TCS-based value-added signatures. Our scheme requires only few multiplications for evaluating a commitment when a small prime is used as a public exponent for the RSA function, and so our scheme can be used for designing the above mentioned value-added schemes very efficiently. Moreover, our scheme provides strong trapdoor opening which can be used for improving the security of a signature, and the conversion is very efficient due to the efficiency of the commitment evaluation algorithm.