Efficient trapdoor commitment as secure as factoring with useful properties

Trapdoor commitment schemes are widely used for adding valuable properties to ordinary signatures or enhancing the security of weakly secure signatures. In this letter, we propose a trapdoor commitment scheme based on RSA function, and prove its security under the hardness of the integer factoring. Our scheme is very efficient in computing a commitment. Especially, it requires only three multiplications for evaluating a commitment when e = 3 is used as a public exponent of RSA function. Moreover, our scheme has two useful properties, key exposure freeness and strong trapdoor opening, which are useful for designing secure chameleon signature schemes and converting a weakly secure signature to a strongly secure signature, respectively.