Efficient proof of a committed number lying in a specific interval
Zhang Jing-liang, MA Li-zhen · Journal of Xidian University · 2006
The existing protocols that are used to prove that a committed number x lies in a specific interval mostly prove that the integer x is no less than a and then repeat the same method to prove that b is no less than x.In order to delete the repetition in these methods a new protocol is proposed by integrating the protocol that two committed numbers are equal with the protocol of the CFT proof.A verifier can be convinced that the committed number x is neither less than the integer a nor more than the integer b after the protocol is operated only once,and hence the exact proof that x lies in the interval is achieved.The proposed protocol is a statistical zero-knowledge proof.In contrast to Boudot's protocol,our method reduces an exponentiation operation;the communication quantity decreases from(16 176) bits to(13 222) bits,and the communication efficiency increases by 18.26 percent.