Abstract: The existing protocols that are used to prove that a committed number (1,3)x(1,3) lies in a specific interval (1,3)［a,b］(1,3) mostly prove that the integer (1,3)x(1,3) is no less than (1,3)a(1,3) and then repeat the same method to prove that (1,3)b(1,3) is no less than (1,3)x(1,3). 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 (1,3)x(1,3) is neither less than the integer a nor more than the integer (1,3)b(1,3) after the protocol is operated only once, and hence the exact proof that (1,3)x(1,3) lies in the interval (1,3)［a, b］(1,3) 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 16176 bits to 13222 bits, and the communication efficiency increases by 18. 26 percent.

Key words: zero-knowledge proof, trap-door commitment, discrete logarithm