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为有效解决多项式函数根的零知识证明问题,基于离散对数的困难性假设,提出了多重离散对数问题,给出了多项式函数根的零知识证明协议,即:通过对多项式的每一项计算对应的离散对数A1,A2,…,An,证明者向验证者提供这些项,验证者根据(A1A2…An)m odp的结论来判定证明者是否拥有该多项式的根。为了防止证明者的欺骗行为,双方需要进行多次交互式证明。理论分析结果表明:证明者欺骗成功的概率随交互式证明次数的增加呈指数衰减,该协议是安全和可靠的。
In order to effectively solve the problem of zero knowledge proof of polynomial function roots, a discrete logarithm problem is proposed based on the difficult assumption of discrete logarithm. A zero-knowledge proof protocol of polynomial function roots is given. That is, Calculate the corresponding discrete logarithm A1, A2, ..., An, the prover provides these items to the verifier, and the verifier decides from the conclusion of (A1A2 ... An) m odp whether the prover possesses the root of the polynomial. In order to prevent the deception of the certifier, both parties need to conduct multiple interactive proofs. The theoretical analysis shows that the probability of successful cheating is exponentially decayed with the increase of the number of interactive proofs, which is safe and reliable.