有限域上可验证随机数的快速构造及安全性分析

摘要

Using the interpolation polynomials in the finite field, and adopting the Lagrange interpolation and Newton interpolation respectively, two methods of constructing verifiable random numbers, are proposed. They have the advantages of high efficiency and no error. Then their security attributes such as uncontrollability and unpredictability are analyzed. Finally some experiments are given to verify the correctness of the two methods.%利用有限域上的插值多项式来构造可验证随机数,并且结合Lagrange插值法与Newton插值法给出了可验证随机数的两种快速构造方法.此方法构造的可验证随机数,具有无误差、效率高的特点.然后对此可验证随机数的不可预测性和不可操控性等安全性进行了分析,最后通过算例验证了此方法的正确性.