Abstract: If using Guan Haiming’s method to construct conformal iterative function, the result of iterating big integer times can not be obtained in practical applications. In order to solve the problem, this paper proposes two solutions reference to the applications of the discrete logarithm problem, uses the special structure method to search a simple polynomial, and constructs a feasible and efficient conformal iterative function. The efficiency of the function is proved, and two applications of ElGamal encryption scheme and Schnorr signature scheme are given.

Key words: conformal iterative depth problem, conformal iterative function, digital signature, public key encryption, signature scheme

摘要： 管海明提出的保形迭代函数构造方法(武汉大学学报: 理学版, 2008年第5期)在实际应用中不能顺利求得迭代大整数次的结果。针对该问题，结合离散对数问题的应用方法，提出2个解决策略，利用特殊构造法寻找一个结构简单的多项式，从而构造一种可行的高效保形迭代函数，分析证明其具有较高的迭代效率，并将该函数用于推广的ElGamal加密方案与Schnorr签名方案。

关键词: 保形迭代深度问题, 保形迭代函数, 数字签名, 公钥加密, 签名方案

CLC Number: 

• TP301.6