期刊名称：International Journal of Security and Its Applications
印刷版ISSN：1738-9976
出版年度：2016
卷号：10
期号：3
页码：439-448
DOI：10.14257/ijsia.2016.10.3.38
出版社：SERSC
摘要：Primitive root is a fundamental concept in modern cryptography as well as in modern number theory. Fermat prime numbers have practical uses in several branches of number theory. As of today, there is no simple general way to compute the primitive roots of a given prime, though there exists methods to find a primitive root that are faster than simply trying every possible number. We prove the equivalence between the primitive roots and the quadratic nonresidues modulo Fermat prime numbers. Therefore, the problem of searching primitive roots is transformed into solving the quadratic residues modulo Fermat primes, which is a much easier problem, having very simple solutions. Theoretical analysis and experimental results verify our conclusion.
关键词：primitive root; Fermat prime; quadratic residue; modular power
