Earticle

초록

영어

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.

목차

Abstract
 1. Introduction
 2. Preliminaries
 3. Main Results
 4. The Proposed Scheme
 5. Experimental Results and Analysis
  5.1. Experimental Results
  5.2. Analysis of the Proposed Scheme
 6. Conclusions and Future Works
 Acknowledgements
 References

키워드

저자

• Dalei Zhang [ School of Computer Science and Technology Anhui University Hefei 230039, China, Institute of Computer and Information Engineering Huainan Normal University Huainan 230001, Anhui, China ]
• Hong Zhong [ School of Computer Science and Technology Anhui University Hefei 230039, China ]

참고문헌

발행기관

간행물

표지보기 관심저널 등록

• 간행물명

  International Journal of Security and Its Applications

• 간기

  격월간

• pISSN

  1738-9976

• 수록기간

  2008~2016

• 등재여부

  SCOPUS

• 십진분류

  KDC 505 DDC 605