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AKS算法对现代密码学的影响 被引量:2

The Effect of AKS Algorithm on Modern Cryptography
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摘要 最近,印度的三个计算机科学家ManindraAgrawal、NeerajKayal和NitinSaxena提出了一个称为AKS的算法。笔者使用这个算法证明了可在多项式时间内对一个整数是否为素数进行确定性的判定,从而解决了一个古老的数学问题。这个结果对于数论和计算复杂性理论的研究与发展具有重要意义。由于现代密码学正是建立在整数分解理论和计算复杂性理论的基础之上,因此这个算法对现代密码学的影响引起了人们的关注。该文将就此进行阐述。 Recently,three computer scientists Manindra Agrawal,Neeraj Kayal and Nitin Saxena in India present an algorithm called AKS.By this algorithm they give a proof that it is possible to determine if a number is a prime in polynomial time.So,they have cracked an age-old mathematical problem.The result has important significance to research and development in both number theory and computational complexity theory.Because modern cryptography is based on the theory of integer factoring and the computational complexity theory,the effect of this algorithm to modern cryptography has been paid significant attention.It will be discussed in this paper.
出处 《计算机工程与应用》 CSCD 北大核心 2003年第11期1-3,54,共4页 Computer Engineering and Applications
基金 国家信息安全管理中心项目(编号:2001-研2-A-017) 黑龙江省青年基金(编号:20010601019)
关键词 AKS算法 现代密码学 RSA算法 AKS algorithm,Modern cryptography,RSA algorithm
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参考文献5

  • 1[1]M Agrawal,N Kayal,N Saxena. Primes is in P.http://www.cse.iitk.ac. in/news/primality.pdf
  • 2[2]http://www.rsasecurity.com
  • 3[3]Michael Sipser. Introduction to Theory of Computation[M].PWS Publishing company, 1997
  • 4[4]http://primes.utm.edu/glossary/page.php/CarmichaelNumber. html
  • 5[5]http://mathworld.wolfram.com

同被引文献12

  • 1李荣森,秦杰,窦文华.RSA系列算法在工程中的应用研究[J].计算机科学,2007,34(2):86-90. 被引量:7
  • 2杨波.现代密码学[M].北京:清华大学出版社,2007.
  • 3MAN1NDRA AGRAWAL, NEERAJ KAYAL, NITIN SAXENA. Primes is in P [ J ]. Ann'Ms of Math. 2004 (160) : 781-793.
  • 4BERRIZBErFIA P. Sharpening " Primes is in P" for a large family of numbers [ J ]. Math. Comp. 2005, 74 ( 252 ) : 2043 -2059.
  • 5YAN SONG YUAN. Number Theory for Computing[ M]. Berlin: Springer-Verlag, 2002.
  • 6RABIN MICHAEL. Probabilistic Algorithmsfor Testing primality[ J ].Journal of Number Theory. 1980 ( 12 ) : 128-138.
  • 7MONIER LOUIS. Evaluation and comparison of two effi- cient probabilistic primality testing algorithms [ J ]. Theo- retica|Computcr Science. 1980(12) :97-108.
  • 8BERNSTEIN J . Proving Primality in Essentially Quartic Random Time [ J ]. Math. Comp. 2007, 76 ( 257 ) : 389-403.
  • 9RICHARD COURANT, HERBERT ROBBINS. What is Mathematics [ M ]. London: Oxford University Press, 2009.
  • 10陈作新.一种基于AES和三素数RPrime RSA认证加密方案[J].计算机应用,2008,28(12):3199-3201. 被引量:2

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