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产生安全椭圆曲线的一种有效方法 被引量:1

An efficient method to generate elliptic curves
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摘要 本文在寻找安全椭圆曲线的CM方法的基础上,实现了一种更具适用性的产生安全椭圆曲线的有效方法。通常,为了抵抗诸如MOV等算法可能的攻击,以域GF(q)上的椭圆曲线为基础的公钥密码系统,对该椭圆曲线必须要求满足以下条件:m阶曲线具有一个形式为2p+1的大素数因子,这里p是一个素数且q21 mod m。这个条件在不损害安全性的情况下对形式为2p+1的大素因子可以放宽到包括形式为2ip+1的素数(i是一个小整数)。因此,适用于公钥密码系统的安全椭圆曲线的数目显著增加。本文对这一方法进行了实现,它表明用该方法来产生适用于公钥密码系统的椭圆曲线比原来的方案快得多。 In this paper, an efficient method to generate elliptic curves for public key cryptosystems based on discrete logarithm problem is presented. Usually, to resist possible attacks, such as MOV reduction, public key cryptosystems based on elliptic curve E over field GF(q) must satify the following condition: the order m of the curve has a large prime factor of the form 2p+1 where p is a prime and q21 mod m. This condition can be relaxed to include primes of the form 2ip+1 (i is a small integer) without compromising security. Hence, the number of elliptic curves suitable for use by public key cryptosystems is increased greatly. We design a method to implement such a scheme, showing that, it is much faster to generate a suitable elliptic curve with this new scheme than with the original scheme.
出处 《通信学报》 EI CSCD 北大核心 2001年第12期94-98,共5页 Journal on Communications
关键词 公钥密码系统 椭圆曲线产生 CM法 public key cryptosystem, elliptic curve generation
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参考文献2

  • 1Lam K Y,Computing and Combinatorics,Second Annual International Conference,COCOON'96,1996年
  • 2Chao J H,Crypto'94,1994年,50页

同被引文献6

  • 1Blake I.Elliptic curves in cryptography,LNS265[M].Cambridge University Press,1999.
  • 2Menzees A J,Vanstone S,Okamoto T.Reducing elliptic curves logarithms to logarithms in a finite field[ J ].IEEE TIT,1993,39(5):1639-1646.
  • 3Morain F.Building cyclic elliptic curves modulo large primes[ A].Davies D W.Advance in Cryptology-EUROCRYPT' 91 Proceedings,LNCS547[ C].Berlin:Springer-Verlag,1991.
  • 4Lam K Y,Ling S,Lucas C K H.Efficient generation of elliptic curves cryptosystems[A].Computing and Communication,Second Annual International Conference[C].COCOON' 96,1996.
  • 5Atkin A,Morain F.Elliptic curves and primality proving[J ].Mathematics of Computation,1996,61(203):29 -68.
  • 6徐秋亮,李大兴.适用于建立密码体制的椭圆曲线的构造方法及实现[J].计算机学报,1998,21(12):1059-1065. 被引量:10

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