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1.
Let μ be an SRB-measure on an Axiom A attractor Δ of a C
2-endomorphism (M, f). As is known, μ-almost every x ϵ Δ is positively regular and the Lyapunov exponents of (f, T f) at x are constants λ(i)(f, μ), 1 ≤ i ≤ s. In this paper, we prove that Lebesgue-almost every x in a small neighborhood of Δ is positively regular and the Lyapunov exponents of (f, T f) at x are the constants λ(i)(f, μ), 1 ≤ i ≤ s. This result is then generalized to nonuniformly completely hyperbolic attractors of endomorphisms. The generic property
of SRB-measures is also proved.
2000 Mathematics Subject Classification. 37D20, 37D25, 37C40.
This work was supported by the 973 Funds of China for Nonlinear Science, the NSFC
10271008, and the Doctoral Program Foundation of the Ministry of Education. 相似文献
2.
Volker Müller 《Journal of Cryptology》1998,11(4):219-234
We discuss new algorithms for multiplying points on elliptic curves defined over small finite fields of characteristic two.
This algorithm is an extension of previous results by Koblitz, Meier, and Staffelbach. Experimental results show that the
new methods can give a running time improvement of up to 50 % compared with the ordinary binary algorithm for multiplication.
Finally, we present a table of elliptic curves, which are well suited for elliptic curve public key cryptosystems, and for
which the new algorithm can be used.
Received 14 January 1997 and revised 4 September 1997 相似文献
3.
提出动力学流关于切丛上联络的一种协变性,求出定常约束力学系统的联络,其测地线方程为系统的运动方程,该联络由系统的动力学函数和约束确定且当动力学流为二阶齐次时约化为通常的动力学联络。 相似文献
4.
YouLin WenQiaoyan XuMaozhi 《电子科学学刊(英文版)》2004,21(5):366-375
The key operation in Elliptic Curve Cryptosystems(ECC) is point scalar multiplication. Making use of Frobenius endomorphism, Mfiller and Smart proposed two efficient algorithms for point scalar multiplications over even or odd finite fields respectively. This paper reduces thec orresponding multiplier by modulo τ^k-1 … τ 1 and improves the above algorithms. Implementation of our Algorithm 1 in Maple for a given elliptic curve shows that it is at least as twice fast as binary method. By setting up a precomputation table, Algorithm 2, an improved version of Algorithm 1, is proposed. Since the time for the precomputation table can be considered free, Algorithm 2 is about (3/2) log2 q - 1 times faster than binary method for an elliptic curve over Fq. 相似文献
5.
对于GF(p)上的椭圆曲线的标量乘计算,Ciet通过引入特征多项式为φ2+2=0的自同态φ,提出一种整数k的φ-NAF分解。对φ-NAF分解使用窗口技术得到k的φ-NAFw分解,通过一定量的存储可以获取更快的计算速度。对该分解的长度和Hamming密度进行较为准确的估计。 相似文献
6.
王维忠 《四川轻化工学院学报》2008,(4):16-17
对一个图而言,有各种不同的自同态。德国数学家Knauer于1990年在文献[1]中首次提出了自同态谱和自同态型的概念,目的是通过图的各种不同的自同态来研究图的代数结构。文献[2]运用自同态型对树进行了刻画,而文献[3]3对直径为3围长为6的2-部图作了讨论,井得到了这类图的自同态型。本文将给出奇圈及其补图的自同态谱和自同态型。 相似文献
7.
8.
研究两条有限链直积上自同态半环的性质。利用有限链直积上的两种二元运算,给出了两条有限链直积的子集构成自同态像集的充要条件,证明了自同态半环的乘法半群是正则半群。通过对有限链直积上的自同态进行分解,得到了自同态半环可由其乘法半群的幂等元集生成;推广了有限链上自同态半群的一些结果。 相似文献
9.
针对非超奇异椭圆曲线上的标量乘算法已经有比较多的研究.与非超奇异曲线不同,超奇异椭圆曲线的自同态环是四元数代数的一个序模,为非交换环.本文主要针对特征大于3的有限域上一类j不变量为0的超奇异椭圆曲线,分析了曲线自同态环及其商环的结构.进而研究了此类曲线上整数表示的性质,并基于这种表示方法提出了一种针对此类曲线的标量乘算法.理论上证明了针对此类超奇异曲线,当选择合适系数集合时,此表示实质上为p-adic展开.实验结果表明:相较于4-NAF等方法,p-adic表示方法提高标量乘效率一倍以上. 相似文献
10.
在椭圆曲线密码体制的实现中,首先要选取安全的椭圆曲线,选取安全椭圆曲线阶的核心步骤是对椭圆曲线阶的计算,SEA算法是计算椭圆曲线的有效算法。本文在实现Fp上SEA算法的前提下,就SEA算法中各方法的综合运用提出了一种方案,并且对用SEA算法选取安全椭圆曲线速度上的优化作了一些讨论,所获得的一些速度指标和国际公开资料上的指标有可比性。 相似文献