素因子

The first kind of the digital signature schemes is based on the discrete logarithm problem and second kind of the digital signature scheme is based on discrete logarithm and factorization problem, the third kind of the digital signature schemes is based on quadratic residue problem.

本文第一章对数字签名方案进行分类，根据数字签名方案所基于的数学问题，将签名方案分为：基于离散对数问题的数字签名方案，基于素因子分解问题的数字签名方案和基于二次剩余问题的签名方案。

By using Chinese Remainder Theorem of input/output series, the internal connection between the structure of prime factor algorithm and Cooley-Tukey algorithms is revealed.

借助于输入输出序列的中国余数定理映射，本文揭示了素因子算法结构和Cooley-Tukey算法结构的内在联系。

It turns out that the modulus of the RSA cryptosystem is easy to factor if the the ratio of the two prime factors of the modulus can be well approximated by a small fraction.(3) A fast public-key encryption scheme is developed by using the Chinese remainder theorem.

2找到了RSA公钥密码算法的一类弱密钥，指出如果RSA数的两个素因子的比值能够被一个小分数有效逼近的话，则RSA数是容易分解的。

We first characterize the groups in which all m∈cdq〓 contain at most 4 prime divisors; and then show the following: if any m∈cdq〓 is nth-power-free then the derived length of solvable group G is bounded by a function f depended only on n; also if cdq〓 has k different p-parts then the p-length of solvable group G is bounded by a function g depended only on k.

首先研究了非线性不可约特征标对应的特征标次数的商至多含有4个素因子的有限群结构。其次，我们证明：若每m∈cdq〓是n次方自由的，则有限可解群G的的导长及p-长都被仅依赖于n的函数所界定；若cdq〓中共有k个两两不同的p-部分，则有限可解群G的p-长能被仅依赖于k的函数所界定。

With the help of its structure, this paper points out that the non-commutative finite solvable subsimple group will necessarily be a qualitative element group. And referring to the nature of qualitative element group, it can be easily identified the conditions that the ordered prime divisors in a solvable initial finite subsimple group should meet. Suppose that G is always a finite group.

利用其结构，指出了非交换可解有限次单群必为质元群，从而利用质元群的性质，可以很容易地初步确定了可解有限次单群的阶中素因子之间所必须满足的条件，主要得到下面的一些结论：定理1 G是非交换的可解有限次单群，则G′是G的唯一的非平凡正规子群，并且G′是初等交换p -群，此时| G |= p~n q，|G′|=p~n，。

The primary theory of numbers aspect related integer property basic content.

摘要本论文主要讨论了整数的离散性、代数性质、有序性、整除性、最大公因数与最小公倍数、素因子分解、同余等初等数论方面的有关整数性质的基本内容。

The security of these new cryptosystems depends on some NP-complete problems in the theory of Diophantine equations and on the difficulty of large number decomposition.

这些体制的安全性依赖于求解丢番图方程中的一些NP完全问题和大数的素因子分解的困难性。

Harn and Kiesler proposed a public-key cryptosystem, digital signature and authentic encryption scheme based on Rabin's cryptosystem, in this chapter, we will analyze the security of H-K digital signature scheme and H-K authentic encryption scheme, and point out that these cryptosystem are insecure.

Shao设计了两种数字签名方案，并称这两种数字签名的安全性建立同时在离散对数和素因子分解问题之上。

Let pi be the distinct prime divisors of m.

将m的相异素因子记作pi。

Complement properdin factor B ; Lupus erythematosus ; systemic ; Psoriasis ; Diabetes mellitus ; insulin-dependent

补体成份；备解素因子B类；红斑狼疮；全身性；牛皮癣；糖尿病；胰岛素依赖型

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。