首先是筛法。相信大家都会筛法。筛法不仅能筛整数,也可以筛多项式,例如我们想对于多项式f(x)在x=1,2...100处的值使用不超过100的质数分解质因数,我们可以枚举所有不超过100的质数p,计算在mod p意义下能使 p|f(x0) 的x0 ,并对 x0+kp 进行分解。 我们考虑一个分解质因数的方法,如果我们有两个不同的数...
Relating to a mathematical expression containing a term of the second degree, such asx2+ 2. ♦ Aquadratic equationis an equation having the general formax2+bx+c= 0, wherea, b,andcare constants. ♦ Thequadratic formulaisx= [-b± √(b2- 4ac)]/2aIt is important in algebra, where ...
作者: C Pomerance 摘要: The quadratic sieve algorithm is currently the method of choice to factor very large composite numbers with no small factors. In the hands of the Sandia National Laboratories team of James Davis and Diane Holdridge, it has held the record for the largest hard number ...
Given a positive integerg≥ 2, we would like to study the number of real and imaginary quadratic fields that have an element of ordergin their ideal class group. Conjectures of Cohen and Lenstra predict a positive probability for such an event. Our goal here is to derive quantitative results...
Q Huang,Z Li,Y Zhang,C Lu 摘要: This paper addresses the problem-how to factor big simple blur integers quickly. We definite simple blur integer at first, and then give some theorems about it. Based on these theorems and the primitive non-sieving quadratic sieve (PNQS), we proposed a ...
740 of Lect ure Notes in Comp uter Science[ C ] . , Sp ringer2Verlag , 1993 ,3242332.R. Peralta, A quadratic sieve on the n-dimensional hypercube , Advances in Cryptology, Crypto '92, Lecture Notes in Comput. Sci. 740 (1993) 324–332...
We seemed to have reached an impasse: the whole point of the sieve was so that we didn't have to do that. Time to check the playbook.ln(a⋅b⋅c⋅d⋅…)=ln(a)+ln(b)+ln(c)+ln(d)+ln(…)That looks pretty useful. If the sum of the ln of all ...
In contrast, the problem of bounding the number of such non-diagonal solutions has commanded attention only comparatively recently, the first non-trivial estimates having been obtained around thirty years ago through the sieve methods applied by Hooley [10, 11] and Greaves [7] in their ...
The quadratic sieve factoring algorithm, 2001. [2] Wade Trappe and Lawrence C. Washington. Introduction to Cryptography: with Coding Theory. Pearson: Prentice Hall, second edition, 2006. 8 http-equiv="content-type"
C. Erickson, N. Kaplan, N. Mendoza, A.M. Pacelli, T. Shayler, Parametrized families of quadratic number fields with 3-rank at least 2, Acta Arith., in press Google Scholar [9] F. Gouvêa, B. Mazur The square-free sieve and the rank of elliptic curves J. Amer. Math. Soc., 4...