筛法时需要在模意义下解 p|(x+⌈n⌉)2−n ,即解 x2≡a(modp) ,解这个方程可以使用Cipolla's Algorithm。 设Π(B)=a ,在最后一步中直接使用 O(a3) 的高斯消元会增大时间复杂度,事实上可以注意到该矩阵是稀疏的(每行只有 O(log) 个非零位置),从而使用用于稀疏矩阵的复杂度为 O(ae)(e...
1) quadratic sieve 二次筛法1. Finally,the algorithm was applied to a quadratic sieve. 最后给出了算法在二次筛法中的应用。2. In this article we study the quadratic sieve in large integer factorization,declare a kind of optimization in choosing algorithms,parameters,hardware and the control of ...
Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus (product of two secret primes), a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed at the Sandia National Laboratories ...
sieve: n. 1.(细眼)筛。 2.(约装一 bushel 的) ... The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second fastest method known (after the general number field sieve). It is still the fastest for integers under 100 decimal digits or so, an...
必应词典为您提供quadratic-sieve的释义,na. 【数】二次节法; 网络释义: 二次筛法;二次筛选法;二次筛选因数分解法;
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 factore since mid-1983. As...
5.1 Helper Functions A set of functions are critical to the Quadratic Sieve algorithm but are not explicitly part of the algorithm. In some cases, there exist other - sometimes faster - algorithms that achieve the same results, but we chose to implement functions described in both our course ...
A branch and bound algorithm is considered to solve linearly constrained, integer quadratic optimization problems. The main result consists in making a rule by which it will be decided in every node of the branch and bound tree which variable is going to branch next such that only a small num...
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2 The XL Algorithm The original description of XL for multivariate quadratic systems can be found in [4]; a more general definition of XL for systems of higher degree is given in [3]. The following gives an introduction of the XL algorithm for quadratic systems; the notation is adapted ...