Factoring with the quadratic sieve on large vector computers
type: Item
instance of: scholarly article
title: Factoring with the quadratic sieve on large vector computers
zbMATH Open document ID: 0684.10005
DOI: 10.1016/0377-0427(89)90370-1
author: Herman te Riele
author: Walter M. Lioen
author: Dik T. Winter
published in: Journal of Computational and Applied Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Let N be a number to be factorized, and let a, b, c be chosen to that \(N=b^ 2-a^ 2c\). Let \(U(x)=a^ 2x+b\), \(V=a\), and \(W(x)=a^ 2x^ 2+2bc+c\); then \(U^ 2\equiv V^ 2W (mod N)\). For various a, b, c, and x, the W's that factorize over a given set of primes are collected until a set whose product is a square is obtained. The authors report results obtained by this method; the best is the factorization of a 93-digit number.
Mathematics Subject Classification ID: 11A41
Mathematics Subject Classification ID: 11-04
zbMATH DE Number: 4120235
zbMATH Keywords: CYBER 205
zbMATH Keywords: NEX SX-2
zbMATH Keywords: quadratic sieve
zbMATH Keywords: vector computers
zbMATH Keywords: factorization
MaRDI profile type: Publication
full work available at URL: 0377-0427(89)90370-1
OpenAlex ID: W2096154872
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description: scientific article; zbMATH DE number 4120235