Factoring with the quadratic sieve on large vector computers
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.
scientific article; zbMATH DE number 4120235
scientific article