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A tale of two sieves
 Notices Amer. Math. Soc
, 1996
"... It is the best of times for the game of factoring large numbers into their prime factors. In 1970 it was barely possible to factor “hard ” 20digit numbers. In 1980, in the heyday of the BrillhartMorrison continued fraction factoring algorithm, factoring of 50digit numbers was becoming commonplace ..."
Abstract

Cited by 40 (2 self)
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It is the best of times for the game of factoring large numbers into their prime factors. In 1970 it was barely possible to factor “hard ” 20digit numbers. In 1980, in the heyday of the BrillhartMorrison continued fraction factoring algorithm, factoring of 50digit numbers was becoming commonplace. In 1990 my own quadratic sieve factoring algorithm had doubled the length of the numbers that could be factored, the record having 116 digits. By 1994 the quadratic sieve had factored the famous 129digit RSA challenge number that had been estimated in Martin Gardner’s 1976 Scientific American column to be safe for 40 quadrillion years (though other estimates around then were more modest). But the quadratic sieve is no longer the champion. It was replaced by Pollard’s number field sieve in the spring of 1996, when that method successfully split a 130digit RSA challenge number in about 15 % of the time the quadratic sieve would have taken. In this article we shall briefly meet these factorization algorithms—these two sieves—and some of the many people who helped to develop them. In the middle part of this century, computational issues seemed to be out of fashion. In most books the problem of factoring big numbers
Factoring large integers using parallel Quadratic Sieve
, 2000
"... Integer factorization is a well studied topic. Parts of the cryptography we use each day rely on the fact that this problem is di�cult. One method one can use for factorizing a large composite number is the Quadratic Sieve algorithm. This method is among the best known today. We present a parallel i ..."
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Cited by 2 (0 self)
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Integer factorization is a well studied topic. Parts of the cryptography we use each day rely on the fact that this problem is di�cult. One method one can use for factorizing a large composite number is the Quadratic Sieve algorithm. This method is among the best known today. We present a parallel implementation of the Quadratic Sieve using the Message Passing Interface (MPI). We also discuss the performance of this implementation which shows that this approach is a good one. 1
The Quadratic Sieve Factoring Algorithm
, 2001
"... Mathematicians have been attempting to find better and faster ways to factor composite numbers since the beginning of time. Initially this involved dividing a number by larger and larger primes until you had the factorization. This trial division was not improved upon until Fermat applied the ..."
Abstract

Cited by 1 (0 self)
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Mathematicians have been attempting to find better and faster ways to factor composite numbers since the beginning of time. Initially this involved dividing a number by larger and larger primes until you had the factorization. This trial division was not improved upon until Fermat applied the