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An Empirical Comparison of the Quadratic Sieve Factoring Algorithm and the Pollard Rho Factoring Algorithm
[article]

2021
*
arXiv
*
pre-print

In this work, we want to implement two existing

arXiv:2111.02967v1
fatcat:lfhvpdjyb5hetlkhjwghjncvja
*factoring**algorithms*- pollard-rho and*quadratic**sieve*- and compare their performance. ... Finally, we verify whether*the**quadratic**sieve*would do better than pollard-rho for*factoring*numbers smaller than 80 bits. ...*Quadratic**Sieve**Algorithm**The*basic*quadratic**sieve**algorithm*is a more complicated*factoring**algorithm*that contains several parts. ...##
###
A Pipeline Architecture for Factoring Large Integers with the Quadratic Sieve Algorithm

1988
*
SIAM journal on computing (Print)
*

We describe

doi:10.1137/0217023
fatcat:qij5r72hfbckxgdgamqkvqwzme
*the**quadratic**sieve**factoring**algorithm*and a pipeline architecture on which it could be efficiently implemented. ... Such a device would be of moderate cost to build and would be able to*factor*100-digit numbers in less than a month. ...*The*authors acknowledge*the*constructive criticisms and helpful suggestions of Peter Montgomery, Andrew Odlyzko, Richard Schroeppel, Sam Wagstaff and*the*referees. ...##
###
The Quadratic Sieve Factoring Algorithm
[chapter]

*
Advances in Cryptology
*

*The*

*quadratic*

*sieve*

*algorithm*i s c u r r e n t l y t h e method of choice t o f a c t o r very l a r g e composite numbers w i t h no small f a c t o r s . ... As of t h i s writing, t h e l a r g e s t number it has cracked i s t h e 71 d i g i t number 9.5 hours on

*the*C r a y ... USE OF A MULTIPLIER

*The*f a c t o r base f o r N i n t h e

*quadratic*

*sieve*

*algorithm*c o n s i s t s of t h o s e primes p S F w i t h ~= 2 o r (N/p) = I . ...

##
###
The Quadratic Sieve Factoring Algorithm on Distributed Memory Multiprocessors

*
Proceedings of the Fifth Distributed Memory Computing Conference, 1990.
*

*The*

*quadratic*

*sieve*

*algorithm*is a powerful method for

*factoring*large integers up to 100 digits. ... Our aim is We propose to modelize all

*the*steps of

*the*

*algorithm*for an implementation on distributed memory multiprocessors:

*the*initialization phase,

*the*generation of

*the*polynomials,

*the*

*sieve*,

*the*...

*The*

*quadratic*

*sieve*

*algorithm*requires

*the*

*factorization*of a matrix of more than 30,000 rows and columns for a 100-digit integer. ...

##
###
Quadratic Sieve Factorization Quantum Algorithm and its Simulation
[article]

2020
*
arXiv
*
pre-print

In this paper, we have designed a quantum variant of

arXiv:2005.11668v1
fatcat:ce42bzrge5fd5ehrrmohazjybi
*the*second fastest classical*factorization**algorithm*named "*Quadratic**Sieve*". ... We have constructed*the*simulation framework of quantized*quadratic**sieve**algorithm*using high-level programming language Mathematica. ...*QUADRATIC**SIEVE**ALGORITHM**Quadratic**sieve*is most extensively used and fastest*algorithm*to find*factors*of number less than 130 decimal digits. ...##
###
Acceleration analysis of the quadratic sieve method based on the online matrix solving

2018
*
Eastern-European Journal of Enterprise Technologies
*

Modification of

doi:10.15587/1729-4061.2018.127596
fatcat:avyvg5oxcjbbhnnmpa2ekhsbcy
*the**quadratic**sieve**algorithm*will allow reducing*the*running time of*the**algorithm*and increasing*the*limit value of*the**factorized*number for which*the**algorithm*of*the**quadratic**sieve*... In 1994,*factorization*of*the*RSA-129 number was performed by means of*the**quadratic**sieve**algorithm*(QS) [4] . ...##
###
A parallel line sieve for the GNFS Algorithm

2014
*
International Journal of Advanced Computer Science and Applications
*

*The*General Number Field

*Sieve*

*algorithm*(GNFS) is currently

*the*best known method for

*factoring*large numbers over than 110 digits. ... This study begins with a discussion of

*the*serial

*algorithm*in general and covers

*the*five steps of

*the*

*algorithm*. Moreover, this approach discusses

*the*parallel

*algorithm*for

*the*

*sieving*step. ... There are many integer

*factorization*

*algorithms*used to

*factor*large numbers, such as Trial division [6] , Pollards p-1

*algorithm*[7] , Lenstra Elliptic Curve

*Factorization*(ECM) [8] ,

*Quadratic*

*Sieve*...

##
###
Sieving Methods for Class Group Computation
[chapter]

1999
*
Algorithmic Algebra and Number Theory
*

As was

doi:10.1007/978-3-642-59932-3_1
dblp:conf/aant/0001JNTW97
fatcat:wcpqd54qwng5rj7qauffxyo3jq
*the*case for*the**quadratic**sieve*,*the*number eld*sieve*w as originally invented for*factoring*integers (see BLP93]). A variation of this*algorithm*has been implemented by D . ... Note that this strategy has very much in common with*the*relation generation part of*the*multiple polynomial*quadratic**sieve**factoring**algorithm*Sil87]. ...##
###
MapReduce for Integer Factorization
[article]

2010
*
arXiv
*
pre-print

*The*

*quadratic*

*sieve*

*algorithm*is split into

*the*different MapReduce phases and compared against a standard implementation. ... Integer

*factorization*is a very hard computational problem. Currently no efficient

*algorithm*for integer

*factorization*is publicly known. ... From

*the*trivial trial division to

*the*classical Fermat's

*factorization*method [4] and Euler's

*factoring*method [5] to

*the*modern

*algorithms*,

*the*

*quadratic*

*sieve*[6] and

*the*number field

*sieve*[ ...

##
###
Factoring Large Numbers with a Quadratic Sieve

1983
*
Mathematics of Computation
*

*The*

*quadratic*

*sieve*

*algorithm*was used to

*factor*a 47-digit number into primes. ... A comparison with Wagstaff's results using

*the*continued fraction early abort

*algorithm*suggests that QS should be faster than CFEA when

*the*number being

*factored*exceeds 60 digits (plus or minus ten or ... Implementation of

*the*

*Quadratic*

*Sieve*.

*The*

*quadratic*

*sieve*

*algorithm*was implemented with a FORTRAN program on an HP3000/series 3 computer. ...

##
###
Factoring large numbers with a quadratic sieve

1983
*
Mathematics of Computation
*

*The*

*quadratic*

*sieve*

*algorithm*was used to

*factor*a 47-digit number into primes. ... A comparison with Wagstaff's results using

*the*continued fraction early abort

*algorithm*suggests that QS should be faster than CFEA when

*the*number being

*factored*exceeds 60 digits (plus or minus ten or ... Implementation of

*the*

*Quadratic*

*Sieve*.

*The*

*quadratic*

*sieve*

*algorithm*was implemented with a FORTRAN program on an HP3000/series 3 computer. ...

##
###
Factoring with the quadratic sieve on large vector computers

1989
*
Journal of Computational and Applied Mathematics
*

*The*results are presented of experiments with

*the*multiple polynomial version of

*the*

*quadratic*

*sieve*

*factorization*method on a CYBER 205 and on a NEC SX-2 vector computer. ... Cohen of

*the*non-existence of odd perfect numbers below 10200.

*The*

*factorized*92-decimal digits number is a record for general purpose

*factorization*methods. ... for

*the*computer time on

*the*NEC SX-2. ...

##
###
INTEGER FACTORIZATION IMPLEMENTATIONS

2016
*
ICTACT Journal on Communication Technology
*

To solve this problem, many

doaj:43dad5a2d0e641b9a5ac0b54c52260f9
fatcat:wmlbhimmqfhbfbhc4qf2ekqgmi
*factorization**algorithms*have been offered with different complexities. Many attempts have been made today to implement these*factorization**algorithms*. ... One difficult problem of mathematics that forms*the*basics of some public key cryptography systems like RSA, is finding*factors*of big numbers. ... They are used in*algorithms*such as*quadratic**sieve*and number field*sieve*in which millions of small numbers get*factorized*in a big number's*factorization*process. ...##
###
Factoring with the quadratic sieve on large vector computers
[chapter]

1990
*
Advances in Parallel Computing
*

*The*results are presented of experiments with

*the*multiple polynomial version of

*the*

*quadratic*

*sieve*

*factorization*method on a Cyber 205 and on a NEC SX-2 vector computer. ... Various numbers in

*the*50-92 decimal digits range have been

*factorized*, as a contribution to (i)

*the*Cunningham project, (ii) Brent's Table of

*factors*of Mersenne numbers, and (iii) a proof by Brent and ... for

*the*computer time on

*the*NEC SX-2. ...

##
###
Suitability of techniques for analyzing particle size of rice husk ash (RHA) from sieve analysis data

2011
*
AMERICAN JOURNAL OF SCIENTIFIC AND INDUSTRIAL RESEARCH
*

Five RHA types form

doi:10.5251/ajsir.2011.2.4.652.659
fatcat:sm456p5t2fa4tlktakrgjvnrda
*the*five levels of one*factor*while*the*four*algorithms*form*the*block or*the*second*factor*at four levels. ...*The*four*algorithms*used were Henderson and Perry's technique, British Standard fitted with*quadratic*equation, British Standard fitted with logarithmic function and ASABE Standard. ... Out of*the*four*algorithms*used for determining particle size,*the*British standard fitted with logarithmic function,*the*British standard fitted with*quadratic*function and ASABE graphical*algorithms*...
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