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

Zongxia Li, William Gasarch
2021 arXiv   pre-print
In this work, we want to implement two existing 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.  ... 
arXiv:2111.02967v1 fatcat:lfhvpdjyb5hetlkhjwghjncvja

A Pipeline Architecture for Factoring Large Integers with the Quadratic Sieve Algorithm

Carl Pomerance, J. W. Smith, Randy Tuler
1988 SIAM journal on computing (Print)  
We describe 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.  ... 
doi:10.1137/0217023 fatcat:qij5r72hfbckxgdgamqkvqwzme

The Quadratic Sieve Factoring Algorithm [chapter]

Carl Pomerance
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 .  ... 
doi:10.1007/3-540-39757-4_17 dblp:conf/eurocrypt/Pomerance84 fatcat:zdlc3qsffrbmthoe6vdhhlgnkq

The Quadratic Sieve Factoring Algorithm on Distributed Memory Multiprocessors

M. Cosnard, J. Philippe
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.  ... 
doi:10.1109/dmcc.1990.555392 fatcat:2igql2iphrbbbmtmrat3rr4n2q

Quadratic Sieve Factorization Quantum Algorithm and its Simulation [article]

Amandeep Singh Bhatia, Ajay Kumar
2020 arXiv   pre-print
In this paper, we have designed a quantum variant of 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.  ... 
arXiv:2005.11668v1 fatcat:ce42bzrge5fd5ehrrmohazjybi

Acceleration analysis of the quadratic sieve method based on the online matrix solving

Stepan Vynnychuk, Vitalii Misko
2018 Eastern-European Journal of Enterprise Technologies  
Modification of 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] .  ... 
doi:10.15587/1729-4061.2018.127596 fatcat:avyvg5oxcjbbhnnmpa2ekhsbcy

A parallel line sieve for the GNFS Algorithm

Sameh Daoud, Ibrahim Gad
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  ... 
doi:10.14569/ijacsa.2014.050727 fatcat:krlltlq2wvbq7k737kcl5hcx3y

Sieving Methods for Class Group Computation [chapter]

Johannes Buchmann, Michael J. Jacobson, Stefan Neis, Patrick Theobald, Damian Weber
1999 Algorithmic Algebra and Number Theory  
As was 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].  ... 
doi:10.1007/978-3-642-59932-3_1 dblp:conf/aant/0001JNTW97 fatcat:wcpqd54qwng5rj7qauffxyo3jq

MapReduce for Integer Factorization [article]

Javier Tordable
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 [  ... 
arXiv:1001.0421v1 fatcat:t3mso4dxwfhmpd5yup7mqqqh6a

Factoring Large Numbers with a Quadratic Sieve

Joseph L. Gerver
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.  ... 
doi:10.2307/2007781 fatcat:kr335ik7c5b3flefwb373h2ew4

Factoring large numbers with a quadratic sieve

Joseph L. Gerver
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.  ... 
doi:10.1090/s0025-5718-1983-0701639-4 fatcat:3nclsmzyd5bntgyrwhj74ytmua

Factoring with the quadratic sieve on large vector computers

Herman Te Riele, Walter Lioen, Dik Winter
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.  ... 
doi:10.1016/0377-0427(89)90370-1 fatcat:zdueiywthzbbhpcvn2qjrfw7fi

INTEGER FACTORIZATION IMPLEMENTATIONS

Reza Alimoradi, Hamid Reza Arkian
2016 ICTACT Journal on Communication Technology  
To solve this problem, many 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.  ... 
doaj:43dad5a2d0e641b9a5ac0b54c52260f9 fatcat:wmlbhimmqfhbfbhc4qf2ekqgmi

Factoring with the quadratic sieve on large vector computers [chapter]

Herman TE RIELE, Walter LIOEN, Dik WINTER
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.  ... 
doi:10.1016/b978-0-444-88621-7.50018-9 fatcat:ncbtkctajrc63kuguf7qddsw5e

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

O. Ijabo, I. Agbede
2011 AMERICAN JOURNAL OF SCIENTIFIC AND INDUSTRIAL RESEARCH  
Five RHA types form 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  ... 
doi:10.5251/ajsir.2011.2.4.652.659 fatcat:sm456p5t2fa4tlktakrgjvnrda
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