## Factoring PapersNote: many of these papers come from other web sites. If the location of the paper is not mentioned, then it is stored at our web site. ## Surveys- A Survey of Modern Integer Factorization Algorithms by Peter L. Montgomery from CiteSeer.
- Some Parallel Algorithms for Integer Factorization by Richard Brent from Richard Brent's ANU homepage (http://gan.anu.edu.au/~brent/pd/rpb193.pdf).
- Integer Factoring by Arjen lenstra from Citeseer.
- A Tale of Two Sieves by Carl Pomerance (pdf, 268K) from http://www.ams.org/notices/199612/pomerance.pdf.
## Elliptic Curve method- Some Integer Factorization Algorithms using Elliptic Curves by Richard Brent from Richard Brent's ANU homepage (http://wwwmaths.anu.edu.au/~brent/pd/rpb102a.pdf).
- Factorization of the Tenth Fermat Number by Richard Brent from Citeseer.
- Three New Factors of Fermat Numbers by R. Brent, R. Crandall, K. Dilcher and C. Van Halewyn from Richard Brent's ANU homepage (http://gan.anu.edu.au/~brent/pd/rpb175a.pdf).
## Quadratic Sieve- Factoring Integers with Large Prime Variations of the Quadratic Sieve by H. Boender and H.J.J. te Riele from Citeseer.
- Factoring Integers with the Self-Initializing Quadratic Sieve by S. Contini.
## Number Field Sieve- The Factorization of the Ninth Fermat Number by A.K. Lenstra, H.W. Lenstra, M.S. Manasse, and J.M. Pollard (postscript, 230K) from Mark Manasse's homepage (http://www.std.org/~msm/common/f9paper.ps).
- The Number Field Sieve by A.K. Lenstra, H.W. Lenstra, M.S. Manasse, and J.M. Pollard (postscript, 160K) from Mark Manasse's homepage (http://www.std.org/~msm/common/nfspaper.ps).
- On Quadratic Polynomials for the Number Field Sieve by Brian Murphy and Richard Brent (zipped, postscript, 93K) from Richard Brent's homepage (ftp://ftp.comlab.ox.ac.uk/pub/Documents/techpapers/Richard.Brent/rpb178.ps.gz).
- Factorization of RSA-140 Using the Number Field Sieve by S. Cavallar, B. Dodson, A.K. Lenstra, P.C. Leyland, W.M. Lioen, P.L. Montgomery, B. Murphy, H.J.J. te Riele, and P. Zimmermann (Compressed postscript, 557K) from CWI (http://www.cwi.nl/ftp/CWIreports/MAS/MAS-R9925.ps.Z).
- Factorization of a 512-bit RSA Modulus by S. Cavallar, B. Dodson, A.K. Lenstra, W.M. Lioen, P.L. Montgomery, B. Murphy, H.J.J. te Riele, K. Aardal, J. Gilchrist, G. Guillerm, P. Leyland, J. Marchand, F. Morain, A. Muffet, Chris Putnam, Craig Putnam, and Paul Zimmermann. (compressed postscript, 130K) from CWI (http://www.cwi.nl/ftp/CWIreports/MAS/MAS-R0007.ps.Z).
- Polynomial selection for the number field sieve integer factorisation algorithm by B. Murphy (compressed postscript, 816K) from http://web.comlab.ox.ac.uk/oucl/work/richard.brent/ftp/Murphy-thesis.ps.gz.
- An Introduction to the General Number Field Sieve by Matthew Briggs (pdf, 850K) from http://scholar.lib.vt.edu/theses/available/etd-32298-93111/unrestricted/etd.pdf.
- Factoring estimates for a 1024-bit RSA modulus by Arjen K. Lenstra, Eran Tromer, Adi Shamir, Wil Kortsmit, Bruce Dodson, James Hughes, Paul Leyland. Available at Eran Tromer's web site.
- On the cost of factoring RSA-1024 by Adi Shamir and Eran Tromer. Available at Eran Tromer's web site.
- GNFS Factoring Statistics of RSA-100, 110, ..., 150 by Kazumaro Aoki, Yuji Kida, Takeshi Shimoyama, and Hiroki Ueda. Available on the crypto eprint archive.
- A Kilobit Special Number Field Sieve Factorization by Kazumaro Aoki, Jens Franke, Thorsten Kleinjung, Arjen Lenstra and Dag Arne Osvik. Available on the crypto eprint archive.
- Factorization of a 768-bit RSA modulus by Thorsten Kleinjung, Kazumaro Aoki, Jens Franke, Arjen Lenstra, Emmanuel Thomé, Joppe Bos, Pierrick Gaudry, Alexander Kruppa, Peter Montgomery, Dag Arne Osvik, Herman te Riele, Andrey Timofeev, and Paul Zimmermann. Available on the crypto eprint archive.
- FACTORISATION OF RSA-220 WITH CADO-NFS by Shi Bai, Pierrick Gaudry, Alexander Kruppa, Emmanuel Thome, and Paul Zimmermann
## Square roots in number fields- Square Roots of Products of Algebraic Numbers by Peter L. Montgomery (zipped, postscript, 118K) from CWI (ftp://ftp.cwi.nl:/pub/pmontgom).
- A Montgomery-Like Square Root for the Number Field Sieve by Phong Nguyen from CiteSeer.
## Linear algebra- Solving Large Sparse Linear Systems over Finite Fields by B. A. LaMacchia and A. M. Odlyzko from CiteSeer.
- A Block Lanczos Algorithm for Finding Dependencies over GF(2) by Peter L. Montgomery (zipped, postscript, 221K) from CWI (ftp://ftp.cwi.nl:/pub/pmontgom).
## Other factoring algorithms- Factorization of the Eighth Fermat Number by Richard Brent and John Pollard, from Richard Brent's homepage (http://web.comlab.ox.ac.uk/oucl/work/richard.brent/pub/pub061.html).
- Using Lucas Sequences to Factor Large Integers Near Group Orders by ZHANG Zhenxiang (postscript, 334K).
## Miscellaneous factoring papers- The Future of Integer Factorization by A.M. Odlyzko (pdf, 140K) from Andrew Odlyzko's homepage (hhttp://www.dtc.umn.edu/~odlyzko/doc/future.of.factoring.pdf).
- On the Complexity of Computing Discrete Logarithms and Factoring Integers by A.M. Odlyzko (pdf, 9K) from Andrew Odlyzko's homepage (http://www.dtc.umn.edu/~odlyzko/doc/arch/factoring.logs.pdf).
## Other relevant papers- Discrete Logarithms in Finite Fields and their Cryptographic Significance by A.M. Odlyzko (pdf, 212K) from Andrew Odlyzko's homepage (http://www.dtc.umn.edu/~odlyzko/doc/arch/discrete.logs.pdf).
- Selecting Cryptographic Key Sizes by A.K. Lenstra and E. Verheul CitSeer.
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