<!-- wp:pagelayer/pl_text {"text":"u003ctable cellpadding=u00228u0022 cellspacing=u00224u0022 style=u0022padding: 4px; margin: 2px; color: rgb(0, 0, 0); font-family: Verdana, Arial, u0026quot;Sans Serifu0026quot;; font-size: 13px;u0022u003eu003ctbodyu003eu003ctru003eu003ctd rowspan=u00222u0022 valign=u0022topu0022 width=u002240%u0022 style=u0022vertical-align: top; padding: 4px;u0022u003eu003ch2 style=u0022font-size: 1.2em; margin-top: 0px;u0022u003eAbout NFS@Homeu003c/h2u003eu003cbru003eu003cspan style=u0022color: rgb(216, 216, 216);u0022u003eNFS@Home is a research project that uses Internet-connected computers to do the lattice sieving step in the Number Field Sieve factorization of large integers. As a young school student, you gained your first experience at breaking an integer into prime factors, such as 15 = 3 * 5 or 35 = 5 * 7. NFS@Home is a continuation of that experience, only with integers that are hundreds of digits long. Most recent large factorizations have been done primarily by large clusters at universities. With NFS@Home you can participate in state-of-the-art factorizations simply by downloading and running a free program on your computer.u003cbru003eu003cbru003eu003c/spanu003eu003cpu003eInteger factorization is interesting from both mathematical and practical perspectives. Mathematically, for instance, the calculation of u003ca href=u0022http://en.wikipedia.org/wiki/Multiplicative_functionu0022 style=u0022text-decoration-line: none; color: rgb(0, 105, 161);u0022u003emultiplicative functionsu003c/au003e in number theory for a particular number require the factors of the number. Likewise, the integer factorization of particular numbers can aid in the proof that an associated number is prime. Practically, many public key algorithms, including the u003ca href=u0022http://en.wikipedia.org/wiki/RSAu0022 style=u0022text-decoration-line: none; color: rgb(0, 105, 161);u0022u003eRSA algorithmu003c/au003e, rely on the fact that the publicly available modulus cannot be factored. If it is factored, the private key can be easily calculated. Until quite recently, RSA-512, which uses a 512-bit modulus (155 digits), was commonly used but can now be easily broken.u003c/pu003eu003cpu003eThe numbers what we are factoring are chosen from the u003ca href=u0022http://homes.cerias.purdue.edu/~ssw/cun/index.htmlu0022 style=u0022text-decoration-line: none; color: rgb(0, 105, 161);u0022u003eCunningham projectu003c/au003e. Started in 1925, it is one of the oldest continuously ongoing projects in computational number theory. The third edition of the book, published by the American Mathematical Society in 2002, is available as a u003ca href=u0022http://www.ams.org/online_bks/conm22/u0022 style=u0022text-decoration-line: none; color: rgb(0, 105, 161);u0022u003efree downloadu003c/au003e. All results obtained since, including those of NFS@Home, are available on the Cunningham project website.u003c/pu003eu003cpu003eNFS@Home is hosted at u003ca href=u0022http://www.fullerton.edu/u0022 style=u0022text-decoration-line: none; color: rgb(0, 105, 161);u0022u003eCalifornia State University Fullertonu003c/au003e, and is supported in part by the u003ca href=u0022http://www.nsf.gov/u0022 style=u0022text-decoration-line: none; color: rgb(0, 105, 161);u0022u003eNational Science Foundationu003c/au003e through u003ca href=u0022https://www.xsede.org/u0022 style=u0022text-decoration-line: none; color: rgb(0, 105, 161);u0022u003eXSEDEu003c/au003e resources provided by the u003ca href=u0022http://www.tacc.utexas.edu/u0022 style=u0022text-decoration-line: none; color: rgb(0, 105, 161);u0022u003eTexas Advanced Computing Centeru003c/au003e, the u003ca href=u0022http://www.sdsc.edu/u0022 style=u0022text-decoration-line: none; color: rgb(0, 105, 161);u0022u003eSan Diego Supercomputer Centeru003c/au003e, the u003ca href=u0022http://www.ncsa.illinois.edu/u0022 style=u0022text-decoration-line: none; color: rgb(0, 105, 161);u0022u003eNational Center for Supercomputing Applicationsu003c/au003e, and u003ca href=u0022http://www.rcac.purdue.edu/u0022 style=u0022text-decoration-line: none; color: rgb(0, 105, 161);u0022u003ePurdue Universityu003c/au003e under grant number TG-DMS100027.u003c/pu003eu003c/tdu003eu003c/tru003eu003c/tbodyu003eu003c/tableu003e","pagelayer-id":"hdl8393"} -->

About NFS@Home NFS@Home is a research project that uses Internet-connected computers to do the lattice sieving step in the Number Field Sieve factorization of large integers. As a young school student, you gained your first experience at breaking an integer into prime factors, such as 15 = 3 * 5 or 35 = 5 * 7. NFS@Home is a continuation of that experience, only with integers that are hundreds of digits long. Most recent large factorizations have been done primarily by large clusters at universities. With NFS@Home you can participate in state-of-the-art factorizations simply by downloading and running a free program on your computer. Integer factorization is interesting from both mathematical and practical perspectives. Mathematically, for instance, the calculation of multiplicative functions in number theory for a particular number require the factors of the number. Likewise, the integer factorization of particular numbers can aid in the proof that an associated number is prime. Practically, many public key algorithms, including the RSA algorithm, rely on the fact that the publicly available modulus cannot be factored. If it is factored, the private key can be easily calculated. Until quite recently, RSA-512, which uses a 512-bit modulus (155 digits), was commonly used but can now be easily broken. The numbers what we are factoring are chosen from the Cunningham project. Started in 1925, it is one of the oldest continuously ongoing projects in computational number theory. The third edition of the book, published by the American Mathematical Society in 2002, is available as a free download. All results obtained since, including those of NFS@Home, are available on the Cunningham project website. NFS@Home is hosted at California State University Fullerton, and is supported in part by the National Science Foundation through XSEDE resources provided by the Texas Advanced Computing Center, the San Diego Supercomputer Center, the National Center for Supercomputing Applications, and Purdue University under grant number TG-DMS100027.

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