NFS@Home is interested in the continued development of open source, publicly available tools for large integer factorization. Over the past couple of years, the capability of open source tools, in particular the lattice sieve of the GGNFS suite and the program msieve, have dramatically improved.

Integer factorization is interesting 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 used. As recently demonstrated by factoring the Texas Instruments calculator keys, these are no longer secure.

NFS@Home BOINC project makes it easy for the public to participate in

**state-of-the-art factorizations**. The project interests is to see how far we can push the envelope and perhaps become competitive with the larger university projects running on clusters, and perhaps even collaborating on a really large factorization.

The numbers are chosen from the Cunningham project. The project is named after Allan Joseph Champneys Cunningham, who published the first version of the factor tables together with Herbert J. Woodall in 1925. This project is one of the oldest continuously ongoing projects in computational number theory, and is currently maintained by Sam Wagstaff at Purdue University. The third edition of the book, published by the American Mathematical Society in 2002, is available as a free download. All results obtained since the publication of the third edition are available on the Cunningham project website.

Concerning target size there are four sievers applications available (http://escatter11.fullerton.edu/nfs/pre ... project:):

lasieved - app for RSALS subproject, uses less than 0.5 GB memory: yes or no

lasievee - work nearly always available, uses up to 0.5 GB memory: yes or no

lasievef - used for huge factorizations, uses up to 1 GB memory: yes or no

lasieve5f - used for huge factorizations, uses up to 1 GB memory: yes or no

**How's the credit distributed per target wu?**

lasieved - 36

lasievee - 44

lasievef - dead

lasieve5f - 130

**Why the difference in credits?**

The more valuable calculation gets more credit. Especially for 16e (lasievef+lasieve5f), the extra credit also awards for the large memory usage.

**What project uses what application?**

lasieved - Oddperfect, n^n+(n+1)^(n+1), Fibonacci, Lucas, Cunningham, Cullen and Woodall for SNFS difficulty below 250.

lasievee - Cunningham, Oddperfect or other for SNFS difficulty above 250 to ~280.

lasievef - dead

lasieve5f - push the state of art for very difficulty factorizations, above SNFS difficulty of 280

The limits depends upon the boundaries chosen for the poly and characteristics of the number being factored. It's advanced math related.

For a (much) more technical description of the NFS, see the Wikipedia article or Briggs' Master's thesis.