NFS@Home uses volunteer computing to factor large composite numbers using the General Number Field Sieve (GNFS) — the asymptotically fastest known algorithm for factoring integers with more than about 110 digits. Integer factorization is one of the central computational problems in number theory, and its difficulty is the foundation of widely deployed public-key cryptographic systems including RSA.
The factoring process in NFS@Home consists of two main phases. The sieving phase (which is distributed to volunteers) searches for pairs of integers that satisfy specific algebraic relations, building up a large matrix of relations. This is the most computationally intensive part and is ideally suited to volunteer computing because each work unit is independent. The linear algebra phase (done centrally on large-memory servers) then uses these relations to find a non-trivial factorization of the target number.
Based at California State University, Fullerton and led by Professor Greg Childers, the project advances several lines of mathematical research. It contributes to the Cunningham Project — a systematic effort since 1925 to factor numbers of the form bn ± 1 for small bases b — and also factors numbers from the Aliquot sequences and other tables maintained by the computational number theory community. Each completed factorization either fills a gap in mathematical tables or provides new data for conjectures about the distribution and properties of prime factors.
Beyond pure mathematics, NFS@Home provides empirical benchmarks for the state of the art in integer factorization, directly informing recommendations for cryptographic key sizes. As factoring algorithms and computing power improve, the minimum safe key length for RSA and similar systems must increase accordingly — making NFS@Home's work relevant to the practical security of internet communications.