A survey on the number field sieve (Q2707574)

The author gives a summary and status report on the Number Field Sieve. Its estimated time is accepted to be \(L(1/3,v)\) with emphasis on estimating \(v\) (currently \((92+26 \sqrt{(13/27)})^{(1/3)})\), [see \textit{D. Coppersmith}, J. Cryptology 6, 169-180 (1993; Zbl 0806.11071)]. Artistry is required in the choice of polynomial. Significant illustrations are between 100 and 200 digits [see \textit{A. K. Lenstra} and \textit{H. W. Lenstra} jun. (eds)., The development of the number field sieve, Lect. Notes Math. 1554, Springer-Verlag (1993; Zbl 0777.00017)].NEWLINENEWLINEFor the entire collection see [Zbl 0932.00040].