Paper 2015/1027
Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case
Taechan Kim and Razvan Barbulescu
Abstract
We introduce a new variant of the number field sieve algorithm for discrete logarithms in $\mathbb{F}_{p^n}$ called exTNFS. The most important modification is done in the polynomial selection step, which determines the cost of the whole algorithm: if one knows how to select good polynomials to tackle discrete logarithms in $\mathbb{F}_{p^\kappa}$, exTNFS allows to use this method when tackling $\mathbb{F}_{p^{\eta\kappa}}$ whenever $\gcd(\eta,\kappa)=1$. This simple fact has consequences on the asymptotic complexity of NFS in the medium prime case, where the complexity is reduced from $L_Q(1/3,\sqrt[3]{96/9})$ to $L_Q(1/3,\sqrt[3]{48/9})$, $Q=p^n$, respectively from $L_Q(1/3,2.15)$ to $L_Q(1/3,1.71)$ if multiple number fields are used. On the practical side, exTNFS can be used when $n=6$ and $n=12$ and this requires to updating the keysizes used for the associated pairingbased cryptosystems.
Note: This is a merged version of two consecutive papers, eprint 2015/1027 and eprint 2015/1076.
Metadata
 Available format(s)
 Publication info
 A minor revision of an IACR publication in Crypto 2016
 Keywords
 Discrete Logarithm ProblemNumber Field SieveFinite FieldsCryptanalysis
 Contact author(s)
 yoshiki1 @ snu ac kr
 History
 20160603: last of 2 revisions
 20151026: received
 See all versions
 Short URL
 https://ia.cr/2015/1027
 License

CC BY
BibTeX
@misc{cryptoeprint:2015/1027, author = {Taechan Kim and Razvan Barbulescu}, title = {Extended Tower Number Field Sieve: A New Complexity for the Medium Prime Case}, howpublished = {Cryptology ePrint Archive, Paper 2015/1027}, year = {2015}, note = {\url{https://eprint.iacr.org/2015/1027}}, url = {https://eprint.iacr.org/2015/1027} }