Polynomial Selection for NFS-DL in non-prime finite fields
I contribute to the polynomial selection for large characteristic
non-prime fields. For the moment, the polynomial selection for
quadratic extensions of large prime fields with the Conjugation method
is available. The polynomial selection for cubic, quartic and sextic
fields is under development, at the state of a magma prototype.
Individual Discrete Logarithms in non-prime finite fields
The code of the paper
2015. Computing Individual Discrete Logarithms Faster
in GF(p^n) with the NFS-DL algorithm.
Asiacrypt 2015, Auckland, New Zealand, November
29-December 3, 2015, LNCS, to appear. HAL:01157378
is also under development, at a Magma stage for the moment. A C/C++
cado-nfs version might be planed for 2016.
I am usually contacted by researchers who would like to use the source
code I developed in my thesis, to compare the efficiency of pairings
over prime order groups and over composite-order groups. This
comparison was discussed in the paper
Comparing the Pairing Efficiency over
Composite-Order and Prime-Order Elliptic Curves. Aurore
Guillevic. ACNS 2013, Banff, Alberta, Canada, LNCS 7954,
pp. 357-372. eprint 2013:218
and for a more recent version,
see the section 3.3 of my thesis available here.
Unfortunately for confidentiality reasons the source code is not
available but here are alternative libraries to efficiently compute pairings
over elliptic curves.
library (in C++) of Diego Aranha and C.P.L Gouvea