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.
Aurore Guillevic.
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.

Pairing Implementation

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.

the RELIC
library (in C++) of Diego Aranha and C.P.L Gouvea

These two above libraries are the fastest ones as far as I
know. Please feel free to contact me if you have better suggestions.
Here is another one I heard about:

If you prefer a more user-friendly version, here are other implementations.

the PARI/GP has a Tate pairing implementation.
PARI is known to be fast, but maybe
it is not optimized specifically for pairings.

Magma comes
with an implementation of Tate pairings, Weil pairings, and Ate
parings.
Magma is a non-free software but maybe your
university or institute has a license for it.

I don't know about SageMath but there should be a pairing
implementation coming with it, maybe this is the PARI-GP one.