\section{Elliptic Curve Cryptography}
Elliptic Curve Cryptogaphy (simply called ECC from now on) is a branch of
cryptography that emerged in the mid-80ties. Like RSA and Diffie-Hellman
it's security is based on the discrete logarithm problem
\footnote{url{http://www.mccurley.org/papers/dlog.pdf}}
\footnote{url{http://en.wikipedia.org/wiki/Discrete_logarithm}}
\footnote{url{http://mathworld.wolfram.com/EllipticCurve.html}}.
Finding the descrete logarithm of an elliptic curve from it's public base
point is thought to be infeaseble. This is known as the Elliptic Curve Descrete
Logarithm Problem (ECDLP). ECC and the underlying mechanisms are not easy
to understand - luckily there have been some great introductions on the topic lately
\footnote{url{http://arstechnica.com/security/2013/10/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography}}
\footnote{url{https://www.imperialviolet.org/2010/12/04/ecc.html}}.
ECC provides for much stronger security with less computonally expensive
operations in comparison to traditional PKI algorithms. (See the section
on keylenghts to get an idea)
The security of ECC relies on the elliptic curves and curve points chosen
as parameters for the algorithm in question. Even before the NSA-leak scandal
there has been a lot of discussion regarding these parameters. A part of the
discussion involved recommended sets of curves and curve points chosen by
different standardization bodies such as NIST. Those parameters came under
question from various cryptographers
\footnote{url{http://cr.yp.to/talks/2013.09.16/slides-djb-20130916-a4.pdf}}
\footnote{url{https://www.schneier.com/blog/archives/2013/09/the_nsa_is_brea.html#c1675929}}
\footnote{url{crypto.stackexchange.com/questions/10263/should-we-trust-the-nist-recommended-ecc-parameters}}.
At the time of writing there is ongoing research as to the security of
various ECC parameters
\footnote{url{safecurves.cr.yp.to}}.
The authors of this paper include configurations and recommendations
with and without ECC - the reader may choose to adopt those settings
as he finds best suited to his environment. The authors will not make
this decision for the reader.
A word of warning: One should get familiar with ECC, different curves and
parameters if one chooses to adopt ECC configurations. Since there is much
discussion on the security of ECC, flawed settings might compromise the
security of the entire system. %% find better wording for last paragraph!
%% mention different attacks on ECC besides flawed parameters!