From 9adda9f5746440212fbe4d7b378942fdbf0ad98e Mon Sep 17 00:00:00 2001 From: Aaron Zauner Date: Thu, 14 Nov 2013 01:25:06 +0100 Subject: [PATCH] changed wording a bit --- src/ECC.tex | 27 ++++++++++++++++----------- 1 file changed, 16 insertions(+), 11 deletions(-) diff --git a/src/ECC.tex b/src/ECC.tex index d1b6c69..e0dda98 100644 --- a/src/ECC.tex +++ b/src/ECC.tex @@ -1,28 +1,32 @@ \section{A note on 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 +cryptography that emerged in the mid-1980ties. 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 +Logarithm Problem (ECDLP). ECC and the underlying mathematical foundation 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}}. +\footnote{\url{https://www.imperialviolet.org/2010/12/04/ecc.html}} +\footnote{\url{http://www.isg.rhul.ac.uk/~sdg/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 +as parameters for the algorithm in question. Well before the NSA-leak scandal +there has been a lot of discussion regarding these parameters and their +potential subversion. A part of the discussion involved recommended sets +of curves and curve points chosen by different standardization bodies such +as the National Institute of Standards and Technology (NIST) +\footnote{\url{http://www.nist.gov}}. +Those parameters came under question repeatedly from the 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{http://crypto.stackexchange.com/questions/10263/should-we-trust-the-nist-recommended-ecc-parameters}}. @@ -34,10 +38,11 @@ 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 + +\textbf{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! +discussion on the security of ECC, flawed settings might very well compromise the +security of the entire system! %% mention different attacks on ECC besides flawed parameters! -- 2.11.0