From d971b1b2d83c5c24f2d1ec247bd75a2e32979703 Mon Sep 17 00:00:00 2001 From: "Andreas M. Antonopoulos" Date: Fri, 6 Sep 2013 18:11:48 -0700 Subject: [PATCH] equations --- ch01.asciidoc | 14 ++++++++++++++ 1 file changed, 14 insertions(+) diff --git a/ch01.asciidoc b/ch01.asciidoc index 90174985..3660d245 100644 --- a/ch01.asciidoc +++ b/ch01.asciidoc @@ -22,6 +22,20 @@ To use public key cryptography, Alice will ask Bob for his public key. Then, Ali Elliptic Curve Cryptography is a type of assymetric or public-key cryptography based on the discrete logarithm problem as expressed by multiplication on the the points of an elliptic curve over a finite prime field. +[latexmath] +++++ +\begin{equation} +{K = G \bigotimes k} +\end{equation} +++++ + +[latexmath] +++++ +\begin{equation} +{y^2 \mod p = (x^3 + 7) \mod p} +\end{equation} +++++ + In elliptic curve cryptography, a predetermined _generator_ point on an elliptic curve is multiplied by a _private key_, which is simply a 256-bit number, to produce another point somewhere else on the curve, which is the corresponding public key. In most implementations, the private and public keys are stored together as a _key pair_. However, it is trivial to re-produce the public key if one has the private key, so storing only the private key is also possible.