From 7a5915ab094767dfa17fcc839b77e8cd7603d782 Mon Sep 17 00:00:00 2001 From: Daira Hopwood Date: Sat, 30 Jan 2021 02:49:40 +0000 Subject: [PATCH] Apply some suggestions from code review Co-authored-by: str4d --- book/src/background/curves.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/book/src/background/curves.md b/book/src/background/curves.md index d9ff3fc..3412a8e 100644 --- a/book/src/background/curves.md +++ b/book/src/background/curves.md @@ -2,7 +2,7 @@ Elliptic curves constructed over finite fields are another important cryptographic tool. -We use elliptic curves because they provide a cryptographic [group](fields.md#Inverses_and_groups), +We use elliptic curves because they provide a cryptographic [group](fields.md#Groups), i.e. a group in which the [discrete logarithm problem](fields#) is hard. There are several ways to define the curve equation, but for our purposes, let @@ -34,7 +34,7 @@ known as the discrete log of $H$ with respect to $G$, is considered computationa infeasible with classical computers. This is called the elliptic curve discrete log assumption. -If an elliptic curve group $\mathbb{G}$ has prime order $q$ (like the ones used in Halo), +If an elliptic curve group $\mathbb{G}$ has prime order $q$ (like the ones used in Halo 2), then it is a finite cyclic group. Recall from the section on [groups](fields.md#Groups) that this implies it is isomorphic to $\mathbb{Z}/q\mathbb{Z}$, or equivalently, to the scalar field $\mathbb{F}_q$. Each possible generator $G$ fixes the isomorphism; then