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Co-authored-by: str4d <thestr4d@gmail.com>
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book/src/background/curves.md
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@ -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