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split into new Ristretto Group section

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Henry de Valence 2018-04-05 14:45:03 -07:00
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docs/ristretto-notes.md
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@ -80,10 +80,14 @@ $$
These are the only points with \\(xy = 0\\); the points with
\\( y \neq 0 \\) are \\(2\\)-torsion.
# The Ristretto Group
We consider two cases:
* cofactor \\(4\\), where \\( \\# \mathcal E(\mathbb F_p) = 4\cdot \ell \\);
* cofactor \\(8\\) with cyclic \\(8\\)-torsion, where \\( \\# \mathcal E(\mathbb F_p) = 8 \cdot \ell \\) and \\( \mathcal E[8] \cong \mathbb Z / 8 \\).
* cofactor \\(8\\) with cyclic \\(8\\)-torsion,
where \\( \\# \mathcal E(\mathbb F_p) = 8 \cdot \ell \\)
and \\( \mathcal E[8] \cong \mathbb Z / 8 \\).
In the cofactor \\(4\\) case, we have \\( \[2\](\mathcal E[4]) =
\mathcal E[2] \\), so that \\( \mathcal E[2] \subseteq \[2\](\mathcal