From 9aa208959d4dba074c7ee6753f5cdbf9f71f74c3 Mon Sep 17 00:00:00 2001 From: Henry de Valence Date: Thu, 5 Apr 2018 14:45:03 -0700 Subject: [PATCH] split into new Ristretto Group section --- docs/ristretto-notes.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/docs/ristretto-notes.md b/docs/ristretto-notes.md index 150cd9a..707c299 100644 --- a/docs/ristretto-notes.md +++ b/docs/ristretto-notes.md @@ -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