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clarify wording

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Henry de Valence 2018-04-04 11:29:36 -07:00
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6
docs/ristretto-notes.md
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@ -1,7 +1,7 @@
Below are some notes on Ristretto, which are not an authoritative
writeup and which may have errors. See also the [Decaf
paper][decaf_paper], the [libdecaf
implementation][ristretto_libdecaf], and the [Sage
implementation of Ristretto][ristretto_libdecaf], and its [Sage
script][ristretto_sage].
Decaf constructs a prime-order group from a cofactor-\\(4\\) Edwards
@ -22,19 +22,17 @@ see the [Decaf paper][decaf_paper] or
[_Jacobi Quartic Curves Revisited_][hwcd_jacobi] by Hisil, Wong,
Carter, and Dawson).
When \\(e = a\^2\\), \\(\mathcal J\_{e,A}\\) has full
When \\(e = a\^2\\) is a square, \\(\mathcal J\_{e,A}\\) has full
\\(2\\)-torsion (i.e., \\(\mathcal J[2] \cong \mathbb Z /2 \times
\mathbb Z/2\\)), and
we can write the \\(\mathcal J[2]\\)-coset of a point \\(P =
(s,t)\\) as
$$
P + \mathcal J[2] = \left\\{
(s,t),
(-s,-t),
(1/as, -t/as\^2),
(-1/as, t/as\^2)
\right\\}.
$$
Notice that replacing \\(a\\) by \\(-a\\) just swaps the last two