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Merge bitcoin-core/secp256k1#1363: doc: minor ellswift.md updates
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c7d900f doc: minor ellswift.md updates (stratospher)

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Tree-SHA512: 161c17d038eb1eed9f5811c3eb92975a821a5274e7f69aa386bfbe5376b3f06f3d0d2887ea3310efbec83424f09ea8e4082e8c02b2fcad3b915625ce5c2007d2
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real-or-random committed Jul 6, 2023
2 parents afd7eb4 + c7d900f commit c9ebca9
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4 changes: 2 additions & 2 deletions doc/ellswift.md
Original file line number Diff line number Diff line change
Expand Up @@ -88,7 +88,7 @@ $$
\begin{array}{lcl}
X(u, t) & = & \left\\{\begin{array}{ll}
\dfrac{g(u) - t^2}{2t} & a = 0 \\
\dfrac{g(u) + h(u)(Y_0(u) + X_0(u)t)^2}{X_0(u)(1 + h(u)t^2)} & a \neq 0
\dfrac{g(u) + h(u)(Y_0(u) - X_0(u)t)^2}{X_0(u)(1 + h(u)t^2)} & a \neq 0
\end{array}\right. \\
Y(u, t) & = & \left\\{\begin{array}{ll}
\dfrac{X(u, t) + t}{u \sqrt{-3}} = \dfrac{g(u) + t^2}{2tu\sqrt{-3}} & a = 0 \\
Expand Down Expand Up @@ -329,7 +329,7 @@ $t$ value for multiple $c$ inputs (thereby biasing that encoding):
it requires $g(u)=0$ which is already outlawed on even-ordered curves and impossible on others; in the second it would trigger division by zero.
* Curve-specific special cases also exist that need to be rejected, because they result in $(u,t)$ which is invalid to the decoder, or because of division by zero in the encoder:
* For $a=0$ curves, when $u=0$ or when $t=0$. The latter can only be reached by the encoder when $g(u)=0$, which requires an even-ordered curve.
* For $a \neq 0$ curves, when $X_0(u)=0$, when $h(u)t^2 = -1$, or when $2w(u + 2v) = 2X_0(u)$ while also either $w \neq 2Y_0(u)$ or $h(u)=0$.
* For $a \neq 0$ curves, when $X_0(u)=0$, when $h(u)t^2 = -1$, or when $w(u + 2v) = 2X_0(u)$ while also either $w \neq 2Y_0(u)$ or $h(u)=0$.

**Define** a version of $G_{c,u}(x)$ which deals with all these cases:
* If $a=0$ and $u=0$, return $\bot.$
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