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Apply suggestions from code review
Co-authored-by: Daira Hopwood <daira@jacaranda.org>
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@ -11,7 +11,8 @@ Formulae:
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Substituting for $\lambda$, we get the constraints:
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- $(x_r + x_q + x_p) \cdot (x_p - x_q)^2 - (y_p - y_q)^2 = 0$
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- Note that this constraint is unsatisfiable for $P + (-P)$, and so cannot be used with arbitrary inputs.
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- Note that this constraint is unsatisfiable for $P \;⸭\; (-P)$ (when $P \neq \mathcal{O}$),
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and so cannot be used with arbitrary inputs.
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- $(y_r + y_q)(x_p - x_q) - (y_p - y_q)(x_q - x_r) = 0$
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@ -76,3 +77,8 @@ A \cdot \left(2y_p \cdot \lambda - 3{x_p}^2\right) &=& 0 & A \wedge y_p \neq 0 &
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$
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Max degree: $4$
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Note: It is the cross-interaction of the two $B$ constraints that fully constrain
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the implications. For example, the contrapositive of the first constraint's implication
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$x_p = 0 \implies B$ is $¬B \implies x_p \neq 0$, which is the other half of the
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second constraint's implication. The same applies to $C$.
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@ -67,4 +67,5 @@ $$
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Then compute $P = [m] \mathcal{V}$, and conditionally negate $P$ using $(x, y) \mapsto (x, s \cdot y)$.
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We can reuse the window table from full-width fixed-base scalar multiplication, but with only $\mathsf{ceil}(64 / 3) = 22$ windows.
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We compute the window table in a similar way to full-width fixed-base scalar multiplication,
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but with only $\mathsf{ceil}(64 / 3) = 22$ windows.
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