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[book] src/design/circuit/gadgets/ecc/var-base-scalar-mul.md: we always do addition (possibly of the zero point) at the end of variable-base scalar mul. 

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
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Daira Hopwood 2021-07-27 01:56:56 +01:00
parent 7895a2a082
commit a6badba32f
1 changed files with 2 additions and 2 deletions
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book/src/design/circuit/gadgets/ecc/var-base-scalar-mul.md
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@ -142,10 +142,10 @@ $\begin{array}{l}
\hspace{1.5em} (x_{A,i-1}, y_{A,i-1}) = \left((x_{A,i}, y_{A,i}) + (x_T, y_T)\right) + (x_{A,i}, y_{A,i})
\end{array}$
If the least significant bit is set $\mathbf{k_0} = 1,$ we return the accumulator $A$. Else, if $\mathbf{k_0} = 0,$ we return $A - T$ (also using complete addition).
If the least significant bit $\mathbf{k_0} = 1,$ we set $B = \mathcal{O},$ otherwise we set ${B = -T}$. Then we return ${A + B}$ using complete addition.
Let $B = \begin{cases}
(0, 0), &\text{ if } \mathbf{k_0} = 1,\\
(0, 0), &\text{ if } \mathbf{k_0} = 1, \\
(x_T, -y_T), &\text{ otherwise.}
\end{cases}$