diff --git a/implementation.tex b/implementation.tex
index ae1be89e7a8dfeb950893f2d294f3a0bf6440b40..e855274b0445e44d97c4fa6386c913939715b0b1 100644
--- a/implementation.tex
+++ b/implementation.tex
@@ -7,8 +7,8 @@ on the Intel \emph{Sandy Bridge} and \emph{Haswell} microarchitectures,
 as well as the ARM \emph{Cortex M4} processor.
 
 The high-level structure of the scalar multiplication is shared among all three implementations. 
-First---before operating on the key $k$---we validate the input point $P$. 
-As mentioned in \Cref{sec:pointvalidation}, we check whether $P$ satisfies $y_P^2 = x_P^3 - 3x_P + 13318$. 
+First---before operating on the key $k$---we validate the input point $P$,
+by checking whether $P$ satisfies $y_P^2 = x_P^3 - 3x_P + 13318$. 
 Because we have not defined any encoding for the neutral element $\mathcal{O}$, 
 this check will implicitly validate that $P \ne \mathcal{O}$.