change wording in secp256k1 full torsion

chapters/elliptic-curves-moonmath.tex

@@ -1308,7 +1308,7 @@ \subsection{Full torsion groups}
 $$
 k = \scriptstyle 192986815395526992372618308347813175472927379845817397100860523586360249056 
 $$
-This means that the embedding degree is very large, which implies that the field extension $\F_{p^k}$ is very large too. To understand how big $\F_{p^k}$ is, recall that an element of $\F_{p^m}$ can be represented as a string $<x_0,\ldots,x_m>$ of $m$ elements, each containing a number from the prime field $\F_p$. Now, in the case of \curvename{secp256k1}, such a representation has $k$-many entries, each of them $256$ bits in size. So, without any optimizations, representing such an element would need $k\cdot 256$ bits, which is too much to be representable in the observable universe. It follows that it is not only infeasible to compute the full $r$-torsion group of \curvename{secp256k1}, but moreover to even write down single elements of that group in general. 
+This means that the embedding degree is very large, which implies that the field extension $\F_{p^k}$ is very large too. To understand how big $\F_{p^k}$ is, recall that an element of $\F_{p^m}$ can be represented as a string $<x_0,\ldots,x_m>$ of $m$ elements, each containing a number from the prime field $\F_p$. Now, in the case of \curvename{secp256k1}, such a representation has $k$-many entries, each of them $256$ bits in size. So, without any optimizations, representing such an element would need $k\cdot 256$ bits. It follows that it is not only infeasible to compute the full $r$-torsion group of \curvename{secp256k1}, but moreover to even write down single elements of that group in general. 
 \end{example}
 \begin{exercise} Consider the full $5$-torsion group $TJJ\_13[5]$ from \examplename{} \ref{ex:TJJ13-full-torsion}. Write down the set of all elements from this group and identify the subset of all elements from $TJJ\_13(\F_{13})[5]$ as well as $TJJ\_13(\F_{13^2})[5]$. Then compute the $5$-torsion group $TJJ\_13(\F_{13^{8}})[5]$ .
 \end{exercise}