deletions | additions       diff --git a/section_Some_cryptographic_applications_This__.tex b/section_Some_cryptographic_applications_This__.tex  index 61a93e4..142288a 100644  --- a/section_Some_cryptographic_applications_This__.tex  +++ b/section_Some_cryptographic_applications_This__.tex 
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and does not share with anyone,  \item Bob has received $g^a$ and so he can compute another exponentiation $(g^a)^b$ in $Z_p$, the results being $g^{(ab)}$, that he keeps secret  and does not share with anyone,  \item now Alice and Bob have the same value, $g^{(ab)}$, $g^{ab}$,  and they start using it as a key. \end{itemize}  We %  Thanks to the research in finite fields developed in the last $30$ years, we  observe that, even if the enemies simultaneously collect $p$, $g$, $g^a$ and $g^b$, then they have a negligible probability to reconstruct $g^{ab}$ and so the key remains hidden from them.  The system we have described is still used today a lot, especially on the Internet.