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\begin{document}

\centerline{\textbf{HW 12 CMSC 456. Morally DUE Dec 2}}
\centerline{\textbf{THIS HW IS TWO PAGES LONG }}


\begin{enumerate}

\item
(0 points)
What is day/time of final?
{\bf READ MID SOLUTIONS! Even for the problems you got right!!!!!!!!!!!!!!}


\item
(30 points)
Zelda does (3,5) secret sharing. The secret is of length 2, so they use the prime 5.
Zelda gives out the following numbers:

$A_1$ gets 3

$A_2$ gets 3

$A_3$ gets 3

$A_4$ gets 3

$A_5$ gets 3

\begin{enumerate}

\item
(15 points)
$A_1$ and $A_2$ get together. Show that for $c = 0,1,2$,
there is a quadratic polynomial over $\Z_5$ where
ALL of the following hold:
\begin{enumerate}
\item
$f(1)=3$
\item
$f(2)=3$
\item
The constant term is $c$ (which is equivalent to $f(0)=c$).
\end{enumerate}
(NOTE: it's also true for $c=3,4$ but I want to spare you the work. This is important because,
if you did the problem with $c=0,1,2,3,4$ you would show that $A_1$ and $A_2$ have learned
NOTHING since all secrets are still possible.) {\bf Show your work.}

\item
(15 points)
What is the secret? {\bf Show your work.}


\end{enumerate}



\item
(40 points)
Show that there is NO way to do $(t,m)$ Verifiable Secret Sharing in a way that
is information-theoretic secure.

({\it WARNING:} The scheme I showed in class for VSS was comp-secure. This has NO
bearing on our problem. Just because there IS a comp-secure scheme does not mean
that there is not an info-secure scheme. DO NOT MAKE THIS MISTAKE!!!!!!!!)

\centerline{\bf GOTO NEXT PAGE}

\newpage

\item
(30 points) Professor Gasarch is grading this one and actually wants ideas on how to improve the course.
Make your answers short and coherent. You can only get this one wrong if you leave it out
or say something incoherent.
\begin{enumerate}
\item
(10 points) What was your favorite topic in the course? Why?
\item
(10 points) What was your least favorite topic in the course? Why?
\item
(10 points) What is your opinion of the dead cat policy? Why?
\item
(0 points, but answer if you have an answer.) Name something to IMPROVE the course aside from
removing your least favorite topic.)
\end{enumerate}

\end{enumerate}

\end{document}