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\centerline{\textbf{HW 11 CMSC 456. Hard Deadline Dec 14.}} 
\centerline{\textbf{VERY IMPORTANT: NO DEAD-CAT EXTENSIONS}}


\begin{enumerate}

\item
(25 points. This requires material from the THIRD packet of slides on secret sharing.)

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


\newpage

\item
(25 points. This requires material from the SECOND packet of slides on secret sharing.) 

Zelda has a secret $s$. She wants to share it with $A_1,A_2,A_3,A_4$ such that

If $A_1$ and $A_2$ and $A_3$ (or any superset) get together they can learn the secret.

If $A_1$ and $A_4$ (or any superset) get together they can learn the secret.

If $A_2$ and $A_4$ (or any superset) get together they can learn the secret.

If $A_3$ and $A_4$ (or any superset) get together they can learn the secret.

NO OTHER set of people who get together can learn anything about the secret. (For Example, $A_1,A_3$
cannot learn anything about the secret.) 

and NOW for the question:
\begin{enumerate}
\item 
(15 points) 
EXPLAIN an info-theoretic secret sharing scheme Zelda can use. Specify:
(1) What Zelda gives to each person, and (2) What each group does to  obtain the secret.
\item
(10 points) 
Let $|s|$ be the length of the secret. 
ROUGHLY how many bits does each $A_i$ get? Your answer should be of the form
$f(|s|) + O(1)$. 
\end{enumerate}






\vfill\eject 
\item 
(30 points. This problem just needs the FIRST packet of Secret Sharing Slides.) 

Zelda is doing info-theoretic $(2,5)$ secret sharing with $A_1,A_2,A_3,A_4,A_5$. 
The secret is 10000000 (in binary).
She will use the polynomial method. 

\begin{enumerate}

\item
(10 points) 
What is the least prime $p$ such that she can do this over mod $p$?


\item
(10 points). Let $p$ be the prime you picked in the last problem.
If Zelda used the prime just below $p$ why is this bad? 


\item 
(10 points) 
Explain the polynomial Secret Sharing Method and point out WHERE 
the fact that $p$ is a prime is used. 

\end{enumerate}

\vfill\eject

\item 
(20 points) The following questions concern the guest lecture by ``Daniel Apon'' from ``NIST''
\begin{enumerate}
\item
(10 points) State something interesting and NON-technical that you learned in 
``Daniel Apon's'' guest lecture. 

\item
(10 points) State something interesting and technical that you learned in 
``Daniel Apon's'' guest lecture. 
\end{enumerate}


\vfill\eject

\item
(0 points but plesae do it to help me out for the next time I teach this course.)
\begin{enumerate}
\item 
What was our favorite part of the course? Why?
\item
What was your least favorite part of the course? Why? 
\end{enumerate}





\end{enumerate}

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