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\def\handoutdate{August 7, 1998}
\def\handoutname{Problem Session 5}
\def\handoutnumber{11}
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{\Large{\bf Problem Session 5}}
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{\bf Problem 5.1: Secret Sharing with cheaters.}

Dishonest trustees can prevent the reconstruction of the
secret by contributing {\em bad} shares $\hat{s_i} \neq s_i$. 
Using the cryptographic tools you have seen so far in the class show how
to prevent this denial of service attack. 


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{\bf Problem 5.2: Zero--Knowledge proof for discrete logarithms}

Let $p$ be a prime and $g$ a generator modulo $p$. 
Given $y=g^x$ Alice claims she knows the discrete logarithm $x$ of $y$. 
She wants to convince Bob of this fact but she does not want to 
reveal $x$ to him. How can she do that?  (Give a zero-knowledge protocol for
this problem.)

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