425 \begin{enumerate}

   425 \begin{enumerate}

   426 \item For each \bl{$b_i$} Bob checks whether \bl{$s_i$} conforms to the protocol

   426 \item For each \bl{$b_i$} Bob checks whether \bl{$s_i$} conforms to the protocol

   427 

   427 

   428 \begin{center}

   428 \begin{center}

   429 \begin{tabular}{ll}

   429 \begin{tabular}{ll}

   431 \bl{$b_i = 1$}: & \bl{$A^{s_i}  \equiv h_i * h_j^{-1}  \;mod\; p$}\\

   431 \bl{$b_i = 1$}: & \bl{$A^{s_i}  \equiv h_i * h_j^{-1}  \;mod\; p$}\\

   432 \end{tabular}

   432 \end{tabular}

   433 \end{center}\bigskip

   433 \end{center}\bigskip

   434 

   434 

   435 Bob was sent

   435 Bob was sent

   436 

   436 

   437 \begin{center}

   437 \begin{center}

   439 \end{center}

   439 \end{center}

   440 

   440 

   441 where the corresponding bits were 

   441 where the corresponding bits were 

   442 \bl{$1$}; Bob does not know \bl{$r_j$}, he does not know any \bl{$r_i$} where the bit was \bl{$1$}

   442 \bl{$1$}; Bob does not know \bl{$r_j$}, he does not know any \bl{$r_i$} where the bit was \bl{$1$}

   443 \end{enumerate}

   443 \end{enumerate}

   463 \bl{$A^{s_{z+1}} \equiv B * h_j^{-1} \;mod \; p$}

   463 \bl{$A^{s_{z+1}} \equiv B * h_j^{-1} \;mod \; p$}

   464 \end{center}

   464 \end{center}

   465 \end{enumerate}\bigskip\pause

   465 \end{enumerate}\bigskip\pause

   466 

   466 

   467 In order to cheat, Alice has to guess all bits in advance. She

   467 In order to cheat, Alice has to guess all bits in advance. She

   469 

   469 

   470 \small\hspace{7mm}

   470 \small\hspace{7mm}

   471 \textcolor{gray}{(explanation $\rightarrow$ \url{http://goo.gl/irL9GK})}

   471 \textcolor{gray}{(explanation $\rightarrow$ \url{http://goo.gl/irL9GK})}

   472 

   472 

   473 \end{frame}

   473 \end{frame}