204 

   204 

   205 Zero-knowledge proof protocols should satisfy:\bigskip

   205 Zero-knowledge proof protocols should satisfy:\bigskip

   206 

   206 

   207 \begin{itemize}

   207 \begin{itemize}

   208 \item \alert{\bf Completeness} If Alice knows the secret, Bob

   208 \item \alert{\bf Completeness} If Alice knows the secret, Bob

   210 \item \alert{\bf Soundness} If Alice does not know the secret,

   210 \item \alert{\bf Soundness} If Alice does not know the secret,

   211       Bob accepts her ``proof'' with a very small probability.

   211       Bob accepts her ``proof'' with a very small probability.

   212 

   212 

   213 \item \alert{\bf Zero-Knowledge} Even if Bob accepts

   213 \item \alert{\bf Zero-Knowledge} Even if Bob accepts

   214       the proof by Alice, he cannot convince anybody else.

   214       the proof by Alice, he cannot convince anybody else.