\relax 
\@writefile{toc}{\contentsline {chapter}{\numberline {2}Public-key Cryptography}{33}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{ch:crypto}{{2}{33}}
\@writefile{toc}{\contentsline {section}{\numberline {2.1}Diffie-Hellman Key Exchange}{33}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.1}Public-key Cryptography}{33}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.2}The Diffie-Hellman Key Exchange Protocol}{33}}
\@writefile{toc}{\contentsline {subsubsection}{Some Quotes}{34}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.3}Let's try it!}{35}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.4}The Discrete Logarithm Problem}{36}}
\@writefile{toc}{\contentsline {subsubsection}{The State of the Art}{37}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.5}Realistic Example}{37}}
\@writefile{toc}{\contentsline {section}{\numberline {2.2}The RSA Cryptosystem}{38}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.1}How RSA works}{38}}
\@writefile{toc}{\contentsline {subsubsection}{One-way Functions}{38}}
\@writefile{toc}{\contentsline {subsubsection}{How Nikita Makes an RSA Public Key}{39}}
\@writefile{toc}{\contentsline {subsubsection}{Sending Nikita an Encrypted Message}{39}}
\@writefile{toc}{\contentsline {subsubsection}{How Nikita Decrypts a Message}{40}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.2}Encoding a Phrase in a Number}{40}}
\newlabel{sec:encode}{{2.2.2}{40}}
\@writefile{toc}{\contentsline {subsubsection}{How Many Letters Can a Number ``Hold''?}{40}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.3}Examples}{40}}
\@writefile{toc}{\contentsline {subsubsection}{A Small Example}{40}}
\@writefile{toc}{\contentsline {subsubsection}{A Bigger Example in PARI}{41}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.4}A Connection Between Breaking RSA and Factoring Integers}{43}}
\@writefile{toc}{\contentsline {section}{\numberline {2.3}Attacking RSA}{43}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.1}Factoring $n$ Given $\varphi (n)$}{44}}
\newlabel{sec:phin}{{2.3.1}{44}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.2}When\nobreakspace  {}$p$ and\nobreakspace  {}$q$ Are Close}{44}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.3}Factoring\nobreakspace  {}$n$ Given\nobreakspace  {}$d$}{45}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.4}RSA Challenge $n$}{47}}
\newlabel{ex:crypto1}{{1}{47}}
\newlabel{ex:crypto2}{{2}{47}}
\newlabel{ex:crypto3}{{3}{48}}
\newlabel{ex:crypto4}{{4}{48}}
\newlabel{ex:crypto5}{{5}{48}}
\newlabel{ex:crypto6}{{6}{48}}
\newlabel{ex:crypto7}{{7}{48}}
\newlabel{ex:crypto8}{{8}{48}}
\newlabel{ex:crypto9}{{9}{49}}
\@setckpt{chapters/crypto}{
\setcounter{page}{50}
\setcounter{equation}{0}
\setcounter{enumi}{9}
\setcounter{enumii}{2}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{2}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{2}
\setcounter{section}{3}
\setcounter{subsection}{4}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{0}
\setcounter{table}{0}
\setcounter{parentequation}{0}
\setcounter{theorem}{4}
}
