104 lines
5.3 KiB
TeX
104 lines
5.3 KiB
TeX
\documentclass{article}
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\usepackage[utf8x]{inputenc}
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\usepackage[margin=1in]{geometry} % Adjust margins
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\usepackage{caption}
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\usepackage{wrapfig}
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\usepackage{subcaption}
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\usepackage{parskip} % dont indent after paragraphs, figures
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\usepackage{xcolor}
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%\usepackage{csquotes} % Recommended for biblatex
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\usepackage{tikz}
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\usepackage{pgfplots}
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\usetikzlibrary{positioning}
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\usepackage{float}
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\usepackage{amsmath}
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\PassOptionsToPackage{hyphens}{url}
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\usepackage{hyperref} % allows urls to follow line breaks of text
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\usepackage[style=ieee, backend=biber, maxnames=1, minnames=1]{biblatex}
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\addbibresource{crypto.bib}
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\usepackage{glossaries}
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\makeglossaries
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\newacronym{DES}{DES}{Data Encryption Standard}
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\newacronym{AES}{AES}{Advanced Encryption Standard}
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\newacronym{RSA}{RSA}{Rivest–Shamir–Adleman Encryption}
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\title{Cryptography}
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\author{Erik Neller}
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\date{\today}
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\begin{document}
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\maketitle
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\section{Introduction}
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Cryptography is ubiquitous in our modern world.
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While the origins of cryptography date back thousands of years, evidence of its use in ancient is sparse.
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\cite{luenberger}
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Most of its use seemed to be reserved for political and military leaders, e.g. notably Mary Queen of Scots,
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who while in prison, plotted to kill Queen Elizabeth using encrypted letters \cite{enwiki:maryofscots}.
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With the widespread adoption of the internet, the need for several cryptographical functions arose.
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Due to its intended original use as a trusted research network (ARPANET),
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almost none of the original protocols were 'secure' in any sense of the word.
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Most notably still today is SMTP, the \textit{Simple Mail Transfer Protocol}, used to send email to servers.
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In its original implementation, it allowed attackers to intercept emails in transit to read and modify them
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and even spoof the sender address to impersonate others.
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SMTP today is secured using a combination of mitigations for these attacks, such as STARTTLS, SPF, DKIM and DMARC,
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emphasizing the need for securely designed protocols.
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\subsection{Security}
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Common goals associated with security include the \textit{CIA triad}, consisting of
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\begin{itemize}
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\item Confidentiality: Prevent unauthorized reading
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\item Integrity: Prevent unauthorized modification
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\item Availability: Prevent denial of service
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\end{itemize}
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With further goals including Authenticity and Non-repudiation. Cryptography can help with all of the aforementioned goals
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except availability.
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This can be achieved using several different applications of cryptography:
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\begin{itemize}
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\item Encryption provides confidentiality by only saving / transmitting an encrypted message.
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\item Hash functions ensure data has not been altered.
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\item Digital signatures confirm a message was indeed sent by who we expect it to be, preventing man-in-the-middle attacks
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where the message is simply swapped out before reaching its destination, as well as providing proof a message was sent (Non-repudiation).
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\item Certificates confirm the sender's identity.
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\end{itemize}
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Importantly, Kerckhoff's principle \cite{enwiki:kerckhoff} is what allows us to go into detail on the following algorithms.
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Embraced by researchers today, it holds that the security of a cryptosystem should only rely on the secrecy of the key,
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allowing and encouraging the publication of cryptographic algorithms. \newline
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It is closely related to Shannon's maxim, stating that
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"one ought to design systems under the assumption that the enemy will immediately gain full familiarity with them".
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This is opposed to \textit{security through obscurity}, which doesnt allow for verification of the cryptographic
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algorithm through a scientific process in the public domain.
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\subsection{Hash Functions}
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A general hash function $h(m)$ is a function that takes a message $m$ of arbitrary and produces an output $h$ called \textit{hash}
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of fixed length. However, not every mathematical function can be considered a hash function.
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The main applications of hash functions include integrity checking and hash maps for efficient data retrieval.
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Depending on the applications, different properties determine the usefulness of a function.
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An obvious desired property is efficiency - every application benefits from faster computing times.
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Also central to all applications of hash functions is a property called \textit{collision resistance}, where there should be no
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efficient way, i.e. no better way than brute force to find $m_1 \neq m_2$ so that $h(m_1) = h(m_2)$.
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Again, for encryption the importance is clear. If a password is stored in hashed form to obfuscate the clear text,
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no security is gained if it is easy for an attacker to find a password that produces the same hash and thus passes the challenge.
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A similar notion holds true for data retrieval. If it is too easy to find collisions, e.g. similar inputs produce similar outputs,
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there will be an uneven distribution in the target domain and thus little to no efficiency gain.
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Another desired property, specifically for encryption is what is usually used synonymously with a hash function: a \textit{one-way function}.
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Given $h(m)$, there should be no method more efficient than brute force to find a matching $m$.
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\subsection{Encryption}
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\section{DES}
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The \acrfull{DES} is a symmetric cipher developed in the 1970s at IBM
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\section{AES}
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\section{RSA}
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\clearpage
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%\printglossary[type=\acronymtype]
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%\printglossary
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\printbibliography
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\end{document}
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