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20
crypto.bib
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@@ -25,3 +25,23 @@
url = "https://en.wikipedia.org/w/index.php?title=Confusion_and_diffusion&oldid=1307746165", url = "https://en.wikipedia.org/w/index.php?title=Confusion_and_diffusion&oldid=1307746165",
note = "[Online; accessed 3-February-2026]" note = "[Online; accessed 3-February-2026]"
} }
@ARTICLE{diffiehellman,
author={Diffie, W. and Hellman, M.},
journal={IEEE Transactions on Information Theory},
title={New directions in cryptography},
year={1976},
volume={22},
number={6},
pages={644-654},
keywords={Cryptography;Receivers;Authentication;Eavesdropping;Costs;Business;Public key cryptography},
doi={10.1109/TIT.1976.1055638}}
@article{rsa,
title={A method for obtaining digital signatures and public-key cryptosystems},
author={Rivest, Ronald L and Shamir, Adi and Adleman, Leonard},
journal={Communications of the ACM},
volume={21},
number={2},
pages={120--126},
year={1978},
publisher={ACM New York, NY, USA}
}

28
crypto.tex
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@@ -110,9 +110,9 @@ Early encryptions intuitively demonstrate two concepts that can be employed to e
\paragraph{Substitution} is used by \paragraph{Substitution} is used by
the simple Caesar cipher, often achieved by rotating two disks against each other, each with the alphabet written out on them. the simple Caesar cipher, often achieved by rotating two disks against each other, each with the alphabet written out on them.
\autoref{tab-caesar} shows a simple caesar cipher where the cipher alphabet is simply shifted by 3 positions from the plaintext alphabet. \autoref{tab:caesar} shows a simple caesar cipher where the cipher alphabet is simply shifted by $+3$ positions from the plaintext alphabet.
In the process of encoding, A is therefore replaced (substituted) with D, B with E, and so on. In the process of encoding, A is therefore replaced (substituted) with D, B with E, and so on.
Upon reception of the message, the same process is done in reverse. Upon reception of the message, the same process is done in reverse, i.e. shifted by $-3$.
\begin{table}[h] \begin{table}[h]
\resizebox{\textwidth}{!}{% \resizebox{\textwidth}{!}{%
@@ -124,15 +124,24 @@ Upon reception of the message, the same process is done in reverse.
\end{tabular}% \end{tabular}%
} }
\caption{A simple substitution cipher demonstrated by a 3-letter shift.} \caption{A simple substitution cipher demonstrated by a 3-letter shift.}
\label{tab-caesar} \label{tab:caesar}
\end{table} \end{table}
This simple encryption is easy to break however for several reasons.
Caesar ciphers in general only offer 26 different keys as further shifts only wrap around to $29 \mod 26 = 3$, with a shift of 26
being equal to the cleartext. \newline
Furter, by shifting every letter by the same amount,
the properties of the source language such as word spacing and letter frequencies are retained in the ciphertext,
leaving it vulnerable to simple attacks.
\paragraph{Transposition}
\paragraph{Transposition} is the process of reordering the plaintext to obtain a ciphertext.
Here, the key can be understood as instructions on how to re-order the ciphertext to obtain the original message.
The \textit{scytale} is one of the earliest implementations of a transposition cipher.
\paragraph{Confusion and Diffusion} \cite{enwiki:confusion-diffusion} \paragraph{Confusion and Diffusion} \cite{enwiki:confusion-diffusion}
\section{DES} \section{DES}\label{sec:des}
The \acrfull{DES} is a symmetric (or private-key) cipher developed in the 1970s at IBM as an archetypal block cipher. The \acrfull{DES} is a symmetric (or private-key) cipher developed in the 1970s at IBM as an archetypal block cipher.
It takes in a block of 64 bits and transforms it to a ciphertext using a key of equal length. It takes in a block of 64 bits and transforms it to a ciphertext using a key of equal length.
Despite suspicions of backdoors engineered into the algorithm due to the involvement of the NSA in the development of \acrshort{DES}, Despite suspicions of backdoors engineered into the algorithm due to the involvement of the NSA in the development of \acrshort{DES},
@@ -145,12 +154,15 @@ The \acrfull{AES} superseded \acrshort{DES} in 2001 after an official selection
Unlike its predecessor, it does not use a Feistel network. Unlike its predecessor, it does not use a Feistel network.
\section{RSA} \section{RSA}
\acrfull{RSA} is an asymmetric (or public-key) cryptographic algorithm used for encryption and digital signing. \acrfull{RSA} is the first asymmetric (or public-key) cryptographic algorithm and can thus be used for encryption and digital signing.
It was named after its eponymous inventors in 1977 after trying to disprove the Diffie-Hellman key exchange. It was named after its eponymous inventors in \citeyear{rsa} after trying to disprove the existence of \textit{trapdoor functions},
a concept introduced by \citeauthor{diffiehellman} in their appropriately named pivotal paper \citetitle{diffiehellman}.
The algorithm they came up with relies on modular arithmetic, which remains the most popular class of asymmetric cryptography. The algorithm they came up with relies on modular arithmetic, which remains the most popular class of asymmetric cryptography.
\begin{enumerate} \begin{enumerate}
\item Choose and randomly and stochastically independet primes $p,q$ of similar size so that \item Choose randomly and stochastically independet primes $p,q$ of similar size so that
$0.1 < | \log_2 p - \log_2 q | < 30 $. $0.1 < | \log_2 p - \log_2 q | < 30 $.
\item Calculate $ N= p \cdot q $ \item Calculate $ N= p \cdot q $
\item Compute Euler's totient function of $ \varphi (N) = (p-1) \cdot (q-1)$ which is kept secret. \item Compute Euler's totient function of $ \varphi (N) = (p-1) \cdot (q-1)$ which is kept secret.