update

crypto.bib

@@ -24,4 +24,24 @@
   year = "2025",
   url = "https://en.wikipedia.org/w/index.php?title=Confusion_and_diffusion&oldid=1307746165",
   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}
+}

crypto.tex

@@ -110,9 +110,9 @@ Early encryptions intuitively demonstrate two concepts that can be employed to e
 
 \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.
-\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.
-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]
 \resizebox{\textwidth}{!}{%
@@ -124,15 +124,24 @@ Upon reception of the message, the same process is done in reverse.
 \end{tabular}%
 }
 \caption{A simple substitution cipher demonstrated by a 3-letter shift.}
-\label{tab-caesar}
+\label{tab:caesar}
 \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}
 
-\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.
 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},
@@ -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.
 
 \section{RSA}
-\acrfull{RSA} is an asymmetric (or public-key) cryptographic algorithm used for encryption and digital signing.
-It was named after its eponymous inventors in 1977 after trying to disprove the Diffie-Hellman key exchange.
+\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 \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.
 
 \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 $.
     \item Calculate $ N= p \cdot q $
     \item Compute Euler's totient function of $ \varphi (N) = (p-1) \cdot (q-1)$ which is kept secret.