diff options
Diffstat (limited to 'Assignment 1')
-rw-r--r-- | Assignment 1/CamilStaps-assignment1-freqs.hs | 39 | ||||
-rw-r--r-- | Assignment 1/CamilStaps-assignment1-shift.hs | 14 | ||||
-rw-r--r-- | Assignment 1/CamilStaps-assignment1.hs | 43 | ||||
-rw-r--r-- | Assignment 1/CamilStaps-assignment1.tex | 110 |
4 files changed, 0 insertions, 206 deletions
diff --git a/Assignment 1/CamilStaps-assignment1-freqs.hs b/Assignment 1/CamilStaps-assignment1-freqs.hs deleted file mode 100644 index 6c6cd47..0000000 --- a/Assignment 1/CamilStaps-assignment1-freqs.hs +++ /dev/null @@ -1,39 +0,0 @@ -import System.Environment -import Data.String.Utils -import qualified Data.List as List - -main = do - args <- getArgs - let input = replace " " "" (head args) - print $ List.reverse $ List.sort $ countfreqs input 1 [] - print $ List.reverse $ List.sort $ countfreqs input 2 [] - print $ List.reverse $ List.sort $ countfreqs input 3 [] - --- countfreqs s n []: calculate occurrence statistics of n-grams in s -countfreqs :: String -> Int -> [Freq] -> [Freq] -countfreqs "" _ fl = fl -countfreqs s n fl - | length s < n = fl - | otherwise = countfreqs (tail s) n (freqsincr fl (take n s) []) - --- freqsincr fl s []: add s to the frequencies in fl -freqsincr :: [Freq] -> String -> [Freq] -> [Freq] -freqsincr [] s fl = fl ++ [Freq { item = s, freq = 1}] -freqsincr (freq:fla) s2 flb - | get_item freq == s2 = fla ++ flb ++ [Freq { item = s2, freq = get_freq freq + 1}] - | otherwise = freqsincr fla s2 (flb ++ [Freq { item = get_item freq, freq = get_freq freq}]) - --- Data type for keeping track of frequencies (Int) of substrings (String) -data Freq = Freq { item :: String, freq :: Int } deriving (Eq) - -get_item :: Freq -> String -get_item = item - -get_freq :: Freq -> Int -get_freq = freq - -instance Ord Freq where - f1 `compare` f2 = get_freq f1 `compare` get_freq f2 - -instance Show Freq where - show f = get_item f ++ " (" ++ show (get_freq f) ++ "x)"
\ No newline at end of file diff --git a/Assignment 1/CamilStaps-assignment1-shift.hs b/Assignment 1/CamilStaps-assignment1-shift.hs deleted file mode 100644 index 35a34e7..0000000 --- a/Assignment 1/CamilStaps-assignment1-shift.hs +++ /dev/null @@ -1,14 +0,0 @@ -import System.Environment -import Data.String.Utils - -main = do - args <- getArgs - let input = replace " " "" (head args) - print $ map (`shiftN` (read $ args!!1)) input - --- shiftN c i: shift c i times forward (i.e. shiftN 'A' 1 == 'B') --- Only for uppercase letters -shiftN :: Char -> Int -> Char -shiftN c 0 = c -shiftN 'Z' i = shiftN 'A' (i-1) -shiftN c i = shiftN (toEnum ((fromEnum c) + 1)) (i-1)
\ No newline at end of file diff --git a/Assignment 1/CamilStaps-assignment1.hs b/Assignment 1/CamilStaps-assignment1.hs deleted file mode 100644 index 6bc6a4c..0000000 --- a/Assignment 1/CamilStaps-assignment1.hs +++ /dev/null @@ -1,43 +0,0 @@ -import System.Environment -import Data.String.Utils -import qualified Data.List as List - -main = do - args <- getArgs - let input = replace " " "" (head args) - putStrLn $ "Running frequency statistics on: " ++ input - print $ List.reverse $ List.sort $ countfreqs input 1 [] - print $ List.reverse $ List.sort $ countfreqs input 2 [] - print $ List.reverse $ List.sort $ countfreqs input 3 [] - print $ map (`shiftN` 18) input - -countfreqs :: String -> Int -> [Freq] -> [Freq] -countfreqs "" _ fl = fl -countfreqs s n fl - | length s < n = fl - | otherwise = countfreqs (tail s) n (freqsincr fl (take n s) []) - -freqsincr :: [Freq] -> String -> [Freq] -> [Freq] -freqsincr [] s fl = fl ++ [Freq { item = s, freq = 1}] -freqsincr (freq:fla) s2 flb - | get_item freq == s2 = fla ++ flb ++ [Freq { item = s2, freq = get_freq freq + 1}] - | otherwise = freqsincr fla s2 (flb ++ [Freq { item = get_item freq, freq = get_freq freq}]) - -data Freq = Freq { item :: String, freq :: Int } deriving (Eq) - -get_item :: Freq -> String -get_item = item - -get_freq :: Freq -> Int -get_freq = freq - -instance Ord Freq where - f1 `compare` f2 = get_freq f1 `compare` get_freq f2 - -instance Show Freq where - show f = get_item f ++ " (" ++ show (get_freq f) ++ "x)" - -shiftN :: Char -> Int -> Char -shiftN c 0 = c -shiftN 'Z' i = shiftN 'A' (i-1) -shiftN c i = shiftN (toEnum ((fromEnum c) + 1)) (i-1)
\ No newline at end of file diff --git a/Assignment 1/CamilStaps-assignment1.tex b/Assignment 1/CamilStaps-assignment1.tex deleted file mode 100644 index 0e0b77d..0000000 --- a/Assignment 1/CamilStaps-assignment1.tex +++ /dev/null @@ -1,110 +0,0 @@ -\documentclass[a4paper]{article} - -\usepackage{a4wide,amsmath,amssymb,url,graphicx,comment,enumerate,color,array,inconsolata,minted,listings} - -\title{Homework $1$} -\author{Camil Staps (s4498062)} - -\newcommand{\R}{\mathbb R} -\newcommand{\Q}{\mathbb Q} -\newcommand{\Z}{\mathbb Z} -\newcommand{\N}{\mathbb N} -\newcommand{\F}{\mathbb F} -\newcommand{\Zstar}{\Z^{^*}} - -\begin{document} -\maketitle - -\section*{Solution} - -\begin{enumerate} -\item \begin{enumerate} - \item This would work: $p_1$ and $p_2$ share $k_1$ and $k_1'$; $p_1$ and $p_3$ share $k_2$ and $k_2'$; and $p_2$ and $p_3$ share also $k_2$ and $k_2'$. Furthermore, none of the executives has two parts of the key ($k_i$ and $k_i'$ for some $i$). - \item $p_2$ and $p_3$ can't compute the key together: together they have only $k_1'$ and $k_2'$, they would need either $k_1$ or $k_2$ in addition to that to be able to compute $k$. Therefore, this is not a suitable solution. - \item $p_1$ can compute $k$ by himself with $k = k_2 \oplus k_2'$, so this is not suitable. - \end{enumerate} - -\item We first compute the one time pad key used, by XOR-ing the ciphertext with the plaintext ``attack by sea''. After that, we XOR the key we found with the plaintext ``attack by air''. Since the first eight bytes of both the plaintext and the key stay the same, we only have to consider the last three bytes. - - \begin{table}[h] - \centering - {\renewcommand{\arraystretch}{1.2} - \begin{tabular}{r | >{\ttfamily}c >{\ttfamily}c >{\ttfamily}c} - Plaintext (8-bit ASCII) & s & e & a \\ - Plaintext (hex) & 73 & 65 & 61 \\\cline{2-4} - Ciphertext (hex) & 2C & F4 & 71 \\\cline{2-4} - Key (XOR of plaintext with ciphertext) & \textbf{5F}& \textbf{91} & \textbf{10} \\\cline{2-4} - New plaintext (8-bit ASCII) & a & i & r \\ - New plaintext (hex) & 61 & 69 & 72 \\\cline{2-4} - New ciphertext (XOR of new plaintext with key) & \textbf{3E} & \textbf{F8} & \textbf{62} - \end{tabular} - } - \end{table} - - The encryption of ``attack by air'' using the same key is thus \texttt{4F 40 20 0D 18 E9 13 33 3E F8 62}. - -\item \begin{enumerate} - \item No, node 25 is a child of node 5, so encrypting with this key will give player 25 access. - \item Yes, this will give players 27 till 30 access. However, 6's parent 2 would give access to player 25 as well. - \item It would be better to use node 1 which gives access to more players whilst not exposing the movie to player 25. - \item Yes, per the reason stated before. - \item Yes, we can't use 26's parent 12 as this would expose the movie to player 25. - \item Yes, we can't use 11's parent 5 per the reason stated at (a), but using this key won't give player 25 access. - \item With node 6 we already cover all players with this key, so this is unnecessary. - \item This key has already been covered with the key in node 1. - \end{enumerate} - - Summarising, we need keys $k_1, k_{11}, k_{26}$ and $k_6$. - -\item We notice that the first eleven letters could correspond to ``Barack Obama'' in plaintext. This gives us: - - \begin{verbatim}BARAC KOBAM A____ ___R_ _A_R_ CA_AM _R_CA __R__ _____\end{verbatim} - - Then we notice we could fit the word ``America(n)'' in, giving: - - \begin{verbatim}BARAC KOBAM AI___ E_IR_ _A_RI CA_AM ERICA __RE_ I_E__\end{verbatim} - - We then realise the plaintext could be ``Barack Obama is the first African American president''. - -\item \begin{enumerate} - \item I wrote a Haskell program which can be found in appendix \ref{App:5a}. The used libraries are used only for basic operations (sorting and reversing lists, replacing substrings in a string) that aren't really part of the main functionality and could be easily written without the libraries. However, this is easier. - - Lines 25 through 37 provide the \texttt{Freq} type which holds a string and an integer, and is used to store the number of occurrences of a substring in a string. - - Lines 13 through 17 provide a method to count $n$-grams occurrences in a string, it returns a list of \texttt{Freq}s. - - Lines 19 through 23 provide a helper method for \texttt{countfreqs} which takes a list of String occurrences and their frequencies, and a String, and increments the frequency of that String in the list by one. - - The \texttt{main} method reads the first command argument, removes spaces and counts and sorts letter, bigram and trigram occurrences in the string. - - \item From the output of the program we find that the trigram \texttt{BPM} occurs the most (7 times) and that the letters \texttt{M}, \texttt{B} and \texttt{P} occur the most as well (respectively 34, 27 and 19 times). From this we guess that \texttt{BPM} could correspond to \texttt{THE} in the plaintext. This would mean a shift of 8. - - We then use the program from appendix \ref{App:5b}, which lets you shift letters in a string. We let it shift $26-8=18$ times, giving: - - \sloppy\texttt{AGOODGLASSINTHEBISHOPSHOSTELINTHEDEVILSSEATTWENTYONEDEGREESANDTHIRTEENMINUTE - SNORTHEASTANDBYNORTHMAINBRANCHSEVENTHLIMBEASTSIDESHOOTFROMTHELEFTEYEOFTHEDEA - THSHEADABEELINEFROMTHETREETHROUGHTHESHOTFIFTYFEETOUT} - - Or: - - \begin{quote}\itshape - A good glass in the bishop's hostel in the devil's seat\\ - twenty-one degrees and thirteen minutes northeast and by north\\ - main branch seventh limb east side shoot from the left eye of the death's-head\\ - a bee line from the tree through the shot fifty feet out.\\ - \par\raggedleft--- \textup{Edgar Allan Poe}, The Gold-Bug - \end{quote} - \end{enumerate} -\end{enumerate} - -\appendix - -\newpage -\section{Sourcecode for assignment 5a} \label{App:5a} -\inputminted[breaklines=true,linenos=true,tabsize=4]{haskell}{CamilStaps-assignment1-freqs.hs} - -\newpage -\section{Sourcecode for assignment 5b} \label{App:5b} -\inputminted[breaklines=true,linenos=true,tabsize=4]{haskell}{CamilStaps-assignment1-shift.hs} - -\end{document} |