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author | Camil Staps | 2016-02-12 15:01:00 +0100 |
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committer | Camil Staps | 2016-02-12 15:01:00 +0100 |
commit | efd533331d6a7f0c51ef857af448a6c84c3084ed (patch) | |
tree | 7f28f4e20a215784f27643ad49029332204528b2 /Assignment 3 | |
parent | Makefile (diff) |
Removed spaces in path
Diffstat (limited to 'Assignment 3')
-rwxr-xr-x | Assignment 3/2des-demo.py | 74 | ||||
-rw-r--r-- | Assignment 3/CamilStaps-assignment3.tex | 219 | ||||
-rw-r--r-- | Assignment 3/LICENSE | 1 | ||||
-rw-r--r-- | Assignment 3/Readme.md | 103 | ||||
-rwxr-xr-x | Assignment 3/break.py | 141 | ||||
-rwxr-xr-x | Assignment 3/des-demo.py | 62 | ||||
-rwxr-xr-x | Assignment 3/des-test.sh | 22 | ||||
-rwxr-xr-x | Assignment 3/nthkey.py | 37 |
8 files changed, 0 insertions, 659 deletions
diff --git a/Assignment 3/2des-demo.py b/Assignment 3/2des-demo.py deleted file mode 100755 index b5b7247..0000000 --- a/Assignment 3/2des-demo.py +++ /dev/null @@ -1,74 +0,0 @@ -#!/usr/bin/python -import sys, getopt, binascii, random -from Crypto.Cipher import DES - -# From http://stackoverflow.com/a/843846/1544337 -# 1 for odd parity, 0 for even parity -# Was used only in a previous version of nthByte -# def parity(b): -# c = 0 -# while b != 0: -# c += 1 -# b &= b - 1 -# return c % 2 - -# Find the nth possibility for a byte with odd parity -oddBytes = [1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,50,52,55,56,59,61,62,64,67,69,70,73,74,76,79,81,82,84,87,88,91,93,94,97,98,100,103,104,107,109,110,112,115,117,118,121,122,124,127,128,131,133,134,137,138,140,143,145,146,148,151,152,155,157,158,161,162,164,167,168,171,173,174,176,179,181,182,185,186,188,191,193,194,196,199,200,203,205,206,208,211,213,214,217,218,220,223,224,227,229,230,233,234,236,239,241,242,244,247,248,251,253,254] -def nthByte(n): - return oddBytes[n] - # c = -1 # This is the old version. The new version uses a faster lookup table. - # b = 0 - # while c != n: - # b += 1 - # if parity(b) == 1: - # c += 1 - # return b - -# Find the nth key in which all bytes have odd parity -def nthKey(n): - key = '' - for b in range(7,-1,-1): - key += chr(nthByte((n >> b*7) & 0x7f)) - return key - -def main(argv): - l = 24 - - # Parse arguments. Use -h for help. - try: - opts, args = getopt.getopt(argv, "hl:") - except getopt.GetoptError: - usage() - sys.exit(2) - - for opt, arg in opts: - if opt == '-h': - usage() - sys.exit() - elif opt == '-l': - l = int(arg) - - # generate two keys - r = random.SystemRandom() - k1 = nthKey(r.randint(0, pow(2, l) - 1)) - k2 = nthKey(r.randint(0, pow(2, l) - 1)) - - print 'k_1: %s' % binascii.b2a_hex(k1) - print 'k_2: %s' % binascii.b2a_hex(k2) - - round1 = DES.new(k1, DES.MODE_ECB) - round2 = DES.new(k2, DES.MODE_ECB) - - # Some random plaintext - ciphertext pairs to verify the working of this code - print 'plaintext : ciphertext' - for n in range(0,10): - pt = '{:016x}'.format(r.randint(0, pow(2, 64) -1)) - ct = round2.encrypt(round1.encrypt(binascii.a2b_hex(pt))) - print pt + ' : ' + binascii.b2a_hex(ct) - -def usage(): - print 'Usage: 2des-demo.py [-l <keylength>]' - print ' keylength : pick keys from the first 2^l keys (default: 24)' - -if __name__ == "__main__": - main(sys.argv[1:])
\ No newline at end of file diff --git a/Assignment 3/CamilStaps-assignment3.tex b/Assignment 3/CamilStaps-assignment3.tex deleted file mode 100644 index da7d433..0000000 --- a/Assignment 3/CamilStaps-assignment3.tex +++ /dev/null @@ -1,219 +0,0 @@ -\documentclass[a4paper]{article} - -\usepackage{amsmath,amssymb,amsthm,url,graphicx,comment,enumerate,color,array,inconsolata,minted,subcaption,adjustbox} -\usepackage[margin=2cm]{geometry} - -\title{Homework $3$} -\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^{^*}} - -\DeclareMathOperator{\ord}{ord} -\DeclareMathOperator{\lcm}{lcm} -\DeclareMathOperator{\lsb}{lsb} -\DeclareMathOperator{\Prob}{Pr} -\DeclareMathOperator{\Adv}{Adv} - -\DeclareMathAlphabet{\pazocal}{OMS}{zplm}{m}{n} - -\usepackage{tikz} -\usetikzlibrary{shapes.multipart,shapes.gates.logic.IEC,shapes.arrows,positioning,decorations.markings} - -\begin{document} -\maketitle - -\section*{Solution} - -\begin{enumerate} -\item - \begin{enumerate} - \item - \begin{enumerate} - \item - \begin{minipage}[t]{\linewidth} - \centering - \adjustbox{valign=t}{% - \begin{tikzpicture}[LFSR/.style={rectangle split, rectangle split horizontal=true, rectangle split parts=#1, draw, anchor=center}, ARROW/.style={draw,thick,single arrow,single arrow head extend=3pt,transform shape}]] - \node[LFSR=5] (register) {\nodepart{one}$s_4$\nodepart{two}$s_3$\nodepart{three}$s_2$\nodepart{four}$s_1$\nodepart{five}$s_0$}; - \node[circle, inner sep=0, below=6mm of register.one south] (xor) {\scalebox{1}{$\oplus$}}; - \draw[->] (register.one south) -- (xor); - \draw[->] (register.two south) |- (xor); - \draw (register.three south) |- (xor); - \draw (register.five south) |- (xor); - \draw (xor.west) -- ++(left:4mm) node[anchor=north] (hook1) {}; - \draw[->] (hook1) |- (register.one west); - \draw[->] (register.five east) -- ++(right:4mm) node[anchor=west] {$\dots$}; - \end{tikzpicture} - } - \end{minipage} - - \item - $$M = \begin{pmatrix} - 0 & 1 & 0 & 0 & 0 \\ - 0 & 0 & 1 & 0 & 0 \\ - 0 & 0 & 0 & 1 & 0 \\ - 0 & 0 & 0 & 0 & 1 \\ - 1 & 0 & 1 & 1 & 1 - \end{pmatrix}$$ - - \item - That bit stream contains $0^L$. We know that $0 \oplus \dots \oplus 0 = 0$, so after $0^L$, only zeros can follow. However, this is not the case. Therefore, this bit stream cannot be a part of the output of this LFSR. - - \item - % In figure \ref{fig:1ai} we see that $c_L=1$. We then check if $C(X)$ is an irreducible polynomial. Since $C(X)=\dots+1$ and $\deg(C(X))=5$, we only need to consider products of two polynomials $f_1,f_2$ for which $\deg(f_1)+\deg(f_2)=5$ and both polynomials have a term $1$. We then check all possible combinations: - - % \begin{table}[h] - % \centering - % \begin{tabular}{>{$}l<{$} >{$}l<{$} | >{$}l<{$}} - % f_1(x) & f_2(x) & (f_1 \circ f_2)(x) = (f_2 \circ f_1)(x) \\\hline - % x^4 + x^3 + x^2 + x + 1 & x + 1 & x^5 + 1 \\ - % x^4 + x^3 + x^2 + 1 & x + 1 & x^5 + x^2 + x + 1 \\ - % x^4 + x^3 + x + 1 & x + 1 & x^5 + x^3 + x^2 + 1 \\ - % x^4 + x^3 + 1 & x + 1 & x^5 + x^3 + x + 1\\ - % x^4 + x^2 + x + 1 & x + 1 & x^5 + x^4 + x^3 + 1\\ - % x^4 + x^2 + 1 & x + 1 & x^5 + x^4 + x^3 + x^2 + x + 1\\ - % x^4 + x + 1 & x + 1 & x^5 + x^4 + x^2 + 1\\ - % x^4 + 1 & x + 1 & x^5 + x^4 + x + 1\\ - - % x^3 + x^2 + x + 1 & x^2 + x + 1 & x^5 + x^3 + x^2 + 1\\ - % x^3 + x^2 + x + 1 & x^2 + 1 & x^5 + x^4 + x + 1\\ - % x^3 + x^2 + 1 & x^2 + x + 1 & x^5 + x + 1\\ - % x^3 + x^2 + 1 & x^2 + 1 & x^5 + x^4 + x^3 + x + 1\\ - % x^3 + x + 1 & x^2 + x + 1 & x^5 + x^4 + 1\\ - % x^3 + x + 1 & x^2 + 1 & x^5 + x^2 + x + 1\\ - % x^3 + 1 & x^2 + x + 1 & x^5 + x^4 + x^3 + x^2 + x + 1\\ - % x^3 + 1 & x^2 + 1 & x^5 + x^3 + x^2 + 1\\ - % \end{tabular} - % \end{table} - - % Since $C(X)$ does not appear in the rightmost column of this table, it is an irreducible polynomial. - - In the figure above we see that $c_L=1$. Using sage, we find that $C(X)$ is a primitive polynomial: - - \begin{minted}[tabsize=0]{python} - sage: Z2P.<x> = GF(2)[] - sage: (x^5+x^3+x^2+x+1).is_primitive() - True - \end{minted} - - The period of this LFSR is then $2^L-1=31$. - - \item - We construct the states using matrix multiplication. As an example we show $M\cdot s_1$: - $$M\cdot s_1 = \begin{pmatrix}0 & 1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 1 \\1 & 0 & 1 & 1 & 1\end{pmatrix} \cdot \begin{pmatrix}0 \\ 0 \\ 0 \\ 0 \\ 1\end{pmatrix} = \begin{pmatrix}0 \\ 0 \\ 0 \\ 1 \\ 1\end{pmatrix} = s_3$$ - We can then continue with $M\cdot s_3$. Using that method, we find the state sequence $s_1$, $s_3$, $s_6$, $s_{12}$, $s_{25}$, $s_{18}$, $s_4$, $s_9$, $s_{19}$, $s_7$, $s_{15}$, $s_{31}$, $s_{30}$, $s_{29}$, $s_{27}$, $s_{23}$, $s_{14}$, $s_{28}$, $s_{24}$, $s_{17}$, $s_2$, $s_5$, $s_{10}$, $s_{21}$, $s_{11}$, $s_{22}$, $s_{13}$, $s_{26}$, $s_{20}$, $s_8$, $s_{16}$, $s_1$, which indeed contains $31$ different states (all states except $s_0$). - \end{enumerate} - - \item - We know with sage that these two polynomials are primitive: - - \begin{minted}[tabsize=0]{python} - sage: (x^3+x+1).is_primitive() - True - sage: (x^5+x^2+1).is_primitive() - True - \end{minted} - - Therefore, the two LFSRs have period $2^L-1$, that is, $7$ for $\text{LFSR}^f$ and $31$ for $\text{LFSR}^g$. Of course, there is also the obvious period $1$ for both LFSRs if we start with $s_0$. - - Combining this we find the periods illustrated in table \ref{tab:1b}. - - \begin{table} - \setlength\extrarowheight{2pt} - \centering - \begin{tabular}{l | l | l | l | l} - Period $\text{LFSR}^f$ & Initial state (e.g.) & Period $\text{LFSR}^g$ & Initial state (e.g.) & Combined period \\\hline - $1$ & \texttt{000} & $1$ & \texttt{00000} & $2^{1\cdot1}-1=1$ \\ - $1$ & \texttt{000} & $31$ & \texttt{00001} & $2^{1\cdot31}-1=2^{31}-1$ \\ - $7$ & \texttt{001} & $1$ & \texttt{00000} & $2^{7\cdot1}-1=2^7-1$ \\ - $7$ & \texttt{001} & $31$ & \texttt{00001} & $2^{7\cdot31}-1=2^{217}-1$ \\ - \end{tabular} - \caption{} - \label{tab:1b} - \end{table} - \end{enumerate} - -\item - \begin{proof} - Given a certain ciphertext $c$ we define the set $M_c$ as the set with all plaintexts that could give $c$ using some key and this cipher: - $$M_c \stackrel{\text{def}}{=} \{m\in\pazocal{M} \mid \exists_{k\in\pazocal{K}}[E(k,m) = c]\}$$ - For all $k\in\pazocal{K}, c\in\pazocal{C}$ we have $D(k,c) = c-k\pmod{256} \in \{0,\dots,255\} = \pazocal{M}$. Therefore, for any $c\in\pazocal{C}$, we have $|M_c| = |\pazocal{K}| = |\pazocal{M}|$, meaning that given a certain ciphertext, any plaintext in $\pazocal{M}$ could be the plaintext corresponding to that ciphertext. Hence, seeing the ciphertext does not give us information about the plaintext, or: - $$\forall_{m\in\pazocal{M},c\in\pazocal{C}}\left[\Prob(m = m' \mid c) = \Prob(m = m')\right].$$ - Therefore, this cipher has perfect secrecy. - \end{proof} - -\item - \begin{enumerate} - \item - $L_2 = R_1 = L_0 \oplus F(k_1,R_0)$ and $R_2 = L_1 \oplus F(k_2,R_1) = R_0 \oplus F(k_2, L_0 \oplus F(k_1, R_0))$. - \item - We are only interested in the left parts of the encryptions, which we shall denote as $L_{2,0}$ and $L_{2,1}$ for the left parts of the could-be encryptions of $m_0$ and $m_1$, respectively. Following the equations found in the last exercise, we have $L_{2,0} = 1^{32} \oplus F(k_1,1^{32}) = \overline{F(k_1,1^{32})}$ and $L_{2,1} = 0^{32} \oplus F(k_1,1^{32}) = F(k_1,1^{32})$. Therefore, in case $F_2$ was used, we have $L_{2,0} = \overline{L_{2,1}}$. For a random permutation this happening has the very small chance of $\frac1{2^{64}}$. - - If an adversary thus checks whether $L_{2,0} \stackrel?= \overline{L_{2,1}}$ and finds out it's true, he has a non-negligible advantage with which he can assume $F_2$ was used. In case this equation does \emph{not} hold, he has a non-negligible advantage with which he can assume a random permutation was used. - \end{enumerate} - -\item - \begin{enumerate} - \item - One key has an effective length of $56$ bits. With two keys we have an effective keylength of $2\cdot56=112$ bits. This gives $|\pazocal{K}| = 2^{112}$. The amount of encryptions we have to perform for exhaustive key search is then $2^{112-1}$. - \item - $D^{2DES}(k_1||k_2, c) = D^{DES}(k_1, D^{DES}(k_2, c))$. - \item - \begin{proof} - \begin{align*} - m &= D^{DES}(k_1, D^{DES}(k_2, c)) \\ - E^{DES}(k_1, m) &= E^{DES}(k_1, D^{DES}(k_1, D^{DES}(k_2, c))) \\ - &\qquad\text{(Encryption and decryption with $k_1$ cancel out)} \\ - E^{DES}(k_1, m) &= D^{DES}(k_2, c) - \end{align*} - \end{proof} - \item - $A = 2^{56}$ since the keylength of one DES key is $56$. A ciphertext block encrypted with DES is $64$ bits long. Without overhead we have then $B=64\cdot2^{56}$. - - We have a block length of $64$ and a key length of $56$. If we compute the encryptions of some plaintext using all possible keys, and the decryptions of some ciphertext using all possible keys, we have two lists of $2^{56}$ 64-bit candidates for a middle point in 2DES. Following the birthday paradox, the probability two values from the two lists are the same is high enough to reasonably expect false alarms\footnote{See \url{http://en.wikipedia.org/wiki/Birthday_problem#Probability_table}}. - \item - See the python files for the answers to exercise i through iv. See \texttt{Readme.md} for explanation and usage information. - - I found the keypair $k_1=\mathtt{0101010101164613}, k_2=\mathtt{0101010102a719c2}$ using: - - \begin{verbatim} - $ ./break.py -p 0123456789ABCDEF -c e0ac28c346fb8de5 -l 24 - Making dictionary (p:0123456789abcdef;l:24)... 417.513822s - Finding matches... 419.125502s - Key generation: 102.954099s - Decryption: 269.473773s - Matching dictionary: 15.134741s - k1: 0101010101164613; k2: 0101010102a719c2 - \end{verbatim} - - This was done on a Lenovo U410, i7-3517U @ 1.9GHz with 8GB RAM and 16GB /swap. It takes about seven minutes to create the dictionary, and again seven minutes to try all keys for the second key and find matches. On lilo, this takes a bit less than five minutes each. - - With $l=24$ we're likely to find only one possible keypair since the chance on false alarms is much lower. For higher $l$, in particular $l=56$, the chance on false alarms is much higher, meaning that the first keypair is most likely \emph{not} the actual keypair. More plaintext-ciphertext pairs can then help to find the right keypair. We do that in this case only for verification: - - \begin{verbatim} - $ ./break.py -p 1122334455667788 -c 49e4857e94f9655d -l 24 - Making dictionary (p:1122334455667788;l:24)... 386.554364s - Finding matches... 424.907323s - Key generation: 106.151418s - Decryption: 271.449573s - Matching dictionary: 15.2167599999s - k1: 0101010101164613; k2: 0101010102a719c2 - $ ./break.py -p 99aabbccddeeff00 -c b5a2eefb51b04401 -l 24 - Making dictionary (p:99aabbccddeeff00;l:24)... 394.505993s - Finding matches... 431.637707s - Key generation: 109.764972s - Decryption: 274.681545s - Matching dictionary: 14.4759990001s - k1: 0101010101164613; k2: 0101010102a719c2 - \end{verbatim} - - An adversary uses a method like \texttt{nthKey} instead of trying all $2^{64}$ possible 64-bit strings since some of the bits are parity bits. If he would try all $2^{64}$ possible 64-bit strings, he would waste time and storage on trying keys that aren't valid anyway. - \end{enumerate} -\end{enumerate} - -\end{document} diff --git a/Assignment 3/LICENSE b/Assignment 3/LICENSE deleted file mode 100644 index 7de325f..0000000 --- a/Assignment 3/LICENSE +++ /dev/null @@ -1 +0,0 @@ -Copyright (c) 2015 Camil Staps <info@camilstaps.nl>
\ No newline at end of file diff --git a/Assignment 3/Readme.md b/Assignment 3/Readme.md deleted file mode 100644 index c7ac538..0000000 --- a/Assignment 3/Readme.md +++ /dev/null @@ -1,103 +0,0 @@ -# Breaking DES with Python -Solutions to the third homework assignment for the NWI-IBC023 Cryptography course, spring 2015, Radboud University Nijmegen. - -See the LICENSE file for the license & copyright information. - -## Dependencies -Python 2.7.6 (other versions may work) with libraries: Crypto, sys, getopt, os.path, binascii, random, time - -## Files - -### des-demo.py (exercise i) -Encrypt or decrypt a specified message using a specified key with DES. See `des-demo.py -h` for usage. - -### des-test.sh -Test des-demo.py using the test vectors from the assignment. - -### nthkey.py (exercise ii) -Demonstration of the working of the `nthKey(n)` method. No command line parameters, edit the number on the last line for another `n`. - -### 2des-demo.py (exercise iii) -2DES using two random keys: chooses two random keys with the right parity using `nthKey(n)`, then performs 2DES on ten random plaintexts using those keys. See `2des-demo.py -h` for usage. - -### break.py (exercise iv) -Breaking 2DES using a known-plaintext attack. Supply at least a plaintext (`-p`) and a ciphertext (`-c`), possibly also a keylength (`-l`). There is an option to save the dictionary to a file (`-s`) if you're planning to reuse it. - -There is detailed timing information for the second stage of the attack: the time used by `nthKey()`, `DES.decrypt()` and finding values in the dictionary. - -Example: - - $ ./break.py -p 6be6065663da8d2c -c 4d0ed7812caeee83 -l 16 - Making dictionary (p:6be6065663da8d2c;l:16)... 1.429026s - Finding matches... 1.618808s - Key generation: 0.403714s - Decryption: 1.048049s - Matching dictionary: 0.046321s - k1: 0101010101011afb; k2: 0101010101012073 - -## Concrete break -I was given the following plaintext-ciphertext pairs: - - 0123456789ABCDEF e0ac28c346fb8de5 - 1122334455667788 49e4857e94f9655d - 99aabbccddeeff00 b5a2eefb51b04401 - -Breaking these (on the Lenovo described under Benchmarks): - - $ ./break.py -p 0123456789ABCDEF -c e0ac28c346fb8de5 -l 24 - Making dictionary (p:0123456789abcdef;l:24)... 417.513822s - Finding matches... 419.125502s - Key generation: 102.954099s - Decryption: 269.473773s - Matching dictionary: 15.134741s - k1: 0101010101164613; k2: 0101010102a719c2 - $ ./break.py -p 1122334455667788 -c 49e4857e94f9655d -l 24 - Making dictionary (p:1122334455667788;l:24)... 386.554364s - Finding matches... 424.907323s - Key generation: 106.151418s - Decryption: 271.449573s - Matching dictionary: 15.2167599999s - k1: 0101010101164613; k2: 0101010102a719c2 - $ ./break.py -p 99aabbccddeeff00 -c b5a2eefb51b04401 -l 24 - Making dictionary (p:99aabbccddeeff00;l:24)... 394.505993s - Finding matches... 431.637707s - Key generation: 109.764972s - Decryption: 274.681545s - Matching dictionary: 14.4759990001s - k1: 0101010101164613; k2: 0101010102a719c2 - -We find k1 = `0101010101164613`; k2 = `0101010102a719c2`. - -## Benchmarks - -### Lenovo U410, i7-3517U @ 1.9GHz, 8GB RAM, 16GB /swap, Ubuntu 14.04 -Creating dictionary: 417.5s, 386.5s, 394.5s (**avg: 399.5s**) -Finding matches: 419.1s, 424.9s, 431.6s (**avg: 425.2s**) - -The exact log is in the Concrete Break section above. - -### Lilo -Creating dictionary: 286.8s, 283.6s, 273.0s (**avg: 281.1s**) -Finding matches: 301.6s, 285.6s, 292.2s (**avg: 293.1s**) - - $ ./break.py -p 0123456789ABCDEF -c e0ac28c346fb8de5 -l 24 - Making dictionary (p:0123456789abcdef;l:24)... 286.83s - Finding matches... 301.56s - Key generation: 64.47s - Decryption: 200.23s - Matching dictionary: 9.27s - k1: 0101010101164613; k2: 0101010102a719c2 - $ ./break.py -p 1122334455667788 -c 49e4857e94f9655d -l 24 - Making dictionary (p:1122334455667788;l:24)... 283.55s - Finding matches... 285.63s - Key generation: 60.66s - Decryption: 189.44s - Matching dictionary: 9.27s - k1: 0101010101164613; k2: 0101010102a719c2 - $ ./break.py -p 99aabbccddeeff00 -c b5a2eefb51b04401 -l 24 - Making dictionary (p:99aabbccddeeff00;l:24)... 272.96s - Finding matches... 292.21s - Key generation: 63.89s - Decryption: 191.04s - Matching dictionary: 9.41s - k1: 0101010101164613; k2: 0101010102a719c2
\ No newline at end of file diff --git a/Assignment 3/break.py b/Assignment 3/break.py deleted file mode 100755 index 7666d33..0000000 --- a/Assignment 3/break.py +++ /dev/null @@ -1,141 +0,0 @@ -#!/usr/bin/python -import sys, getopt, binascii, random, time, os.path, time -from Crypto.Cipher import DES - -dictionary = {} - -# From http://stackoverflow.com/a/843846/1544337 -# 1 for odd parity, 0 for even parity -# Was used only in a previous version of nthByte -# def parity(b): -# c = 0 -# while b != 0: -# c += 1 -# b &= b - 1 -# return c % 2 - -# Find the nth possibility for a byte with odd parity -oddBytes = [1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,50,52,55,56,59,61,62,64,67,69,70,73,74,76,79,81,82,84,87,88,91,93,94,97,98,100,103,104,107,109,110,112,115,117,118,121,122,124,127,128,131,133,134,137,138,140,143,145,146,148,151,152,155,157,158,161,162,164,167,168,171,173,174,176,179,181,182,185,186,188,191,193,194,196,199,200,203,205,206,208,211,213,214,217,218,220,223,224,227,229,230,233,234,236,239,241,242,244,247,248,251,253,254] -def nthByte(n): - return oddBytes[n] - # c = -1 # This is the old version. The new version uses a faster lookup table. - # b = 0 - # while c != n: - # b += 1 - # if parity(b) == 1: - # c += 1 - # return b - -# Find the nth key in which all bytes have odd parity -def nthKey(n): - key = '' - for b in range(7,-1,-1): - key += chr(nthByte((n >> b*7) & 0x7f)) - return key - -# Create a dictionary for the first 2^l keys and a given plaintext -def createDictionary(plaintext, l): - for n in range(0, pow(2, l)): - encryption = DES.new(nthKey(n), DES.MODE_ECB).encrypt(plaintext) - if encryption in dictionary: - dictionary[encryption].append(n) - else: - dictionary[encryption] = [n] - -# Read the dictionary from a file if it exists, or generate it -def readOrMakeDictionary(plaintext, l): - if os.path.isfile('dict-' + binascii.b2a_hex(plaintext) + '-' + str(l) + '.txt'): - with open('dict-' + binascii.b2a_hex(plaintext) + '-' + str(l) + '.txt') as f: - for line in f: - dictionary[binascii.a2b_hex(line[:16])] = [int(x) for x in line[17:-1].split(',')] - return False - else: - createDictionary(plaintext, l) - return True - -# Save the dictionary to a file -def saveDictionary(plaintext, l): - dictionary_file = open('dict-' + binascii.b2a_hex(plaintext) + '-' + str(l) + '.txt', 'w') - for encryption in dictionary: - dictionary_file.write(binascii.b2a_hex(encryption) + ':' + ','.join(str(x) for x in dictionary[encryption]) + '\n') - print 'Saved dictionary as dict-' + binascii.b2a_hex(plaintext) + '-' + str(l) + '.txt' - -def main(argv): - l = 24 - plaintext = '' - ciphertext = '' - save_dictionary = False - - # Parse arguments. Use -h for help. - try: - opts, args = getopt.getopt(argv, "hl:p:c:s") - except getopt.GetoptError: - usage() - sys.exit(2) - - for opt, arg in opts: - if opt == '-h': - usage() - sys.exit() - elif opt == '-l': - l = int(arg) - elif opt == '-p': - plaintext = binascii.a2b_hex(arg) - elif opt == '-c': - ciphertext = binascii.a2b_hex(arg) - elif opt == '-s': - save_dictionary = True - - assert plaintext != '' - assert ciphertext != '' - - # Make the dictionary if it doesn't exist yet - print 'Making dictionary (p:' + binascii.b2a_hex(plaintext) + ';l:' + str(l) + ')...', - timer = time.clock() - if not readOrMakeDictionary(plaintext, l): - save_dictionary = False - print str(time.clock() - timer) + 's' - - if save_dictionary: - saveDictionary(plaintext, l) - - # Find matches - print 'Finding matches...', - timer = time.clock() - time_key = time_decryption = time_matching = 0 - matches = [] - for k in range(0, pow(2,l)): - # Generate key - time_t = time.clock() - key = nthKey(k) - time_key += time.clock() - time_t - - # Decrypt - time_t = time.clock() - des = DES.new(key, DES.MODE_ECB) - decryption = des.decrypt(ciphertext) - time_decryption += time.clock() - time_t - - # Find matches - time_t = time.clock() - if decryption in dictionary: - [matches.append({'k1': nthKey(i), 'k2': key}) for i in dictionary[decryption]] - time_matching += time.clock() - time_t - print str(time.clock() - timer) + 's' - - print 'Key generation: ' + str(time_key) + 's' - print 'Decryption: ' + str(time_decryption) + 's' - print 'Matching dictionary: ' + str(time_matching) + 's' - - for match in matches: - print 'k1: ' + binascii.b2a_hex(match['k1']) + '; k2: ' + binascii.b2a_hex(match['k2']) - -def usage(): - print 'Usage: break.py -p <plaintext> -c <ciphertext> [-l <keylength>] [-s]' - print ' plaintext : plaintext of the known-plaintext attack' - print ' ciphertext : ciphertext of the known-plaintext attack' - print ' keylength : pick keys from the first 2^l keys (default: 24)' - print ' -s : save the dictionary for this plaintext and keylength to a file' - -if __name__ == "__main__": - main(sys.argv[1:])
\ No newline at end of file diff --git a/Assignment 3/des-demo.py b/Assignment 3/des-demo.py deleted file mode 100755 index 0a4954f..0000000 --- a/Assignment 3/des-demo.py +++ /dev/null @@ -1,62 +0,0 @@ -#!/usr/bin/python - -# Copyright (c) 2015 Camil Staps <info@camilstaps.nl> - -import sys, getopt, binascii -from Crypto.Cipher import DES - -def main(argv): - key = '' - plaintext = '' - ciphertext = '' - - # Parse arguments. Use -h for help. - try: - opts, args = getopt.getopt(argv, "hk:p:c:", ["key=","plaintext=","ciphertext="]) - except getopt.GetoptError: - usage() - sys.exit(2) - - for opt, arg in opts: - if opt == '-h': - usage() - sys.exit() - elif opt in ("-k", "--key"): - key = binascii.a2b_hex(arg) - elif opt in ("-p", "--plaintext"): - plaintext = binascii.a2b_hex(arg) - elif opt in ("-c", "--ciphertext"): - ciphertext = binascii.a2b_hex(arg) - - if key == '' or plaintext == '' and ciphertext == '': - usage() - sys.exit(2) - - # PyCrypto does the hard work - cipher = DES.new(key, DES.MODE_ECB) - - encryption = '' - decryption = '' - - if plaintext != '': - encryption = cipher.encrypt(plaintext) - if ciphertext != '': - decryption = cipher.decrypt(ciphertext) - - # When plaintext and ciphertext are provided, output if DES[k](p) = c. Otherwise, output the encryption / decryption. - if encryption != '' and decryption != '': - print encryption == ciphertext - elif encryption != '': - print binascii.b2a_hex(encryption) - elif decryption != '': - print binascii.b2a_hex(decryption) - -def usage(): - print 'Usage: des-demo.py -k <key> [-p <plaintext>] [-c <ciphertext>]' - print ' key : an 8-byte value entered as hexadecimal numbers' - print ' plaintext : an 8-byte value entered as hexadecimal numbers' - print ' ciphertext : an 8-byte value entered as hexadecimal numbers' - print 'At least one of plaintext and ciphertext should be provided. When both are provided, we check if DES[k](p) = c.' - -if __name__ == "__main__": - main(sys.argv[1:]) diff --git a/Assignment 3/des-test.sh b/Assignment 3/des-test.sh deleted file mode 100755 index 15a5402..0000000 --- a/Assignment 3/des-test.sh +++ /dev/null @@ -1,22 +0,0 @@ -#!/bin/sh - -echo "Testing encryption:" -./des-demo.py -k 133457799BBCDFF1 -p 0123456789abcdef -./des-demo.py -k 752878397493CB70 -p 1122334455667788 -./des-demo.py -k 752878397493CB70 -p 99AABBCCDDEEFF00 -./des-demo.py -k 5B5A57676A56676E -p 675A69675E5A6B5A -./des-demo.py -k 0101010101010102 -p 0102030405060708 - -echo "Testing decryption:" -./des-demo.py -k 133457799BBCDFF1 -c 85E813540F0AB405 -./des-demo.py -k 752878397493CB70 -c B5219EE81AA7499D -./des-demo.py -k 752878397493CB70 -c 2196687E13973856 -./des-demo.py -k 5B5A57676A56676E -c 974AFFBF86022D1F -./des-demo.py -k 0101010101010102 -c 6613fc98d6d2f56b - -echo "Testing comparison:" -./des-demo.py -k 133457799BBCDFF1 -p 0123456789abcdef -c 85E813540F0AB405 -./des-demo.py -k 752878397493CB70 -p 1122334455667788 -c B5219EE81AA7499D -./des-demo.py -k 752878397493CB70 -p 99AABBCCDDEEFF00 -c 2196687E13973856 -./des-demo.py -k 5B5A57676A56676E -p 675A69675E5A6B5A -c 974AFFBF86022D1F -./des-demo.py -k 0101010101010102 -p 0102030405060708 -c 6613fc98d6d2f56b
\ No newline at end of file diff --git a/Assignment 3/nthkey.py b/Assignment 3/nthkey.py deleted file mode 100755 index 40cf0cf..0000000 --- a/Assignment 3/nthkey.py +++ /dev/null @@ -1,37 +0,0 @@ -#!/usr/bin/python - -# Copyright (c) 2015 Camil Staps <info@camilstaps.nl> - -import binascii - -# From http://stackoverflow.com/a/843846/1544337 -# 1 for odd parity, 0 for even parity -# Was used only in a previous version of nthByte -# def parity(b): -# c = 0 -# while b != 0: -# c += 1 -# b &= b - 1 -# return c % 2 - -# Find the nth possibility for a byte with odd parity -oddBytes = [1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,50,52,55,56,59,61,62,64,67,69,70,73,74,76,79,81,82,84,87,88,91,93,94,97,98,100,103,104,107,109,110,112,115,117,118,121,122,124,127,128,131,133,134,137,138,140,143,145,146,148,151,152,155,157,158,161,162,164,167,168,171,173,174,176,179,181,182,185,186,188,191,193,194,196,199,200,203,205,206,208,211,213,214,217,218,220,223,224,227,229,230,233,234,236,239,241,242,244,247,248,251,253,254] -def nthByte(n): - return oddBytes[n] - # c = -1 # This is the old version. The new version uses a faster lookup table. - # b = 0 - # while c != n: - # b += 1 - # if parity(b) == 1: - # c += 1 - # return b - -# Find the nth key in which all bytes have odd parity -def nthKey(n): - key = '' - for b in range(7,-1,-1): - key += chr(nthByte((n >> b*7) & 0x7f)) - return key - -# Example -print binascii.b2a_hex(nthKey(765637))
\ No newline at end of file |