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1 Completing the Enigma Challenge
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2 ###############################
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3
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4 :date: 2012-07-22 13:30
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5 :tags: Enigma, Py-Enigma, Cpp-Enigma, C++
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6 :slug: completing-the-enigma-challenge
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7 :author: Brian Neal
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8
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9 Since my last `blog post
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10 <http://deathofagremmie.com/2012/06/06/introducing-py-enigma/>`_, I have spent
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11 almost all my free time working on `Dirk Rijmenants' Enigma Challenge
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12 <http://users.telenet.be/d.rijmenants/en/challenge.htm>`_. I'm very happy to
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13 report that I cracked the last message on the evening of July 10. I thought it
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14 might be interesting to summarize my experiences working on this challenge in a
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15 blog post.
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16
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17 The first nine
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18 --------------
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19
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20 I had a lot of fun building Py-Enigma_, an Enigma machine simulator library
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21 written in Python_ based on the information I found on Dirk's `Technical Details
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22 of the Enigma Machine`_ page. After I had built it and played with it for a
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23 while, I discovered Dirk also had an `Enigma Challenge`_. I decided this would
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24 be a good test for Py-Enigma_, and it may give me some ideas on how to improve
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25 the library for breaking messages.
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26
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27 The first nine messages were pretty easy to solve using Py-Enigma_. Dirk gives
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28 you most of the key information for each problem, and one can then write a small
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29 program to brute force the missing information. I was able to solve the first
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30 nine messages in a weekend. This was very enjoyable, as it did require some
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31 thinking about how to simulate the problem and then executing it. I also learned
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32 about `Python's itertools <http://docs.python.org/library/itertools.html>`_
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33 library, which contains some very handy functions for generating permutations
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34 and combinations for brute forcing a solution.
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35
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36 Dirk did a great job on the messages. They referenced actual events from World
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37 War II and I ended up spending a fair amount of time on Wikipedia reading about
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38 them. Translating the messages from German to English was a bit difficult, but I
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39 relied heavily on `Google Translate <http://translate.google.com>`_.
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40
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41 Message 10
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42 ----------
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43
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44 But then I came to the last message. Here, Dirk doesn't give you any key
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45 information, just ciphertext. Gulp. If you include 2 possible reflectors, the
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46 Enigma machine's key space for message 10 is somewhere around 2 x 10\
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47 :sup:`23` keys, so it is impossible to brute force every possible key, unless
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48 you can afford to wait around for the heat death of the universe.
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49
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50 I then did some research, and learned about a technique for brute-forcing only
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51 the rotor and message settings, and then performing a heuristic technique called
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52 "hill-climbing" on the plugboard settings. I am deeply indepted to Frode Weierud
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53 and Geoff Sullivan, who have published high level descriptions of this
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54 technique. See Frode's `The Enigma Collection
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55 <http://cryptocellar.org/Enigma/>`_ page and Geoff's `Crypto Barn
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56 <http://www.hut-six.co.uk/>`_ for more information.
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57
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58 Python is too slow, or is it?
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59 -----------------------------
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60
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61 After a week or so of studying and tinkering, I came up with a hill-climbing
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62 algorithm in Python. I then started an attempt to break message 10, but after
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63 running the program for a little over 24 hours, I realized it was too slow. I
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64 did a "back of the envelope" calculation and determined I would need several
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65 hundred years to hill-climb every rotor and message setting. This was a bit
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66 disappointing, but I knew it was a possibility going in.
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67
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68 I then set out, somewhat reluctantly, to port Py-Enigma to C++. These days I
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69 don't do any C++ at home, only at work. However I got much happier when I
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70 decided this was an opportunity to try out some new C++11 features (the embedded
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71 compiler we use at work has no support for C++11). Okay, things are fun again! I
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72 have to say that C++11 is really quite enjoyable, and I made good use of the new
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73 ``auto`` style variable declarations, range-based for-loops, and brace-style
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74 initialization for containers like ``vector`` and ``map``.
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75
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76 C++ is too slow, or is it?
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77 --------------------------
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78
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79 It took a fair amount of time to re-tool my code to C++11. I ensured all my unit
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80 tests originally written in Python could pass in C++, and that I could solve
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81 some of the previous messages. I then re-implemented my hill-climbing
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82 algorithm in C++ and made another attempt at cracking message 10.
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83
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84 My C++ solution was indeed faster, but only by a factor of 8 or 9. I calculated
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85 I would need about 35 years to hill-climb all rotor and message settings, and I
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86 didn't really want to see if I could out-live my program. My morale was very low
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87 at this point. I wasn't sure if I could ever solve this self-imposed problem.
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88
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89 Algorithms & Data Structures are key
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90 ------------------------------------
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91
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92 I had wanted to test myself with this problem and had avoided looking at anyone
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93 else's source code. However, at this juncture, I needed some help. I turned to
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94 Stephan Krah's `M4 Message Breaking Project
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95 <http://www.bytereef.org/m4_project.html>`_. Stephan had started a distributed
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96 computing attack on several 4-rotor naval Enigma machine messages. He had
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97 graciously made his source code available. Perhaps I could get some hints by
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98 looking at his code.
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99
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100 Indeed, Stephen's code provided the break I needed. I discovered a very cool
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101 trick that Stephen was doing right before he started his hill-climb. He
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102 pre-computed every path through the machine for every letter of the alphabet.
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103 Since hill-climbing involves running the message through the machine roughly
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104 600 to 1000 times, this proved to be a huge time saver. After borrowing this
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105 idea, my hill-climbing times for one fixed rotor & message setting went down
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106 from 250 milliseconds to 2!
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107
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108 I immediately stopped looking at Stephen's code at this point; I didn't bother
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109 to compare our hill-climbing algorithms. I believe both of us are influenced by
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110 Weierud & Sullivan here. I was now convinced I had the speed-up I needed to make
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111 a serious attempt at message 10 again.
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112
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113 This showed me how critically important it is to have the right data structure
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114 and algorithm for a problem. However there were two other lessons I needed to
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115 learn before I was successful.
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116
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117 Utilize all your computing resources
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118 ------------------------------------
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119
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120 Up to this point my cracking program was linear. It started at the first rotor
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121 and message setting, then hill-climbed and noted the score I got. Then it
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122 proceeded to the next message setting and hill-climbed, noting the score of that
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123 attempt, and so on. There were two problems with this approach.
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124
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125 I realized if I could do some sort of multi-processing, I could search the key
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126 space faster. I thought about forking off multiple processes or maybe using
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127 threads, but that was over-thinking it. In the end, I added command-line
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128 arguments to the program to tell it where in the key space to start looking. I
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129 could then simply run multiple instances of my program. My development laptop,
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130 which runs Ubuntu, is from 2008, and it has 2 cores in it. My desktop PC (for
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131 gaming), has 4 cores! I next spent a couple nights installing MinGW_ and getting
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132 my application to build in that environment. I could now run 6 instances of my
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133 cracking program. Hopefully this would pay off and shorten the time further.
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134
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135 (I didn't even attempt to commandeer my wife's and kids' computers. That
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136 wouldn't have gone down so well.)
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137
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138 How do you know when you are done?
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139 ----------------------------------
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140
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141 The final problem that I had was determining when my cracking program had in
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142 fact cracked the message. The hill-climbing attempts produced scores for each
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143 key setting. Up to this point, based on running my program on messages 1 through
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144 9, I had noticed that when I got a score divided by the message length of around
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145 10 I had cracked the message. But my tests on messages 1 through 9 were
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146 hill-climbing using the known ring settings. My message cracker was using a
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147 shortcut: I was only searching ring settings on the "fast" rotor to save time.
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148 This would let me get the first part of a message, but if the middle or
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149 left-most rotor stepped at the wrong time the rest of the message would be
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150 unintelligible.
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151
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152 To verify my message cracking program, I ran it on some of the previous
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153 messages. I was shooting for a score divided by message length of 10. Using this
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154 heuristic, I was in fact able to crack some of the previous messages, but not
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155 others. It took me a while to realize that not searching the middle rotor's ring
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156 setting was causing this. The light bulb came on, and I realized that my
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157 heuristic of 10 is only valid when I search all the ring settings. Instead I
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158 should just keep track of the highest scores. When you get close enough, the
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159 score will be significantly higher than average score. Thus I may not know when
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160 I am done until I see a large spike in the score. I would then have to write
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161 another program to refine the solution to search for the middle and left-most
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162 ring setting.
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163
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164 Success at last
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165 ---------------
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166
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167 It took a little over a month of evenings and weekends to get to this point.
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168 I even had a false start where I ran my program on 6 cores for 1.5 days only to
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169 realize I had a bug in my code and I was only searching ring setting 0 on the
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170 fast ring. But once I had that worked out, I started a search on 6 cores on a
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171 Sunday night. I checked the logs off and on Monday, but no significant spike in
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172 the scores were noted. Before leaving for work on Tuesday I checked again, and
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173 noticed that one instance of my program had found a score twice as high as any
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174 other. Could that be it? I really wanted to stay and find out, but I had to go
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175 to work! Needless to say I was a bit distracted at work that day.
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176
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177 After work, I ran the settings through my Python application and my heart
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178 pounded as I recognized a few German words at the beginning of the message. In
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179 fact I had gotten around 75% of the message, then some garbage, but then the
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180 last few words were recognizable German. I then wrote another application to
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181 search the middle ring setting space. Using the highest score from that program
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182 allowed me to finally see the entire message. I cannot tell you how happy and
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183 relieved I was at the same time!
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184
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185 Final thoughts
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186 --------------
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187
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188 For a while I didn't think I was going to be smart enough or just plain up to
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189 the task of solving message 10. Looking back on it, I see a nice progression of
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190 trying things, experimenting, setbacks, and a few "a-ha" moments that lead to the
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191 breakthrough. I am very grateful to Dirk Rijmenants for creating the challenge,
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192 which was a lot of fun. And I also wish to thank Frode Weierud and Geoff
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193 Sullivan for their hill-climbing algorithm description. Thanks again to Stephan
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194 Krah for the key speedup that made my attempt possible.
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195
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196 For now I have decided not to publish my cracking program, since it is a tiny
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197 bit specific to Dirk's challenge. I don't want to ruin his Enigma Challenge by
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198 giving anything away. I don't believe my broad descriptions here have revealed
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199 too much. Other people need to experience the challenge for themselves to fully
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200 appreciate the thrill and hard work that go into code breaking.
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201
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202 I should also note that there are other ways of solving Dirk's challenge. You
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203 could, with a bit of patience, solve messages 1 through 9 with one of the many
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204 Enigma Machine GUI simulators (Dirk has a fine one). I'm not certain how
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205 you could break message 10 using a GUI simulator and trial and error, however.
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206
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207 It is my understanding that this style of Enigma message breaking was not the
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208 technique used by the allied code-breakers during the war. I believe they used
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209 knowledge of certain key words, or "cribs", in messages received in weather
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210 reports and other regular messages to find the key for the day. I look forward
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211 to reading more about their efforts now.
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212
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213 Finally, I have published the C++11 port of Py-Enigma_, which I am calling
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214 (rather unimaginatively) Cpp-Enigma_ on bitbucket. I hope Cpp-Enigma_ and
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215 Py-Enigma_ are useful for other people who want to explore the fascinating world
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216 of Enigma codes.
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217
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218 .. _Py-Enigma: https://bitbucket.org/bgneal/enigma
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219 .. _Python: http://www.python.org
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220 .. _Technical Details of the Enigma Machine: http://users.telenet.be/d.rijmenants/en/enigmatech.htm
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221 .. _Enigma Challenge: http://users.telenet.be/d.rijmenants/en/challenge.htm
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222 .. _Cpp-Enigma: https://bitbucket.org/bgneal/cpp-enigma
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223 .. _MinGW: http://www.mingw.org/
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