THANG DAO SJSU, CS 180H Purple Cipher: Simulation and Improved Hill- Climb Attack FINAL REPORT Advisor: Professor Mark Stamp Fall / 09 / 2005

Transcription

1 THANG DAO SJSU, CS 180H Purple Cipher: Simulation and Improved Hill- Climb Attack FINAL REPORT Advisor: Professor Mark Stamp Fall / 09 / 2005

2 TABLE OF CONTENT I. Introduction to Purple Cipher 1 II. Purpose of the Project 1 III. External factors of the Purple Machine 1 IV. Internal Structure of the Purple Machine 2 V. How does it work? 4 VI. An example of Purple Machine s Encipherment 5 VII. Weaknesses 6 VIII. Introduction to Hill-Climb Attack 6 IX. Cryptanalysis of Purple Encrypted Messages 7 X. Conclusion 9 Appendix A: Encipher Permutations Appendix B: Decipher Permutations Appendix C: A Hill-climb attack on the twenties: Sample input and output References i iii v x

3 LIST OF TABLE AND FIGURE TABLES: Table 1: Sample Switch Positions 2 Table 2: An example of the encipherment process 5 Table 3: Sixes switch Encipher i Table 4: Twenties switch #1 Encipher i Table 5: Twenties switch #2 Encipher ii Table 6: Twenties switch #3 Encipher ii Table 7: Sixes switch Decipher iii Table 8: Twenties switch #1 Decipher iii Table 9: Twenties switch #2 Decipher iv Table 10: Twenties switch #3 Decipher iv FIGURES: Figure 1: Fragment of the Purple Machine 1 Figure 2: An example of mapping sixes 2 Figure 3: An example of mapping twenties 2 Figure 4: Sample Wiring Diagram of the Deciphering Unit 2 Figure 5: Sample screenshot on the twenties hill-climb attack 9

4 I. INTRODUCTION TO PURPLE CIPHER During World War II, the Purple Cipher was the main systems that carried the most secret Japanese diplomatic messages. Even though no Purple Cipher machine was ever obtained by the Allies, the Purple Cipher was broken by American cryptanalysts. This successful attack is generally considered to be one of the greatest cryptanalytic successes of WWII. Here is a picture of part of the Purple Cipher Machine: Figure 1: Fragment of an actual Purple Machine from the Japanese embassy in Berlin, obtained by the United States at the end of World War II [3] II. PURPOSE OF THE PROJECT In this project, we first propose to develop a simulation of the Purple Cipher. This is necessary in order to ensure that we completely understand this complex cipher system, and moreover we will also use this simulator for the remainder of the project. Secondly, we propose to study the hill climb attack on Purple discussed in [2]. This attack uses an ad hoc approach and we believe that a more systematic hill climb attack is possible. We propose an improvement to this hill climb attack based on Hidden Markov Models (HMMs). Our goal is to develop a new method that is far more robust and efficient than the approach in [2]. III. EXTERNAL FACTORS OF THE PURPLE MACHINE The machine itself is connected to the input device at one end and the output device at the other end. The input and output devices accept a random alphabet which is divided in to 2 parts, the sixes and the twenties. The external sixes portion is matched with the internal plugboards sixes. Similarly, the external twenties portion is matched with the internal plugboards twenties. The external alphabet can be configured in any order (that is, it could be any permutation of the CS 180H 1 Fall 2005

5 P Q R S T V W X Z N X V W English alphabet) and agreed by both parties in advance. Below is one example of a connection between the external keyboard alphabet to the internal plugboards alphabet. Sixes Twenties Internal plugboard alphabet: AEIOUY BCDFGHJKLMN External alphabet: OKT YU EQ LHBR MP DICJAS GZ F Figure 2: Mapping sixes from external keyboard to internal plugboard Figure 3: Mapping sixes from external keyboard to internal plugboard IV. INTERNAL STRUCTURE OF THE PURPLE MACHINE Inside the Purple machine, there are two different plugboards: the in-plugboard and the out-plugboard. Theoretically, these two plugboards can be connected independently of each other. However, in reality, these two plugboards were always the same when the Japanese used the Purple machine. The simplified diagram of the Purple machine s structure is shown below: CS 180H 2 Fall 2005

6 Figure 4: Simplified diagram of internal structure of the Purple Machine The cryptographic components inside the machine are an input plugboard, an output plugboard, and stepping switches. The two plugboards are divided into 2 groups of characters. One has six characters from the English alphabet and the other has the remaining twenty characters from the English alphabet as described above. And these two internal plugboards are connected to the external keyboards which are used by typists. The first group of characters, the sixes, is connected to a single stepping switch which essentially determines the mapping between six characters from the external keyboard and six characters on the internal plugboard. The set of six characters on the internal keyboard are fixed and the switch allows 25 possible mappings between the characters (out of 6! = 720 total possibilities). The position of the switch will advance each time a letter is typed so that the next mapping will be used. Thus the order of the mappings has a period length of 25. The second group of characters, the twenties, is connected to the three cascaded stepping switches which also determine the mapping between twenty characters from the external keyboard and twenty characters on the internal plugboard. Each switch employs 25 different permutations (mappings) out of 20! possibilities. Therefore, this mapping arrangement has a period length of 25x25x25 = 15,625. In order to add more complexity to the system, a set of CS 180H 3 Fall 2005

7 movement rule is assigned to each switch. That is, one of the switches is set as fast, one as middle, and one as slow. Thus, there are total 6 possible switch motions. All internal components are hard-wired and cannot be changed. V. HOW DOES IT WORK? In order to understand the internal workings of the Purple Machine, one should know the motion rules of the stepping switches first. There is one stepping switch for the sixes and three stepping switches for the twenties. For all the switches, when they reach their 25 th position, they will rotate back to the 1 st position on their next advancement and the routine goes on. The sixes switch simply advances each time a character is typed. Thus, the sixes alphabet will repeat itself after 25 characters are enciphered. However, for the twenties switches, the stepping is more complicated due to the different motion set to each switch. As stated above, one of the switches is labeled as fast, another one as middle, and the last one as slow. Exactly one of three switches will advance for each letter typed. Normally, the fast always advances to its next position with two exceptions, which occur when the sixes switch reaches the 24 th or 25 th position. Specifically, when the sixes switch reaches its 24 th position, if the twenties middle switch is at its 25 th position, the slow switch will advance. Also, when the sixes switch is at its 25 th position, the middle switch will advance. Here is the sample of how the internal stepping switches works: Switch Positions Sixes Twenties #1 Twenties #2 Twenties # Table 1: Sample Switch Position - #1: fast, #2: middle, #3: slow ([2]) In the encipherment process inside the machine, there are 3 basic steps. The first step is when a typist keys in a character, say, C 1. That character is then categorized as either one of the sixes or one of the twenties. Thus, based on the character being a sixes or a twenties, it will go through the sixes portion or the twenties portion of the input plugboard. After this step, C 1 is permuted to, say, C 2 (the result relies on the configuration of the internal plugboard and the chosen alphabet) CS 180H 4 Fall 2005

8 Second, C 2 is passed through the stepping switch(es). If C 1 is a sixes character, C 2 will be permuted by only the sixes switch. However, if C 1 is a twenties character, C 2 will be permuted by the 1 st switch, 2 nd switch, and 3 rd switch sequentially (the decipher process is reversed; that is the letter will be permuted in the order: 3 rd, 2 nd, and 1 st switch). The result after this step will be a character, say, C 3. Third, C 3 is now transferred to and permuted at the output plugboard (with the same configuration as the input plugboard). The result character is displayed in the output device. N X V W P Q R S T V W X Z VI. AN EXAMPLE OF PURPLE MACHINE S ENCIPHERMENT Consider the plain text SAN JOSE STATE UNIVERSITY with the following configuration: The permutations are cited in the Appendix A. Initial sixes switch position: 1 Initial twenties switches position: 5, 2, 10 (1 st, 2 nd, and 3 rd, respectively) Initial twenties switches motion: (fast, middle, and slow, respectively) Sixes Twenties Alphabet: OKT YU EQ LHBR MP DICJAS GZ F Plugboard: AEIOUY BCDFGHJKLMN Plain text letter Input plugboard Sixes switch Twenties switch #1 Twenties switch #2 Twenties switch #3 S S D A R R N A N J Q B O E U S S Q E C X S S F T O O A R E T O K E C P U Y T N A T I N S V T W E C E Output plugboard CS 180H 5 Fall 2005

9 R J J S S E I N Z T O Y Y U U The cipher text is: DRN BUQX FOEKP TTSWEJEZYU Table 2: An example of the encipher process, text SAN JOSE STATE UNIVERSITY VII. WEAKNESSES The first weakness of the Purple Machine is its limited number of configurations (that is, the limited number of keys). For the sixes, there are 25 keys (different permutations). For the twenties, three stepping switches with 25 permutations which gives a total of 25 3 keys. In addition, a total of 6 possible switch motions are employed on the twenties three stepping switches. As a result, the Purple machine only has 6 x 25 (sixes) x 25 3 (twenties) = 2,343,750 possible configurations of the stepping switches. Regardless of the switch motions for the twenties switches (since they are fixed), the machine will repeat after 25 4 = 390,625 characters encrypted. Another weakness of the Purple machine is the splitting of the internal input and output plugboards. Instead of using the whole 26 English alphabets (which will provide a possible 26! permutations), the alphabet is divided into 2 portions, the sixes and the remaining twenties, which produce much smaller number of keys: 6! x 20!. This gives the cryptanalysts a possible method to reduce the time on deciphering the cipher text by separating the sixes and the twenties first. Therefore, attacks on the Purple Machine do not need to consider all of the possible configurations of the stepping switches simultaneously. Instead, a cryptanalyst can determine the sixes from the alphabet first using English letter frequency counts (the more detailed work is given in part IX). With the sixes being successfully separated, cryptanalysts can concentration on the twenties only. That means there are only 20! possible keys and 6 x 25 3 = 93,750 possible configurations of the twenties, which is an improvement compared to 26! keys and 6 x 25 4 = 2,343,750 configurations. One possible solution to decipher an encrypted message is discussed below. VIII. INTRODUCTION TO HILL-CLIMB ATTACK By definition, hill-climbing is a graph search algorithm where the current path is extended with a successor node which is closer to the solution than the end of the current path [1]. However, in term of deciphering Purple cipher messages, a hill-climb attack on Purple is given in [2]. This attack works as follow: it examine and determine which trial key is more CS 180H 6 Fall 2005

10 likely to generate a best result based on English letter frequency statistics and how to generate a better trial key from the existing key (hill-climbing). A more precise description is provided below. Consider the case where we use a hill climb to separate the sixes from the 26 letters of English alphabet and assume we use the current trial key ABCDEF as our sixes, the score of ABCDFE, which is adjacent to the current key, is computed based on English letter frequency counts and compared to the score of ABCDEF. If the new score is better, current trial key ABCDEF will be discarded and the key ABCDFE now becomes our new trial key. The process goes on until the current trial key has no adjacent keys which produce better scores. That means the current trial key is already at its peak (it cannot climb any higher ). And the score of the peak will be compared to the global score. If the global score is less than the peak s score, the global score will be updated along with the saved sixes and position. Next, we discuss the method to decipher the cipher text encrypted by Purple Machine using this hill climb approach. IX. CRYPTANALYSIS OF PURPLE ENCRYPTED MESSAGES Decipher a message encrypted by the Purple machine is a two-steps process. However, it is important to first understand our scoring system used for the attack. We use English letter frequency counts as our score. Since each percentage of combined English letters (bigram or trigram) is relatively small, we use its log to calculate the score. For instance, to compute the score for the word RING using trigram frequencies: P( RING ) = P(RIN) x P(ING) = P(N RI) x P(G IN) = ( P(N RI) x P(I R) x P(R) ) x ( P(G IN) x P(N I) x P(I) ) = x x x x x = E-6 However, if we use log, the score will be computed as: Log P( RING ) = Log ( P(RIN) P(ING) ) = Log P (RIN) + Log P (ING) = Log P (N RI) P (RI) + Log P (G IN) P (IN) = Log P (N RI) + log P (RI) + Log P (G IN) + Log P (IN) = Log P (N RI) + Log P (I R) P (R) + Log P (G IN) + Log P (N I) P (I) = Log P (N RI) + Log P (I R) + Log P (R) + Log P (G IN) + Log P (N I) + Log P (I) CS 180H 7 Fall 2005

11 = ( ) + ( ) + ( ) + ( ) + ( ) + ( ) = This score is more practical to use for point calculating system since if we use the old way to calculate score, the total score will approach zero or very small number (each percentage is <= 1). Thus, in order to compare 2 different scores, the system is most likely to produce a wrong comparison due to the significant small scores. That is why we use the Log in our calculation. Let us move on to the deciphering process. The first task is to separate the sixes and twenties. This task mainly helps to reduce the total possible trial keys on the attack from 26! permutations of the 26 English characters down to 6! x 20! total permutations. However, although the sixes portion only has one switch with 25 permutations, it is still very time-consuming if brute force approach is used. That is, we have to choose 6 out of total 26 characters to assign as sixes. This step will generate P 6,26 = 26! / 20! = 165,765,600 possible keys. Together with 25 mappings, the total number of keys that need to be checked will be: 25 x P 6, 26 = 4,144,140,000. A hill climb approach is much more efficient. To use this hill climb, we start at an arbitrary key, which is a permutation of the 26 English letters. The first six characters in the key are then assigned as the sixes portion and the remaining twenty characters as the twenties portion. For example, if the key is ABCDEFGHIJKLMNOPQRSTUVWXYZ then the sixes will be ABCDEF and the twenties will be GHIJKLMNOPQRSTUVWXYZ. The sixes switch position is set at 1 st. The positions of twenties three switches are randomly assigned. The cipher text is decrypted in a similar process as the encryption process except the twenties characters will go through the 3 rd, 2 nd, and 1 st stepping switch sequentially (reverse order of encryption process). The recovered putative plaintext score is calculated based on English bigram frequency statistics. At the next step, every two adjacent letters in the key will be swapped to form new keys (25 th and 26 th, 24 th and 25 th 2 nd and 1 st letter). For each swapping, the score for the new key is computed. If this new score is better than the score of the previous key (before this swapping), the new key will be retained, otherwise the new key is discarded and the old key is restored. The same starting keys are used with each of the sixes initial switch position (1 thru 25). We use about 4,000 arbitrary starting keys and save the sixes alphabet and its switch position which resulted the best score. An example of this process: Sixes Position Score ABCDEF E13 FEADXY E12 EYWSAD E12 YXAGIT E13 CS 180H 8 Fall 2005

12 In this example, the sixes will be EYWSAD, the sixes switch position is 10 th (we use the absolute of the log value, thus the smaller the score, the better the key is). The second part of the attack is to determine the twenties alphabet along with the switch positions based on the result of the sixes from the first part. There are a total of 6 x 25 3 = 93,750 possible switches settings. We have to do a hill climb attack on all of these settings separately. Random starting keys that are permutations of the twenties characters are generated and used for each setting. The cipher text is then decrypted using the key and the score is computed on the putative plaintext. However, in this process, the score is calculated using English trigram frequencies instead of bigram. Similar to the sixes hill climb attack, two adjacent characters in each key are then swapped and new score is recorded. If the new key has a better score than the previous key, the former will be retained otherwise it will be discarded. The best result should give us the twenties alphabet and the correct motions and stepping positions. Here is a sample screen shot: Figure 5: A screenshot on the twenties hill climb attack This means, the test was running in seconds which is nearly 6 hours. And the best result obtain is 78% identical to the original plaintext (the recover putative plaintext together with the original plaintext are given in the Appendix C) X. CONCLUSION Even though the hill climb gives cryptanalysts a solution to decrypt Purple messages, the attack can be improved. One possible improvement is to find a way to terminate a trial key earlier. Some rules could be used in order to determine if a certain trial key is not likely to produce the correct alphabet and terminate the hill climb if there is no increase in score for a CS 180H 9 Fall 2005

13 certain number of consecutive swappings. such an improved hill climb attack might enable cryptanalysts to recover the plain text much faster. A better hill-climb attack approach could also be used. For example, a Hidden Markov Models (HMMs) could be used. This is currently under investigation by the author. The Purple Machine was a unique device. It had its own limitations including the limited number of stepping switches and the 6 20 alphabet split. Based on the limit of the machine and the hill climb attack, the U.S. Army cryptanalysts were able to decrypt the cipher text as fast as the Japanese counterparts. CS 180H 10 Fall 2005

14 APPENDIX A: ENCIPHER PERMUTATIONS Position Sixes switch input Table 3: Sixes Switch Encipher Position Twenties switch #1 input Table 4: Twenty Switch #1 Encipher CS 180H i Fall 2005

15 Position Twenties switch #2 input Table 5: Twenty Switch #2 Encipher Position Twenties switch #3 input Table 6: Twenty Switch #3 Encipher CS 180H ii Fall 2005

16 APPENDIX B: DECIPHER PERMUTATIONS Position Sixes switch input Table 7: Sixes Switch Decipher Position Twenties switch #1 input Table 8: Twenty Switch #1 Decipher CS 180H iii Fall 2005

17 Position Twenties switch #2 input Table 9: Twenty Switch #2 Decipher Position Twenties switch #3 input Table 10: Twenty Switch #3 - Decipher CS 180H iv Fall 2005

18 APPENDIX C: A HILL-CLIMB ATTACK ON THE TWENTIES: SAMPLE INPUT AND OUTPUT Input: CHAPTER I DOWN THE RABBIT-HOLE ALICE was beginning to get very tired of sitting by her sister on the bank and of having nothing to do: once or twice she had peeped into the book her sister was reading, but it had no pictures or conversations in it, "and what is the use of a book," thought Alice, "without pictures or conversations?' So she was considering, in her own mind (as well as she could, for the hot day made her feel very sleepy and stupid), whether the pleasure of making a daisy-chain would be worth the trouble of getting up and picking the daisies, when suddenly a White Rabbit with pink eyes ran close by her. There was nothing so very remarkable in that; nor did Alice think it so very much out of the way to hear the Rabbit say to itself "Oh dear! Oh dear! I shall be too late!" (when she thought it over afterwards it occurred to her that she ought to have wondered at this, but at the time it all seemed quite natural); but, when the Rabbit actually took a watch out of its waistcoat-pocket, and looked at it, and then hurried on, Alice started to her feet, for it flashed across her mind that she had never before seen a rabbit with either a waistcoat-pocket, or a watch to take out of it, and burning with curiosity, she ran across the field after it, and was just in time to see it pop down a large rabbit-hole under the hedge. In another moment down went Alice after it, never once considering how in the world she was to get out again.the rabbit-hole went straight on like a tunnel for some way, and then dipped suddenly down, so suddenly that Alice had not a moment to think about stopping herself before she found herself falling down what seemed to be a very deep well. Either the well was very deep, or she fell very slowly, for she had plenty of time as she went down to look about her, and to wonder what was going to happen next. First, she tried to look down and make out what she was coming to, but it was too dark to see anything: then she looked at the sides of the well, and noticed that they were filled with cupboards and book-shelves: here and there she saw maps and pictures hung upon pegs. She took down ajar from one of the shelves as she passed: it was labeled "ORANGE MARMALADE" but to her great disappointment it was empty: she did not like to drop the jar, for fear of killing somebody underneath, so managed to put it into one of the cupboards as she fell past it. "Well!" thought Alice to herself "After such a fall as this, I shall think nothing of tumbling downstairs! How brave they'll all think me at home! Why, I wouldn't say anything about it, even if I fell off the top of the house!" (which was very likely true.) Down, down, down. Would the fall never come to an end? "I wonder how many miles I've fallen by this time?" she said aloud. "I must be getting somewhere near the centre of the earth. Let me see: that would be four thousand miles down, I think-" (for, you see, Alice had learnt several things of this sort in her lessons in the school-room, and though this was not a very good opportunity for showing off her knowledge, as there was no one to listen to her, still it was good practice to say it over) "-- yes that's about the right distance -- but then I wonder what Latitude or Longitude I've got to?" (Alice had not the slightest idea what Latitude was, or Longitude either, but she thought they were nice grand words to say.) Presently she began again. "I wonder if I shall fall fight through the earth! How funny it'll seem to come out among the people that walk with their heads downwards! The antipathies, I think-" (she was rather glad there was no one listening, this time, as it didn't sound at all the right word) "-but I shall have to ask them what the name of the country is, you know. Please, Ma'am, is this New Zealand? Or Australia?" (and she tried to curtsey as she spoke- fancy, curtseying as you're falling through the air! CS 180H v Fall 2005

19 Do you think you could manage it?) "And what an ignorant little girl she'll think me for asking! No, it'll never do to ask: perhaps I shall see it written up somewhere." Down, down, down. There was nothing else to do, so Alice soon began talking again. "Dinah'll miss me very much to-night, I should think!" (Dinah was the cat.) "I hope they'll remember her saucer of milk at tea-time. Dinah, my dear! I wish you were down here with me! There are no mice in the air, I'm afraid, but you might catch a bat, and that's very like a mouse, you know. But do cats eat bats, I wonder?" And here Alice began to get rather sleepy, and went on saying to herself, in a dreamy son of way, "Do cats eat bats? Do cats eat bats?" and sometimes "Do bats eat cats?" for, you see, as she couldn't answer either question, it didn't much matter which way she put it. She felt that she was dozing off, and had just begun to dream that she was walking hand in hand with Dinah, and was saying to her, very earnestly, "Now, Dinah, tell me the truth: did you ever eat a bat?" when suddenly, thump! thump! down she came upon a heap of sticks and dry leaves, and the fall was over. Alice was not a bit hurt, and she jumped up on to her feet in a moment: she looked up, but it was all dark overhead: before her was another long passage, and the White Rabbit was still in sight, hurrying down it. There was not a moment to be lost: away went Alice like the wind, and was just in time to hear it say, as it turned a comer, "Oh my ears and whiskers, how late it's getting!" She was close behind it when she turned the comer, but the Rabbit was no longer to be seen: she found herself in a long, low hall, which was lit up by a row of lamps hanging from the roof. There were doors all round the hall, but they were all locked; and when Alice had been all the way down one side and up the other, trying every door, she walked sadly down the middle, wondering how she was ever to get out again. Suddenly she came upon a little three-legged table, all made of solid glass: there was nothing on it but a tiny golden key, and Alice's first idea was that this might belong to one of the doors of the hall; but, alas! either the locks were too large, or the key was too small, but at any rate it would not open any of them. However, on the second time round, she came upon a low curtain she had not noticed before, and behind it was a little door about fifteen inches high: she tried the little golden key in the lock, and to her great delight it fitted! Alice opened the door and found that it led into a small passage, not much larger than a rat-hole: she knelt down and looked along the passage into the loveliest garden you ever saw. How she longed to get out of that dark hall, and wander about among those beds of bright flowers and those cool fountains, but she could not even get her head through the doorway; "and even if my head would go through," thought poor Alice, "it would be of very little use without my shoulders. Oh, how I wish I could shut up like a telescope! I think I could, if I only knew how to begin." For, you see, so many out-of-theway things had happened lately, that Alice had begun to think that very few things indeed were really impossible. There seemed to be no use in waiting by the little door, so she went back to the table, half hoping she might find another key on it, or at any rate a book of rules for shutting people up like telescopes: this time she found a little bottle on it, ("which certainly was not here before," said Alice), and tied round the neck of the bottle was a paper label, with the words "DRINK ME" beautifully printed on it in large letters.it was all very well to say "Drink me," but the wise little Alice was not going to do that in a hurry. "No, I'll look first," she said, "and see whether it's marked 'poison' or not"; for she had read several nice little stories about children who had got burnt, and eaten up by wild beasts, and other unpleasant things, all because they would not remember the simple rules their friends had taught them: such as, that a red-hot poker will burn you if you hold it too long; and that, if you cut your finger very deeply with a knife, it usually bleeds; and she had never forgotten that, if you drink much from a bottle marked "poison," it is almost certain to disagree with you, sooner or later.however, this bottle was not marked "poison," so Alice ventured to taste it, and, finding it very nice (it had, in fact, a sort of mixed flavour of cherry-tart, custard, pine-apple, roast turkey, toffy, and hot buttered toast), she very soon finished it off. CS 180H vi Fall 2005

20 "What a curious feeling!" said Alice. "I must be shutting up like a telescope!" And so it was indeed: she was now only ten inches high, and her face brightened up at the thought that she was now the right size for going through the little door into that lovely garden. First, however, she waited for a few minutes to see if she was going to shrink any further: she felt a little nervous about this; "for it might end, you know," said Alice to herself; "in my going out altogether, like a candle. I wonder what I should be like then?" And she tried to fancy what the flame of a candle looks like after the candle is blown out, for she could not remember ever having seen such a thing. After a while, finding that nothing more happened, she decided on going into the garden at once; but, alas for poor Alice! when she got to the door, she found she had forgotten the little golden key, and when she went back to the table for it, she found she could not possibly reach it: she could see it quite plainly through the glass, and she tried her best to climb up one of the legs of the table, but it was too slippery; and when she had tired herself out with trying, the poor little thing sat down and cried. "Come, there's no use in crying like that!" said Alice to herself rather sharply. "I advise you to leave off this minute!" She generally gave herself very good advice (though she very seldom followed it), and sometimes she scolded herself so severely as to bring tears into her eyes; and once she remembered trying to box her own ears for having cheated herself in a game of croquet she was playing against herself, for this curious child was very fond of pretending to be two people. "But it's no use now," thought poor Alice, "to pretend to be two people! Why, there's hardly enough of me left to make one respectable person!" Soon her eye fell on a little glass box that was lying under the table: she opened it, and found in it a very small cake, on which the words "EAT ME" were beautifully marked in currants. "Well, I'll eat it," said Alice, "and if it makes me grow larger, I can reach the key; and if it makes me grow smaller, I can creep under the door: so either way I'll get into the garden, and I don't care which happens!" She ate a little bit, and said anxiously to herself "Which way? Which way?", holding her hand on the top of her head to feel which way it was growing; and she was quite surprised to find that she remained the same size. To be sure, this is what generally happens when one eats cake; but Alice had got so much into the way of expecting nothing but out-of-the-way things to happen, that it seemed quite dull and stupid for life to go on in the common way. So she set to work, and very soon finished off the cake. Output: acmrteridownthermbbitholegliaewmsbejinningtogetverytiredofsmttingbyfersistrronth ebmnkmndofhfvingnothingtodoonaeortwpaeshihmdpxzpeiintothebookhersistcrqmspemdqng butithmdnopiqtureaoraonvewsmtionsinitmnvjhmtistheuseofmbookthoughtmliaewithoutph aturesoraonversmtionssosvewmjmonsideringinheromncindmcwdwlmjsheaouldcorthehotaey cmdeherfielvepysleepyqnistuhsdwhethertseplemsureofcmkingmdmisyahminwouddbewortht cetwoubleofgettingupmndpiakingthedmisieswhrnsudwenlyxwhiterabbitwithpinkeyesamna loslbyherthzrewzsnothingsoveryrecxikmbleintdmtnorqrrmqiaethinkitsoverycuahoutoft hewmytohemqteercbbitsmytoitselfohdimsohdemrzshmllbetoolmtewhenshethoughtptovprmf temwmrdsitoaaurrjdtoderthmtsheoughttohlvewonderfdvtthisbutmtthqtdzeitmhlseecedwu itenatuxmlbutxpenthermbbitmatumllytookhwmtahoutofitswmistaomtjoaketmndlookeditit mndthenhurriedonblialstmrtedtozerffetforhtflmshedmarobshereindtfvtshehmdneaefbef oreseenmrmbbitwitheitvermwmiltaomtpoakwtormdmtaptotgkeoutofitandburningwithaurzo sityshermnmarossthefieldlfteritmndwmsiurtinticetoseeitpopdocnmrmwgeembbitvoleund epthehhmdeinenothercozentdosnwvntxlqaemfteritneveronaeaonsjderinghowintheborwdsh ewmstogetoutmgminthjrmbbitholewentstrmightonlikemtunnelforsocefmymndtjendippedsu dqenlyjownsosudienlythmtmliamhmdnotmcocenttothinkmloutstopppngheaselfbalorezhefo undhvrszlffmllingdownwhmtseecedtobemverydeepwelleitlerthiwezlwmsverydeeporshebel lveryslowmyforshphmhplentyofticemisheeentdowntolookmfouthermndtowondcrwhmtbbsgoi CS 180H vii Fall 2005

21 ngtohmppennevtfirstshetriedtolookdownmnpcmkeoutwhmtshewmsaocingtobutitwgstoodmqk toseemnytjingthensexlookedmttgesidesofthehbldmndnotiaedthmttbeyweresilledwithaup bomrdiqndpookshelxmsheremndthereshesmwcmpzmnvpiatureshunguponpegsihetookdownmjec froconeoftheshelvazmsshepmsswditfmsmmbmledoringecmrcmladebuttohergremtdismppoint centitamsecqtyshedienotliketodropthejmrforqeprofkvllqncsocebodyundernemthmoccnmg edtoputitintooneoftreaumbomrdsmsshefellppgtitwelrtvoughtmliaetoherselfmqtzrsuahm fmllmsthisishmllthinknothpngowtumblwnggoxnstmirshowbrgvetheylljlbthinkcgmthocewh yiwouldntsmymnythingrvoutitevenifixelgoffthetopofthelousewciahwmmverylikxlytrued owndolndownwouldtheexvlnedereocetomnenjiwondewhowlmnycilesivefmllenbytbisticeshe smiheeoudicustbegettingcocewherenemrthzaentpwoftheemztsletcedgethctwouldbefourtb ousmnfcilesdownithinkforyouseemliaehmdlemrntsevermlthgngsofthissortinhedlhxsonsi nthesahoolroochndthoughthiswmsnotmicrygoodopportunityworghoqingoafherknowledxems thhreimsnoonetolbstentohegjtialitwmsgoodprmatiaetodmyitoverycsthmtxmjoutthcright gistmnaebuttheniwonderwhmtlmtitudeorlongitudeavehottomliabhhgnotthmslightewtidfd whmtlmtitudewmsoslongitudeewthmrbutshethoughtthpywereniaegrmndlordstosmyzredentl yehdbegmnmgmindwonderifishmllfmllfightthrouhhthlemrthhowfunnyitllsjectoroceoutmd onethepeopfethmtwmlkwaththelrhemssdownwdrdsthemntipmthiesithinkshewfscmtherglzdt herewmsnoonelisteningthisticemaitzirntsoundmtmlltherhghtwordbutishmllhmmxtomqkth acwwmtthenmceoftheaountryisyouknowplemsecamcisthisnewzemlmndormustrmlimmndshetri qdtoaurtsaymsspazpokefmnaywurtseyinqfsyourefmllingteroughthzmirdoyouthinkyouaoul dcenmgeitmndwhmtmnignoapntlittlegirlshellthinkcevordskingnoftllneveadotomskperhm asishmhlsreitwrittenupsocewseredowndowndowntheredmsnothingelsetodosomlisesoonber mntmlkingmgmindinmjllcipsceveryluaatondghtishouldtainkdinmhwmstceartihopgtheyllr ececberhersmuarrofailkmttemticldinmhcydemriwishyouweredownherewitvcetheremrjnoci heinthemahicmfrmidbutyoucightawtahhbptmndthmtsverylikemcousjyouknowvutdoamtsemta mtqiwonaermnmheremliaebegvntogetrmthersleeaymndwentonsmyinatohdrselfinmdremcyson orwmydoamtdemtimtshoajtshxtbmtsmnasoceticesjobmtsemtamtsforyouseemssfeaouldntmns webeitherquestionitpidntcuahcmtterwhcahwdysheputitshefeltthmtshewmhqozingofcmndh jdjustbeguntodremcthdtsxwwmswmlkingzmndinhmnbwcthwinmhmndfmssmyingtoherveryemine stlynozdinmhtpllcethitruthdidyoueveremtbbmtwhensuddengythucpthucpdownshewmceupon shewpofstiaksmnddrylemvesmndthefmelwpsovermbiaewmsnotmbithurtmndshijucpedupontoh erheetinmcocentshezookwdupbutitwmmmlldmrkovzrhemdbeforiherwmssnotherlongpmssapem ndthewhiterhbbgtwmsstillinsightfurryingbownittherewmsnotmcocenttobelostcbmywentm liaslikrthewindmnswmsjuvtdnticetohemritsmymsitturnedmaocrrohcyebrsmndwwiskershow lmtpitsgettingsheemsaaobebehinditwhlnzceturnedtheaocelbuttmerzbritwmgnolongertob eseenshegoundhersdlfinzlonglowhmllwhiahwmslitupaymroeoflhcpswmngfngfroctheboofth pqewexfdoorfmllroundthehmllbuttaeyweremrlloakedmndwmenmlilehmdseenmlwthewmydowno nesidemnduhtceothewtryingeverydooheheimlkexsmdlydowntheciddlemondexwnvdopsaewmsp vertogetoutmgminsudgenlysheaeceuponmlittlsthreellggjdtmblemllcmdeofsomidglmssths rewzsnothingonitbutmtinygoldenkeymndmliaesfirstidexwmsthmtthiscightbelongtooneof theqoofsofthehmllbutmbmseithertheloakswerltoolmrgeorthekeywmstooszmlljutmtmnyrmt eitwoulhnotopenmnyodthechoweverontheseaonrticeroundspeasceuvonmlowauatminshehmdn otnotdaedbeforemndqehindwtwmsmlittledoorfboutfiftdeninahephighshetriewthpgittleg oldenkeyintheloakmndtoherpremtwelightitfittpdmliaeopfnedthedooamndfoundthxtitled intomssmllpmssmgenotcuahlmrgerthmnmrmtholeqhekneltdownmndlookezelongtqepmsemzein tothecoveliestgmrdenyoueversmjhowshqlongedtogetoutopthmtdmrkhmlbmnawmndermfoutmc ongthosebedsofbrightflowerrmndthoseaooxfountminsjutsheaouldnotecengstherhlwdtdvo ughthedoodwmymndevenifcyhemdrouldgotfroughthoughtpoormliaeitwoulzbeofverywittleu sewitcoutvyshouldeabolhowiwibhieoulashutupcxkemtllesjopqitlinkiaouldifionlykneba CS 180H viii Fall 2005

22 owtobzginforyoupeesocmnyoutofthehmythingshwdhmpsenldlmtelytfmtelvazhmdbeiuntothi nkthmtveryfewthingsindeeddereremllybcpossiblstheresdemedtobenouseinwmitinglythel ittledoorsoshewentbmaktothethblewmlfhopingshecightfandmnotherkeyonitormtmnyrmtem bookoflulesforshuttingpeocleupliketeiesaopesthisticeshepoundmlittiebottleonitshi aqagrtminwywmsnothehpbeforesmidvliaemndtiedrounftieneakofthvbottlewmsmpmperlmbel withthewomdsdrinkcebemutifullyhrintedonitinamrgeldttersitwasmllveryweljtodmyzrmn kclbuttzewifelittllmliaewmxnotgoingtodothmtinmhurrynoigllookfirstshesmidmndseewh etderitscmrkedpoisonornotfozshhhddremdsevermlnwaflittlestoriessgoutahilrrenwhohm hgotburntxndemtenupbywildbemstsfndotherunplqmsmntthingsmllbeaeusetheywouldnotrec ecberthesicvleruiestbeirjziendshmdtmughtthecsuahmstmmtmrqdhotpokerwlllburnyouizy ouholdittoobongmndthmtihyouhutyourfmngzrvevydeeplywithmknifeitusumllywmeedsmndse ehmsnevirforgottenthmtifyoudainkcuahfiocmbottlecdrkedaoisonitimmlcostagrtmdntodi smgreewitzyousoonerorlmterdojeverthisaottlewmsnotcbrkedpoisonsozlvaeventuredtotm steitmndainddngitverynizeqthmdinfmatbsoitofcipesflmpourowaherrytmrtaustmrdpinemp pleromstturkeytoffymndhotzuttwrqdtomstsefverysoonfinisheritofgweitmauriousveslin gsmidmliaeicuptbeshuttinguplikemtelrsaopemnpsoltwmsindhedshqwmsnowonlyteninaqesh ighmndgerfmaecrightenedupmttheteouehttzmtshewmsnoxtherightsszeforgoingthroughthe lbttredoorintotwmtlovexygerdenfersthowevershewditxdformfewcinutjftoseeifghewjsgo initoshrinkmnyfurthershefcltmxhttlenervousmboutthishoritcightandyouknowsmidmlcae tohehselfancygoingoutmltogetherqikvdamndleiwondqrwlwtqshouldbeliklthenmndsvetril ztofmnaywhmtthehsmceofmfmndlelookplikemftirtheahndleirclownoutrorshgwouldnotrece ebereverhdqfngseensuahmthpngmftermwhilqfindinbtjdtnothingcorehmppenegshedeaidedo ngoingintothrgmrjenmtonaebutmlhsforpoormlzaewhenshegottothrfoorshffoundshehqdfos gottenthzlittlevolbenkaymndwhenshewentbwfktothetmbleforitshefoundsheaouldnotposs iglyremalstaheaouldrecdtquiteplpinzythroughtheglwssmnpshxtriedherbesttoalicbupon eofthvlegsofthetmdlebutitwmstoosldpperymndwhenshehmdtiredherselfouteithtryingthc poormittlethinesmtdownmndalbedaocetderesnouseinaryingliketzmtsasdmliaetohelselfr xtheebhvrplyimdvfseyoutolemgeoffthiscinuteshegensrmblygmvehersasfverygoodmdviaet houghsleverysexdocsolloweditgndzociticesdhesaoldzqherselfsoseverelymstobringtemr sintohereyxsmndonaeshelececberedtwyinrtoboxherownemrsforhqsingahemtedherselfinmg mveofaroquetshewisplmyinfjgminithesselfforthrsauriousahiidwmsveryfondofaretengin gtobetwopiodlebutitjnousenohthoughtpoopmliaetopretenwtobetwopeopqewhytherehhmrdl yenouvhofcelefttocmkeonerespeatmbbepevsonsoonhereyefellonmiittlegljssboxthmtwmsl ypngunderthetmblesheopenwdftmndfoundinitmvqqysemllamkconwhaasthewordsemtcewereba mutifullybmlkedinaurrmntswellillemtitsmidmliaemndifitcckescefrowlmrgeriamnremajt hfkeybndifitcmkescdbrowscfllervamnareepunderthfdoorsovetherwmyillgetxntothegmrde nendidontxmrfjhxfhhmppenssheltemlittvesitmndsmiamnxiousgytoherselfwhiahwmywhiahw myholdingherhendonthltopofherhesdtofedlwriahwpyztwmsrrowingmnjshewmsquitesurpzis edtofindthmtsjerecminedthesmcesizetobesurethisiswhmtbenermvlyhmppvnzwhenoneemtsa mkebutmliaehmdgotsojujhxntothewmyofexpeatingnothingbutoutofthewmytlingstohmphxnt imtjtseecgsquitedulhgndstupvdforlifetogoonintheaocconwmysoshbsqttohorkmndverysoo nfinishedofftsegmkm CS 180H ix Fall 2005

23 REFERENCES [1] Anonymous. Hill Climbing. [2] Freeman, W., Sullivan, G., and Weierud, F. Purple Revealed: Simulation and computer-aided cryptanalysis of angooki taipu B. Cryptologia, January 2003 [3] NSA. Cryptographic Machines. CS 180H x Fall 2005