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 Frequency Analysis to Break the Kama Sutra Substitution Cipherby Judith Koeller, University of Waterloo, Canada, jakoelle@math.uwaterloo.caNote: This worksheet demonstrates the use of Maple for breaking a historical substitution cipher using frequency analysis.\302\251 2005 Judith Koeller
In the 4th century BC, the Indian text "Kama Sutra" proposed a method of encrypting text. Each letter of the alphabet was paired with one other letter. A ciphertext was formed by replacing each letter in the plaintext with its paired letter. When this scheme is used in the English language, the number of possible keys is surprisingly high: around 7.9 * 10^12. An exhaustive attack on such a scheme would be unwieldly using a modern computer, and it was certainly infeasible at the time this scheme was suggested.The art of cryptanalysis (systematic techniques used to break ciphers) traces back to Arab Islamic society, from 750-900 AD. al Kindi proposed the technique of frequency analysis to break substitution ciphers like that proposed in the Kama Sutra text. Frequency analysis recognizes that in long blocks of text, certain letters tend to occur much more frequently than others. When a big enough sample text is used in a particular language, certain patterns occur predictably, for example in English text, the most common letters are E, T and N while Q and Z are used infrequently. Different languages have different typical frequency patterns.In this worksheet, letters of the English alphabet will be paired at random according to the Kama Sutra scheme. A block of text will be encrypted by swapping letters according to this pairing. The user can refer to the frequency patterns for the English language and the letter frequencies in the ciphertext to try to determine the letter pairings and hence receover the original plaintext. The Maplet uses the user's pairing of letters to guess at the plaintext, and tracks how many guesses have been made.#"Kama Sutra" Mapletwith(Maplets[Elements]):with(StringTools):with(combinat, randperm):#Returns a text selected at "random"SomeText := proc() local str, nSentences, choice: nSentences := 20: choice := RandomTools[Generate](integer(range=1..nSentences)): str:= array(1..nSentences): str[1] := "If youth, throughout all history, had had a champion to stand up for it; to show a doubting world that a child can think; and, possibly, do it practically, you wouldn't constantly run across folks today who claim that a child don't know anything.": str[2] := "He always wishes me a good weekend, never tells me how his went, even though I say I'm curious about the time he spent. He reticently listens to my vocal fervency. I'm an open book and he's a mystery to me.": str[3] :="Once upon a time there were three little pigs who lived in three houses all in a row. One pig's house was made of straw. The second pig's house was made of wood. The third pig had a house built out of bricks.": str[4] := "In the news today, southern Ontario is digging out from a tornado that hit the town of Fergus. It is unusual for tornadoes to hit this area. The town hall was especially badly damaged.": str[5] := "By the time she submitted her Grade 8 science project on the water quality of the Bay of Quinte, she was well on her way. As a bonus, she discovered that limnology, the study of physical, chemical and biological properties of inland waters, allowed her to pursue other interests like canoeing, scuba diving and travelling.": str[6] := "Since my area of research is Latin American testimonial literature, my main contribution comes from analyzing the different discourse strategies employed by survivors and the different ways they express what is sometimes unbearable to describe. It helps to speak Spanish.": str[7] := "In last Friday's news item on the University of Waterloo visit by Iraqi scientists seeking to reverse an ecological disaster in the country's Mesopotamian Marshes, the Wetlands Group was incorrectly named. The group, including UW Prof. Barry Warner, brings together wetlands specialists from across the campus.": str[8] := "UW and China's Tsinghua University have signed a Memorandum of Understanding for Educational and Scientific Cooperation. The five-year exchange agreement will promote collaboration among faculty members, departments and research institutes.": str[9] := "Faculty from the CEMC and the Faculty of Mathematics including the School of Computer Science will visit Ontario schools, free of charge in most cases. We can conduct contest preparation sessions for students, and discuss studies and careers in mathematics. We also enjoy the opportunity to network with teachers. For more information, contact the CEMC Office.": str[10] := "All grade 11 students can benefit from the Fermat Contest. The Hypatia contest is aimed at students in the top 25% of the class. Hypatia was an ancient mathematician. The Hypatia contest is a long-answer contest.": str[11] := "I can't make up my mind, someone has to help me. She has told me in so many words that she wants me back with her again. She says 'Why don't you come back home to me? Why don't you come where you belong? I want you by my side.'": str[12] := "There were green alligators and long-necked geese, some humpty-backed camels and some chimpanzees, some cats and rats and elephants, and sure as you're born, the loveliest of all was the unicorn.": str[13] := "There once was tree in a yard outside a window. In the spring the tree grew lovely green leaves, but every autumn the leaves turned bright colours and dropped off the tree. Then the tree was bare during the long winter.": str[14] := "Potatoes are good. Potatoes are great. One day I went to the store for some potatoes, but the store was closed and anyways it was out of potatoes. So what could I do but start a quest to the ends of the earth for potatoes?": str[15] := "Launched in 1990 with three staff members and two small camps, ESQ has grown to 18 groups each summer, with more than 100 high school and university leaders involved. Parents from as far away as Hong Kong and the Northwest Territories send children to the camp. Others have asked if similar programs can be started in countries as far away as Cuba and Peru.": str[16] := "The UW libraries are on reduced, between terms hours, with both Dana Porter and the Davis Centre closing at 6 tonight and open only from 12 to 6 on Saturday and Sunday. The map library, and the architecture library in Cambridge, won't be open over the weekend at all. Another library note: they're still cleaning up the first floor of the Dana Porter Library": str[17] :="Warrior football camp is also still in progress, and other teams are preparing for the fall season as well. The soccer Warriors, both men and women, will face squads from McMaster University on Sunday in Hamilton. Men's rugby starts August 31, baseball September 3, football September 5, and so it goes.": str[18] :="Canadian high school students, backed by UW, did well this year at the International Olympiad in Informatics, a computer programming competition in Poland. The four students, selected for their scores on the Canadian Computing Competition, a nation-wide contest organized by UW's mathematics faculty, each earned a medal. Topping the list was a student of Vaughan Road Academy in Toronto, earning a gold medal for his 17th-place finish among 283 contestants from 72 countries.": str[19] :="UW is looking forward to the arrival of some 5,000 new first-year students on the Labour Day weekend. Most will take part in an orientation program before fall term classes begin on September 12. Fee payments are due September 7, or earlier in some cases.": str[20] :="Five respected professional schools are based in the faculties: Accountancy, Architecture, Computer Science, Optometry, and Planning, with a sixth, the School of Pharmacy, to begin admitting students in 2006 or 2007. A program in Software Engineering is offered jointly by the faculties of Engineering and Mathematics. The University is also home base for a stand alone degree granting academic unit, the Centre for Business, Entrepreneurship, and Technology.": return str[choice];end:#Returns a string like c, but with all occurences of the character t1 replaced with t2 and all occurences of t2 replaced with t1SwapPair := proc(t1,t2,c,s) local str, ind, len, Ut1, Lt1, Ut2, Lt2, ThisLetter: str := "": len := Length(convert(c,string)): Ut1 := UpperCase(t1): Lt1 := LowerCase(t1): Ut2 := UpperCase(t2): Lt2 := LowerCase(t2): for ind from 1 by 1 to len do ThisLetter := convert(substring(c,ind),string): if ThisLetter = Ut1 then str:= cat(str,Ut2); elif ThisLetter = Ut2 then str := cat(str,Ut1); elif ThisLetter = Lt1 then str:= cat(str,Lt2); elif ThisLetter = Lt2 then str := cat(str,Lt1); elif IsAlphaNumeric(ThisLetter) then #if a letter or number is not being swapped, include it as it str := cat(str,ThisLetter); else if s then #spaces and punctuation will be included only is the s flag is set to true str := cat(str,ThisLetter); end if: end if: end do: return str;end:#accepts PermString, a string of letters, and c, a text to be changed#Goes through the letters l1, l2, l3, l4,... of PermString in pairs.#In the string c, replaces all occurrences of letter l1 with l2 and l2 with l1, l3 with l4 and l4 with l3, etc. Returns the result.Swap := proc(PermString,c,p,Space) local str, len, ind, t1, t2,ltr, warning, reps: str := c: warning:= "": len := Length(convert(PermString,string)): if (len mod 2) = 1 then warning := "WARNING: YOUR PAIRING OF LETTERS CONTAINS AN ODD NUMBER OF LETTERS. ": end if: for ind from 1 by 1 to 26 do ltr := NthWord("ABCDEFGHIJKLMNOPQRSTUVWXYZ",ind): reps := CountCharacterOccurrences(PermString,UpperCase(ltr))+ CountCharacterOccurrences(PermString,LowerCase(ltr)): if reps > 1 then warning := cat(warning,"WARNING: YOUR PAIRING OF LETTERS CONTAINS THE LETTER "): warning := cat(warning, ltr): warning := cat(warning, " MORE THAN ONCE. "): end if: end do: for ind from 1 by 2 to len do t1 := substring(PermString,ind): t2 := substring(PermString,ind+1): str := SwapPair(t1,t2,str,Space): end do: if str = p then str := cat("CONGRATULATIONS! YOU HAVE RECOVERED THE ORIGINAL PLAINTEXT: ",str): else str := cat(warning,str): end if: return str;end:#Accepts the integer contents of a text box, and returns that integer incremented by one. # Silly function except it gets around data type issues.AddOne := proc(t) local n: n := convert(t,int): n := n+1: return n:end:# For a given text, returns a string with the frequencies of each character in the string, sorted from most to least common character. Frequencies := proc(text) local str: str := CharacterFrequencies(UpperCase(text),"ABCDEFGHIJKLMNOPQRSTUVWXYZ"): str := sort([%], ( u,v) -> evalb(rhs(u) >= rhs(v))); return convert(str,string):end:#For the specified letter pairs, adjusts the ciphertext by swapping letter pairs. Increments the counter for number of attempts.FindPlaintext:=()->Action( Evaluate('plain' = 'Swap(perm,CipherText, PlainText,Spaces)'), Evaluate('attempts' = 'AddOne(attempts)')):PlainText := SomeText(): #Choose some plaintext at "random"PermString := Permute("abcdefghijklmnopqrstuvwxyz",randperm(26)): #Choose a way to pair the letters of the alphabetCipherText := Swap(PermString,PlainText,PlainText,true): #Calculate the ciphertext when the plaintext has the letters swapped accordingly.Freq := Frequencies(CipherText): #Calculate the frequencies of characters in the ciphertextEnglishFreq := Frequencies("aaaaaaa b ccc dddd eeeeeeeeeeeee fff gg hhhh iiiiiii j k llll mmm nnnnnnnn ooooooo ppp q rrrrrrrr ssssss ttttttttt uuu v ww x yy z"): #Calculate "typical" English character frequencies for comparisonLabelWidth := 155:LabelWidth2 := 770:KamaSutraMaplet := Maplet( Window('title'= "Frequency Analysis and the Kama Sutra Substitution Cipher", BoxLayout['BL1']( BoxColumn('halign'=left, BoxRow(Label['l1']("Ciphertext: ",'width'=LabelWidth,'halign'=left), TextBox['cipher'](CipherText,'background'=white,'foreground'= red,'height'=6,'editable'=false,'width'=50,'tooltip'="The ciphertext was made by substituting letters in pairs from the plaintext.")), BoxRow(Label['l2']("Ciphertext Frequencies: ",'width'=LabelWidth,'halign'=left), TextBox['frequencies'](Freq,'background'=white,'foreground'= red,'height'=3,'editable'=false,'width'=50,'tooltip'="Summary of how often each letter appears in the ciphertext")), BoxRow(Label['l3']("English Frequencies: ",'width'=LabelWidth,'halign'=left), TextBox['englfreq'](EnglishFreq,'background'=white,'foreground'= black,'height'=3,'editable'=false,'width'=50,'tooltip'="Summary of how often each letter appears in long blocks of English text")), BoxRow(Label['l5']("Instructions: Enter a string of letters and click 'Guess at Plaintext'. ",'halign'=left,'width'=LabelWidth2)), BoxRow(Label['l52']("For each pair of letters in the string, the ciphertext will have those letters swapped. ",'halign'=left,'width'=LabelWidth2)), BoxRow(Label['l6']("E.g. For the Pairing of Letters ABCD, A will be swapped with B and C will be swapped with D. ",'halign'=left,'width'=LabelWidth2)), BoxRow(Label['l7']("Pairing of Letters: ",'halign'=left), TextField['perm']("ABCD",'background'=white,'foreground'= black,'editable'=true,'font'=Font("Monospaced"),'width'=26,'tooltip'="Determine the pairings of letters that will recover the plaintext."), Button("Guess at Plaintext",'onclick'=FindPlaintext()), Label['l10']("",'foreground'=gray,'width'=160),'halign'=left), BoxRow(Label['l8']("Number of Attempts: ",'halign'=left,'width'=LabelWidth), TextField['attempts']("0",'background'=white,'foreground'= black,'editable'=false,'width'=4), CheckBox['Spaces']('caption'="Show spaces and punctuation",'value'=true,'tooltip'="For an extra challenge, hide the spaces and punctuation.",'onchange'=FindPlaintext()), Label['l11'](" ",'foreground'=gray,'width'=322) ), BoxRow(Label['l4'](" Guess Plaintext: ",'width'=LabelWidth,'halign'=left), TextBox['plain']("",'background'=white,'foreground'= blue,'height'=6,'editable'=false,'width'=50)) ) #box column) #box layout) #window): #mapletMaplets[Display](KamaSutraMaplet);Legal Notice: The copyright for this application is owned by Maplesoft. The application is intended to demonstrate the use of Maple to solve a particular problem. It has been made available for product evaluation purposes only and may not be used in any other context without the express permission of Maplesoft.
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