[...]... separated by hyphens or spaces for convenience The first group indicates the language area, the second identifies the publisher, the third is the publisher’s serial number and the last group is the single digit check digit The sum (known as the check sum) should produce a multiple of 11; if it doesn’t there is an error in the ISBN For example: 1-2 3 4-5 6789-X produces a check sum of 1(1)ϩ2(2)ϩ3(3)ϩ4(4)ϩ5(5)ϩ6(6)ϩ7(7)ϩ8(8)ϩ9(9)ϩ10(10)... what the cryptographers want and the cryptanalysts fear Error detecting and correcting codes A different class of codes are those which are intended to ensure the accuracy of the information which is being transmitted and not to hide its content Such codes are known as error detecting and correcting codes and they have been the subject of a great deal of mathematical research They have been used from the. .. particularly for simple systems The Julius Caesar cipher could be regarded as using a one-page code-book where opposite each letter of the alphabet is printed the letter three positions further on in the alphabet However, for most of the systems we shall be dealing with the distinction will be clear enough In particular the Enigma, which is often erroneously referred to as the Enigma code’, is quite definitely... number, known as the modulus Typical values of the modulus in cryptography are 2, 10 and 26 Whichever modulus is being used all the numbers which occur are replaced by their remainders when they are divided by the modulus If the remainder is negative the modulus is added so that the remainder becomes non-negative If, for example, the modulus is 26 the only numbers that can occur are 0 to 25 If then we add... needed to make the solution both easy to obtain and unique We return to this question later There are two other points worth noting about the example and the substitution alphabet above The first point is that the task of decryption was made easier than it need have been because the words in the cipher were separated by spaces, thus giving away the lengths of the words of the original message There are two... unchanged in the cipher alphabet (M1) Gamblers have been known to make money because of this, for if two people each shuffle a pack of cards and then compare the cards from the packs one at a time there is a 63% chance that at some point they will each draw the same card before they reach the end of the pack The gambler who knows this will suggest to his opponent that they play for equal stakes, with the gambler... Caesar’s cipher The problem of ensuring the security of messages was considered by the ancient Greeks and by Julius Caesar among others The Greeks thought of a bizarre solution: they took a slave and shaved his head and scratched the message on it When his hair had grown they sent him off to deliver the message The recipient shaved the slave’s head and read the message This is clearly both a very insecure... is the ISBN (International Standard Book Number) This is composed of either 10 digits, or 9 digits followed by the letter X (which is interpreted as the number 10), and provides a check that the ISBN does not contain an error The check is carried out as follows: form the sum 1 times (the first digit) ϩ2 times (the second digit) ϩ3 times (the third digit) and so on to ϩ10 times (the tenth digit) The. .. of mathematical ideas, techniques, symbols and jargon [ix] x preface It is the author’s belief, based upon experience, that there is a middle way and that, without going into all the details, it is possible to convey to non-specialists the essentials of some of the mathematics involved even in the more modern cipher systems My aim therefore has been to introduce the general reader to a number of codes. .. ink, (2) the use of microdots, tiny photographs of the message on microfilm, stuck onto the message in a non-obvious place, (3) ‘embedding’ the message inside an otherwise innocuous message, the words or letters of the secret message being scattered, according to some rule, throughout the non-secret message The first two of these have been used by spies; the outstandingly successful ‘double agent’ Juan . throughout the world. He is also the co-author of books on computers in mathematics, computers in literary and linguistic research, and numerical analysis. Codes and ciphers Julius Caesar, the Enigma. Africa http://www.cambridge.org First published in printed format ISBN 0-5 2 1-8 1054-X hardback ISBN 0-5 2 1-0 089 0-5 p a p erback ISBN 0-5 1 1-0 421 8-3 eBook R. F. Churchhouse 2004 2001 (netLibrary) © Contents Prefaceix 1Introduction1 Someaspectsofsecurecommunication1 JuliusCaesar’scipher2 Somebasicdefinitions3 Threestagestodecryption:identification,breakingandsetting4 Codesandciphers5 Assessingthestrengthofaciphersystem7 Errordetectingandcorrectingcodes8 Othermethodsofconcealingmessages9 Modulararithmetic10 Modularadditionandsubtractionofletters11 Gender11 Endmatter12 2FromJuliusCaesartosimplesubstitution13 JuliusCaesarciphersandtheirsolution13 Simplesubstitutionciphers15 Howtosolveasimplesubstitutioncipher17 LetterfrequenciesinlanguagesotherthanEnglish24 Howmanylettersareneededtosolveasimplesubstitutioncipher?26 3Polyalphabeticsystems28 StrengtheningJuliusCaesar:Vigenèreciphers28 HowtosolveaVigenèrecipher30 Indicators33 Depths34 Recognising‘depths’34 HowmuchtextdoweneedtosolveaVigenèrecipher?37 Jefferson’scylinder37 [v] 4Jigsawciphers40 Transpositions40 Simpletransposition40 Doubletransposition44 Otherformsoftransposition48 Assessmentofthesecurityoftranspositionciphers51 Doubleenciphermentingeneral52 5Two-letterciphers54 Monographtodigraph54 MDTMciphers56 Digraphtodigraph58 Playfairencipherment59 Playfairdecipherment60 CryptanalyticaspectsofPlayfair61 DoublePlayfair61 6Codes6 4 Characteristicsofcodes64 One-partandtwo-partcodes65 Codeplusadditive67 7Ciphersforspies72 Stencilciphers73 Bookciphers75 Letterfrequenciesinbookciphers79 Solvingabookcipher79 Indicators86 Disastrouserrorsinusingabookcipher86 ‘Garbo’’sciphers88 One-timepad92 8Producingrandomnumbersandletters94 Randomsequences94 Producingrandomsequences95 Coinspinning95 Throwingdice96 Lotterytypedraws97 Cosmicrays97 Amplifiernoise97 Pseudo-randomsequences98 Linearrecurrences99 Usingabinarystreamofkeyforencipherment100 Binarylinearsequencesaskeygenerators101 contents vi Cryptanalysisofalinearrecurrence104 Improvingthesecurityofbinarykeys104 Pseudo-randomnumbergenerators106 Themid-squaremethod106 Linearcongruentialgenerators107 9TheEnigmaciphermachine110 Historicalbackground110 TheoriginalEnigma112 Enciphermentusingwiredwheels116 EnciphermentbytheEnigma118 TheEnigmaplugboard121 TheAchillesheeloftheEnigma121 Theindicator‘chains’intheEnigma125 Aligningthechains128 IdentifyingR1anditssetting128 DoublyencipheredEnigmamessages132 TheAbwehrEnigma132 10TheHagelinciphermachine133 Historicalbackground133 StructureoftheHagelinmachine134 EnciphermentontheHagelin135 ChoosingthecagefortheHagelin138 Thetheoretical‘workfactor’fortheHagelin142 SolvingtheHagelinfromastretchofkey143 AdditionalfeaturesoftheHagelinmachine147 Theslide147 Identifyingtheslideinaciphermessage148 Overlapping148 SolvingtheHagelinfromciphertextsonly150 11BeyondtheEnigma153 TheSZ42:apre-electronicmachine153 DescriptionoftheSZ42machine155 EnciphermentontheSZ42155 BreakingandsettingtheSZ42158 ModificationstotheSZ42159 12Publickeycryptography161 Historicalbackground161 Securityissues163 Protectionofprogramsanddata163 Enciphermentofprograms,dataandmessages164 Contents. 2004 2001 (netLibrary) © Contents Prefaceix 1Introduction1 Someaspectsofsecurecommunication1 JuliusCaesar’scipher2 Somebasicdefinitions3 Threestagestodecryption:identification,breakingandsetting4 Codesandciphers5 Assessingthestrengthofaciphersystem7 Errordetectingandcorrectingcodes8 Othermethodsofconcealingmessages9 Modulararithmetic10 Modularadditionandsubtractionofletters11 Gender11 Endmatter12 2FromJuliusCaesartosimplesubstitution13 JuliusCaesarciphersandtheirsolution13 Simplesubstitutionciphers15 Howtosolveasimplesubstitutioncipher17 LetterfrequenciesinlanguagesotherthanEnglish24 Howmanylettersareneededtosolveasimplesubstitutioncipher?26 3Polyalphabeticsystems28 StrengtheningJuliusCaesar:Vigenèreciphers28 HowtosolveaVigenèrecipher30 Indicators33 Depths34 Recognising‘depths’34 HowmuchtextdoweneedtosolveaVigenèrecipher?37 Jefferson’scylinder37 [v] 4Jigsawciphers40 Transpositions40 Simpletransposition40 Doubletransposition44 Otherformsoftransposition48 Assessmentofthesecurityoftranspositionciphers51 Doubleenciphermentingeneral52 5Two-letterciphers54 Monographtodigraph54 MDTMciphers56 Digraphtodigraph58 Playfairencipherment59 Playfairdecipherment60 CryptanalyticaspectsofPlayfair61 DoublePlayfair61 6Codes6 4 Characteristicsofcodes64 One-partandtwo-partcodes65 Codeplusadditive67 7Ciphersforspies72 Stencilciphers73 Bookciphers75 Letterfrequenciesinbookciphers79 Solvingabookcipher79 Indicators86 Disastrouserrorsinusingabookcipher86 ‘Garbo’’sciphers88 One-timepad92 8Producingrandomnumbersandletters94 Randomsequences94 Producingrandomsequences95 Coinspinning95 Throwingdice96 Lotterytypedraws97 Cosmicrays97 Amplifiernoise97 Pseudo-randomsequences98 Linearrecurrences99 Usingabinarystreamofkeyforencipherment100 Binarylinearsequencesaskeygenerators101 contents vi Cryptanalysisofalinearrecurrence104 Improvingthesecurityofbinarykeys104 Pseudo-randomnumbergenerators106 Themid-squaremethod106 Linearcongruentialgenerators107 9TheEnigmaciphermachine110 Historicalbackground110 TheoriginalEnigma112 Enciphermentusingwiredwheels116 EnciphermentbytheEnigma118 TheEnigmaplugboard121 TheAchillesheeloftheEnigma121 Theindicator‘chains’intheEnigma125 Aligningthechains128 IdentifyingR1anditssetting128 DoublyencipheredEnigmamessages132 TheAbwehrEnigma132 10TheHagelinciphermachine133 Historicalbackground133 StructureoftheHagelinmachine134 EnciphermentontheHagelin135 ChoosingthecagefortheHagelin138 Thetheoretical‘workfactor’fortheHagelin142 SolvingtheHagelinfromastretchofkey143 AdditionalfeaturesoftheHagelinmachine147 Theslide147 Identifyingtheslideinaciphermessage148 Overlapping148 SolvingtheHagelinfromciphertextsonly150 11BeyondtheEnigma153 TheSZ42:apre-electronicmachine153 DescriptionoftheSZ42machine155 EnciphermentontheSZ42155 BreakingandsettingtheSZ42158 ModificationstotheSZ42159 12Publickeycryptography161 Historicalbackground161 Securityissues163 Protectionofprogramsanddata163 Enciphermentofprograms,dataandmessages164 Contents