,,manual ,,for ,,the ,,solution ,,of ,,military ,,ciphers ,,by ,,parker ,,hitt ,captain of ,infantry1 ,u4 ,s4 ,a4 ,,press ,,of ,,the ,,army ,,service ,,schools ,fort ,leavenworth1 ,kansas #aiaf ,,manual ,,for ,,the ,,solution ,,of ,,military ,,ciphers ,,by ,,parker ,,hitt ,captain of ,infantry1 ,united ,states ,army ,,introduction ,the history of war teems with occasions where the interception of dispatches and orders written in plain language has resulted in defeat and disaster for the force whose intentions thus became known at once to the enemy4 ,for this reason1 prudent generals have used cipher and code messages from time immemorial4 ,the necessity for exact expression of ideas practically excludes the use of codes for military work although it is possible that a special tactical code might be useful for preparation of tactical orders4 ,it is necessary therefore to fall back on ciphers for general military work if secrecy of communication is to be fairly well assured4 ,it may as well be stated here that no practicable military cipher is mathematically indecipherable if intercepted2 the most that can be expected is to delay for a longer or shorter time the deciphering of the message by the interceptor4 ,the capture of messengers is no longer the only means available to the enemy for gaining information as to the plans of a commander4 ,all radio messages sent out can be copied at hostile stations within radio range4 ,if the enemy can get a fine wire within one hundred feet of a buzzer line or within thirty feet of a telegraph line1 the message can be copied by induction4 ,messages passing over commercial telegraph lines1 and even over military lines1 can be copied by spies in the offices4 ,on telegraph lines of a permanent nature it is possible to install high speed automatic sending and receiving machines and thus prevent surreptitious copying of messages1 but nothing but a secure cipher will serve with other means of communication4 ,it is not alone the body of the message which should be in cipher4 ,it is equally important that1 during transmission1 the preamble1 place from1 date1 address and signature be enciphered2 but this should be done by the sending operator and these parts must1 of course1 be deciphered by the receiving operator before delivery4 ,a special operators' cipher should be used for this purpose but it is difficult to prescribe one that would be simple enough for the average operator1 fast and yet reasonably safe4 ,some form of rotary cipher machine would seem to be best suited for this special purpose4 ,it is unnecessary to point out that a cipher which can be deciphered by the enemy in a few hours is worse than useless4 ,it requires a surprisingly long time to encipher and decipher a message1 using even the simplest kind of cipher1 and errors in transmission of cipher matter by wire or radio are unfortunately too common4 ,kerckhoffs has stated that a military cipher should fulfill the following requirements3 #ast4 ,the system should be materially1 if not mathematically1 indecipherable4 #b;d4 ,it should cause no inconvenience if the apparatus and methods fall into the hands of the enemy4 #c;d4 ,the key should be such that it could be communicated and remembered without the necessity of written notes and should be changeable at the will of the correspondents4 #dth4 ,the system should be applicable to telegraphic correspondence4 #eth4 ,the apparatus should be easily carried and a single person should be able to operate it4 #fth4 ,finally1 in view of the circumstances under which it must be used1 the system should be an easy one to operate1 demanding neither mental strain nor knowledge of a long series of rules4 ,a brief consideration of these six conditions must lead to the conclusion that there is no perfect military cipher4 ,the first requirement is the one most often overlooked by those prescribing the use of any given cipher and1 even if not overlooked1 the indecipherability of any cipher likely to be used for military purposes is usually vastly overestimated by those prescribing the use of it4 ,if this were not true1 there would have been neither material for1 nor purpose in1 the preparation of these notes4 ,of the hundreds of actual cipher messages examined by the writer1 at least nine-tenths have been solved by the methods to be set forth4 ,these messages were prepared by the methods in use by the ,united ,states ,army1 the various ,mexican armies and their secret agents1 and by other methods in common use4 ,the usual failure has been with very short messages4 ,foreign works consulted lead to the belief that many ,european powers have used1 for military purposes1 cipher methods which vary from an extreme simplicity to a complexity which is more apparent than real4 ,what effect recent events have had on this matter remains to be seen4 ,it is enough that the cipher experts of practically every ,european country have appealed to the military authorities of their respective countries time and again to do away with these useless ciphers and to adopt something which offers more security1 even at the expense of other considerations4 ,the cipher of the amateur1 or of the non-expert who makes one up for some special purpose1 is almost sure to fall into one of the classes whose solution is an easy matter4 ,the human mind works along the same lines1 in spite of an attempt at originality on the part of the individual1 and this is particularly true of cipher work because there are so few sources of information available4 ,in other words1 the average man1 when he sits down to evolve a cipher1 has nothing to improve upon2 he invents and there is no one to tell him that his invention is1 in principle1 hundreds of years old4 ,the ciphers of the ,abb ,tritheme1 #adii1 are the basis of most of the modern substitution ciphers4 ,in view of these facts1 no message should be considered indecipherable4 ,very short messages are often very difficult and may easily be entirely beyond the possibility of analysis and solution1 but it is surprising what can be done1 at times1 with a message of only a few words4 ,in the event of active operations1 cipher experts will be in demand at once4 ,like all other experts1 the cipher expert is not born or made in a day2 and it is only constant work with ciphers1 combined with a thorough knowledge of their underlying principles1 that will make one worthy of the name4 ,,chapter ,i ,,equipment ,,for ,,cipher ,,work ,success in dealing with unknown ciphers is measured by these four things in the order named2 perseverance1 careful methods of analysis1 intuition1 luck4 ,the ability at least to read the language of the original text is very desirable but not essential4 ,cipher work will have little permanent attraction for one who expects results at once1 without labor1 for there is a vast amount of purely routine labor in the preparation of frequency tables1 the rearrangement of ciphers for examination1 and the trial and fitting of letter to letter before the message begins to appear4 ,the methods of analysis given in these notes cover only the simpler varieties of cipher and it is1 of course1 impossible to enumerate all the varieties of these4 ,it is believed that the methods laid down are sound and several years of successful work along this line would seem to confirm this belief4 ,for more advanced work there is no recourse but to study the ,european authorities whose writings are mostly in ,french1 ,german1 and ,italian and1 unfortunately1 are rarely available in ,english translations4 ,under intuition must be included a knowledge of the general situation and1 if possible1 the special situation which led to the sending of the cipher message4 ,the knowledge or guess that a certain cipher message contains a particular word1 often leads to its solution4 ,as to luck1 there is the old miner's proverb3 ,gold is where you find it4 ,the equipment for an office1 where much cipher work is handled1 will now be considered4 ,the casual worker with ciphers can get along with much less1 but the methods of filing and keeping a record of all messages studied should be followed wherever possible4 ,the interchange of results between individuals and between offices should be encouraged and1 in time of active operations1 should be mandatory4 ,an enemy may be using the same cipher in widely separated parts of the zone of operations and it is useless labor to have many cipher offices working on intercepted messages1 all in the same cipher1 when one office may have the solution that will apply to all of them4 ,cipher work requires concentration and quiet and often must proceed without regard to hours4 ,the office should be chosen with these points in mind4 ,a clerical force is desirable and even necessary if there is much work to do4 ,the clerk or clerks can soon be trained to do the routine part of the analysis4 ,it is believed that each ,field ,army should have such an office where all ciphers intercepted by forces under command of the ,field ,army ,commander should be sent at once for examination4 ,this work naturally falls to the ,intelligence section of the ,general ,staff at this headquarters4 ,a special radio station1 with receiving instruments only1 should be an adjunct to this office and its function should be to copy all hostile radio messages whether in cipher or plain text4 ,such a radio station requires but a small antenna2 one of the pack set type or any amateur's antenna is sufficient1 and the station instruments can be easily carried in a suit case4 ,three thoroughly competent operators should be provided1 so that the station can be listening in during the entire twenty-four hours4 ,the office should be provided with tables of frequency of the language of the enemy1 covering single letters and digraphs2 a dictionary and grammar of that language2 copies of the ,war ,department ,code1 ,western ,union ,code and any other available ones2 types of apparatus or1 at least1 data on apparatus and cipher methods in use by the enemy2 and a safe filing cabinet and card index for filing messages examined4 ,a typewriter is also desirable4 ,the office work on a cipher under examination should be done on paper of a standard and uniform size4 ,printed forms containing twenty-six ruled lines and a vertical alphabet are convenient and save time in preparation of frequency tables4 ,any new cipher methods which are found to be in use by the enemy should1 when solved1 be communicated to all similar offices in the ,army for their information4 ,unless an enemy were exceedingly vigilant and changed keys and methods frequently1 such an office would1 in a few days1 be in a position to disclose completely all intercepted cipher communications of the enemy with practically no delay4 ,,chapter ,,ii ,,principles ,,of ,,mechanism ,,of ,a ,,written ,,language ,with a few exceptions1 notably ,chinese1 all modern languages are constructed of words which in turn are formed from letters4 ,in any given language the number of letters1 and their conventional order is fixed4 ,thus ,english is written with #bf letters and their conventional order is ,a1 ,b1 ,c1 ,d1 ,e1 etc4 ,some letters are used very frequently and others rarely4 ,in fact1 if ten thousand consecutive letters of a text be counted and the frequency of occurrence of each letter be noted1 the numbers found will be practically identical with those obtained from any other text of ten thousand letters in the same language4 ,the relative proportion of occurrence of the various letters will also hold approximately for even very short texts4 ,such a count of a large number of letters1 when it is put in the form of a table1 is known as a frequency table4 ,every language has its own distinctive frequency table and1 for any given language1 the frequency table is almost as fixed as the alphabet4 ,there are minor differences in frequency tables prepared from texts on special subjects4 ,for example1 if the text be newspaper matter1 the frequency table will differ slightly from one prepared from military orders and will also differ slightly from one prepared from telegraph messages4 ,but these differences are very slight as compared with the differences between the frequency tables of two different languages4 ,again there is a fixed ratio of occurrence of every letter with every other for any language and this1 put in table form1 constitutes a table of frequency of digraphs4 ,in the same way a table of trigraphs1 showing the ratio of occurrence of any three letters in sequence1 could be prepared1 but such a table would be very extensive and a count of the more common three letter combinations is usually used4 ,other tables1 such as frequency of initial and final letters of words1 might be of value but the common practice is to put cipher text into groups of five or ten letters each and eliminate word forms4 ,this is almost a necessity in telegraphic and radio communication to enable the receiving operator to check correct receipt of a message4 ,he must get five letters1 neither more nor less1 per word or he is sure a mistake has been made4 ,there is little difficulty1 as a rule1 in restoring word forms in the deciphered message4 ,we will now take up1 in order1 the various frequency tables and linguistic peculiarities of ,english and ,spanish4 ,frequency tables for ,french1 ,german1 and ,italian for single letters will follow4 ,all frequency tables have been re-calculated from at least ten thousand letters of text and compared with existing tables4 ,no marked difference has been found in any case between the re-calculated tables and those already in use4 ,data for ,solution of ,ciphers in ,english ,table ,i4--,normal frequency table4 ,frequency for ten thousand letters and for two hundred letters4 ,this latter is put in graphic form and is necessarily an approximation4 ,taken from military orders and reports1 ,english text4 #aj1jjj ,letters #bjj ,letters ,a #ggh #af #aaaaaaaaaaaaaaaa ,b #ada #c #aaa ,c #bif #f #aaaaaa ,d #djb #h #aaaaaaaa ,e #abgg #bf #aaaaaaaaaaaaaaaaaaaaaaaaaa ,f #aig #d #aaaa ,g #agd #c #aaa ,h #eie #ab #aaaaaaaaaaaa ,i #ffg #ac #aaaaaaaaaaaaa ,j #ea #a #a ,k #gd #b #aa ,l #cgb #g #aaaaaaa ,m #bhh #f #aaaaaa ,n #fhf #ad #aaaaaaaaaaaaaa ,o #hjg #af #aaaaaaaaaaaaaaaa ,p #bbc #d #aaaa ,q #h ,r #fea #ac #aaaaaaaaaaaaa ,s #fbb #ab #aaaaaaaaaaaa ,t #hee #ag #aaaaaaaaaaaaaaaaa ,u #cjh #f #aaaaaa ,v #aab #b #aa ,w #agf #c #aaa ,x #bg ,y #aif #d #aaaa ,z #ag ,vowels ,,aeiou #ch4cg2 consonants ,,lnrst #ca4hf2 consonants ,,jkqxz #a4gg4 ,the vowels may be safely taken as #dj1 consonants ,,lnrst as #cj and consonants ,,jkqxz as #b4 ,order of letters3 ,e ,t ,o ,a ,n ,i ,r ,s ,h ,d ,l ,u ,c ,m ,p ,f ,y ,w ,g ,b ,v ,k ,j ,x ,z ,q4 ,table ,,ii4--,frequency table for telegraph messages1 ,english text4 ,this table varies slightly from the standard frequency table because the common word the is rarely used in telegrams and there is a tendency to use longer and less common words in preparing telegraph messages4 #aj1jjj ,letters #bjj ,letters ,a #hac #af #aaaaaaaaaaaaaaaa ,b #adi #c #aaa ,c #cjf #f #aaaaaa ,d #dag #h #aaaaaaaa ,e #acai #bf #aaaaaaaaaaaaaaaaaaaaaaaaaa ,f #bje #d #aaaa ,g #bja #d #aaaa ,h #chf #h #aaaaaaaa ,i #gaa #ad #aaaaaaaaaaaaaa ,j #db #a #a ,k #hh #b #aa ,l #cib #h #aaaaaaaa ,m #bgc #f #aaaaaa ,n #gah #ad #aaaaaaaaaaaaaa ,o #hdd #ag #aaaaaaaaaaaaaaaaa ,p #bdc #e #aaaaa ,q #ch #a #a ,r #fgg #ad #aaaaaaaaaaaaaa ,s #fef #ac #aaaaaaaaaaaaa ,t #fcd #ac #aaaaaaaaaaaaa ,u #cba #f #aaaaaa ,v #acf #c #aaa ,w #aff #c #aaa ,x #ea #a #a ,y #bjh #d #aaaa ,z #f ,in this table the vowels ,,aeiou #dj4jh1 consonants ,,lnrst #cj4gg and consonants ,,jkqxz #b4be4 ,orders of letters3 ,e ,o ,a ,n ,i ,r ,s ,t ,d ,l ,h ,u ,c ,m ,p ,y ,f ,g ,w ,b ,v ,k ,x ,j ,q ,z4 ,table ,,iii4--,table of frequency of digraphs1 duals or pairs 7,english74 ,this table was prepared from #bj1jjj letters1 but the figures shown are on the basis of #b1jjj letters4 ,for this reason they are1 to a certain extent1 approximate2 that is1 merely because no figures are shown for certain combinations1 we should not assume that such combinations never occur but rather that they are rare4 ,the letters in the horizontal line at the top and bottom are the leading letters2 those in the vertical columns at the sides are the following letters4 ,thus in two thousand letters we may expect to find ,,ah once and ,,ha twenty-six times4 ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a #a #g #aj #bb #c #b #bf #d #b #b #g #h #aa #b #i #ac #ab #i #b #d #a #ab ,b #e #a #b #a #a #a #a #b #b #a #c #a ,c #f #a #a #ad #b #aa #aa #c #b #c #a #a #a #a ,d #f #ab #cj #a #b #d #cj #a #d #a #a #a #a #c ,e #aa #ad #af #ab #b #f #cc #aj #b #f #ah #ad #ab #a #g #cf #aa #ab #b #af #e #a #a ,f #c #b #h #b #a #b #b #a #c #be #c #a #a #a ,g #d #a #c #b #aa #b #c #a ,h #a #aa #b #d #a #d #a #b #a #a #b #aj #ej #c #b ,i #b #a #d #ab #f #e #a #ab #a #e #i #h #ab #a #c #ab #ac #bb #b #c #f #a #a ,j #a ,k #a #a #b #b #a #a ,l #ad #f #b #a #f #a #a #a #f #i #c #f #c #c #b #c #e ,m #g #c #ac #b #b #c #d #a #aj #d #a #a #b ,n #ch #c #be #b #a #ca #c #b #b #ci #d #c #aa #b ,o #a #a #ab #d #h #h #c #ab #ah #b #d #g #h #c #g #ac #ae #bb #b #f #a #e ,p #b #a #h #a #b #d #b #c #b #a #h #a #d #c #a ,q #b #a #a #a ,r #af #a #c #c #dj #c #f #b #f #a #b #a #be #h #b #b #h #aa #b ,s #af #a #c #be #a #b #ag #a #b #a #ab #g #b #i #aa #f #aa #a #f ,t #be #a #c #ab #ac #e #b #c #bj #b #a #bd #h #b #af #bj #aa #f #b #b #g ,u #a #b #a #f #a #c #b #b #c #c #a #ag #a #e #c #e #e #a ,v #c #a #e #e #c #b #e #a ,w #a #b #h #a #a #a #a #b #d #b #c #c ,x #a #d #b #a #a ,y #c #b #b #d #a #a #h #a #b #a #c #a #g ,z #a #a #a ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,table ,,iv4--,order of frequency of common pairs to be expected in a count of #b1jjj letters of military or semi-military ,english text4 7,based on a count of #bj1jjj letters74 ,,th #ej ,,at #be ,,st #bj ,,er #dj ,,en #be ,,io #ah ,,on #ci ,,es #be ,,le #ah ,,an #ch ,,of #be ,,is #ag ,,re #cf ,,or #be ,,ou #ag ,,he #cc ,,nt #bd ,,ar #af ,,in #ca ,,ea #bb ,,as #af ,,ed #cj ,,ti #bb ,,de #af ,,nd #cj ,,to #bb ,,rt #af ,,ha #bf ,,it #bj ,,ve #af ,table ,v4--,table of recurrence of groups of three letters to be expected in a count of #aj1jjj letters of ,english text4 ,,the #hi ,,tio #cc ,,edt #bg ,,and #ed ,,for #cc ,,tis #be ,,tha #dg ,,nde #ca ,,oft #bc ,,ent #ci ,,has #bh ,,sth #ba ,,ion #cf ,,nce #bg ,,men #bj ,table ,,vi4--,table of frequency of occurrence of letters as initials and finals of ,english words4 ,based on a count of #d1jjj words2 this table gives the figures for an average #ajj words and is necessarily an approximation1 like ,table ,,iii4 ,english words are derived from so many sources that it is not impossible for any letter to occur as an initial or final of a word1 although ,q1 ,x and ,z are rare as initials and ,b1 ,i1 ,j1 ,q1 ,v1 ,x and ,z are rare as finals4 ,letters ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,initial #i #f #f #e #b #d #b #c #c #a #a #b #d #b #aj #b - #d #e #ag #b - #g - #c - ,final #a - - #aj #ag #f #d #b - - #a #f #a #i #d #a - #h #i #aa #a - #a - #h - ,it is practically impossible to find five consecutive letters in an ,english text without a vowel and we may expect from one to three with two as the general average4 ,in any twenty letters we may expect to find from #f to #i vowels with #h as an average4 ,among themselves the relative frequency of occurrence of each of the vowels1 7including ,y when a vowel7 is as follows3 ,a1 #ai4e ,e1 #cb4j ,i1 #af4g ,o1 #bj4b ,u1 #h4j ,y1 #c4f ,the foregoing tables give all the essential facts about the mechanism of the ,english language from the standpoint of the solution of ciphers4 ,the use to be made of these tables will be evident when the solution of different types of ciphers is taken up4 ,data for the ,solution of ,ciphers in ,spanish ,the ,spanish language is written with the following alphabet3 ,a ,b ,c ,,ch ,d ,e ,f ,g ,h ,i ,j ,l ,,ll ,m ,n ,o ,p ,q ,r ,,rr ,s ,t ,u ,v ,x ,y ,z while the exact sense often depends upon the use of accents over the vowels4 ,however1 in cipher work it is exceedingly inconvenient to use the permanent digraphs1 ,,ch1 ,,ll and ,,rr and they do not appear as such in any specimens of ,spanish or ,mexican cipher examined4 ,accented vowels and are also not found and we may1 in general1 say that a cipher whose text is ,spanish will be prepared with the following alphabet3 ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,x ,y ,z and the receiver must supply the accents and the tilde over the ,n to conform to the general sense4 ,however1 many ,mexican cipher alphabets contain the letters ,k and ,w4 ,this is particularly true of the ciphers in use by secret service agents who must be prepared to handle words like ,,new ,,york1 ,,wilson and ,,washington4 ,the letters ,k and ,w will1 however1 have a negligible frequency except in short messages where words like these occur more than once4 ,in this connection1 if a cipher contains ,mexican geographical names like ,,chihuahua1 ,,mexico1 ,,muzquiz1 the letters ,h1 ,x and ,z will have a somewhat exaggerated frequency4 ,in ,spanish1 the letter ,q is always followed by ,u and the ,u is always followed by one of the other vowels1 ,a1 ,e1 ,i or ,o4 ,as ,,que or ,,qui occurs not infrequently in ,spanish text1 particularly in telegraphic correspondence1 it is well worth noting that1 if a ,q occurs in a transposition cipher1 we must connect it with ,u and another vowel4 ,the clue to several transposition ciphers has been found from this simple relation4 ,table ,,vii4--,normal frequency table for military orders and reports1 calculated on a basis of #aj1jjj letters of ,spanish text4 ,the graphic form is on a basis of #bjj letters4 #aj1jjj ,letters #bjj ,letters ,a #aceb #bg #aaaaaaaaaaaaaaaaaaaaaaaaaaa ,b #ajb #b #aa ,c #dgd #i #aaaaaaaaa ,d #ebd #aj #aaaaaaaaaa ,e #adjb #bh #aaaaaaaaaaaaaaaaaaaaaaaaaaaa ,f #ia #b #aa ,g #acg #c #aaa ,h #ajb #b #aa ,i #fjf #ab #aaaaaaaaaaaa ,j #da #a #a ,l #eag #aj #aaaaaaaaaa ,m #cjj #f #aaaaaa ,n #fai #ab #aaaaaaaaaaaa ,o #hah #af #aaaaaaaaaaaaaaaa ,p #beg #e #aaaaa ,q #hg #b #aa ,r #gea #ae #aaaaaaaaaaaaaaa ,s #gbd #ad #aaaaaaaaaaaaaa ,t #dbb #h #aaaaaaaa ,u #chg #g #aaaaaaa ,v #he #b #aa ,x #f ,y #ajc #b #aa ,z #db #a #a ,in this table the vowels ,,aeiou #de4fe2 consonants ,,lnrst #cj4cc2 consonants ,,jkqxz #a4gf4 ,order of letters3 ,e ,a ,o ,r ,s ,n ,i ,d ,l ,c ,t ,u ,m ,p ,g ,y 7,,bh7 ,f ,q ,v ,z ,j ,x4 ,table ,,viii4--,table of frequency of digraphs1 duals or pairs1 ,spanish text4 ,like ,table ,,iii1 this table is on the basis of #b1jjj letters although prepared from a count of #bj1jjj letters4 ,for this reason it is1 to a certain extent an approximation2 that is1 merely because no figures are shown for certain combinations1 we should not assume that such combinations never occur but rather that they are rare4 ,the letters in the horizontal lines at the top and bottom are the leading letters2 those in the vertical columns at the sides are the following letters4 ,thus1 in two thousand letters1 we may expect to find ,,ai twice and ,,ia twenty-three times4 ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,x ,y ,z ,a #i #d #ai #aa #e #f #ag #bc #ed #ah #i #c #bj #bi #aa #ba #h #f #b #e ,a ,b #f #c #a #d ,b ,c #bd #f #f #bd #e #c #h #h #i #e #b #b ,c ,d #ca #bi #c #ai #ac #aj #i #d ,d ,e #ab #b #f #ei #aj #a #e #g #b #ab #ah #bb #d #i #ch #be #bh #be #c #c ,e ,f #d #d #d #c #c #a ,f ,g #b #d #h #d #b ,g ,h #b #ab #aj #b #a ,h ,i #b #bc #af #e #b #c #aa #ac #f #aj #e #c ,i ,j #c #b #a ,j ,l #ba #c #f #ci #c #c #g #ba #e #f #ab #b #b ,l ,m #ab #f #e #a #f #ae #g #b #f #a ,m ,n #cb #df #b #h #cb #ab #b ,n ,o #bf #bb #b #f #c #d #i #af #b #h #bj #ae #g #aa ,o ,p #ac #c #b #d #i #b #g #d #aa ,p ,q #aa #e #a #b #c #a ,q ,r #dj #bg #b #d #d #cf #c #aa #ag #c ,r ,s #ci #eb #aj #g #ad #b #ad #c ,s ,t #e #ac #d #d #ah #e #f #cj ,t ,u #b #d #b #f #c #d #e #b #f #d #ag #ae #b #a ,u ,v #b #b #b #b #b #b ,v ,x ,x ,y #e #f #b #e #b #b ,y ,z #a #b #a #d #b ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,x ,y ,z ,table ,,ix4--,order of frequency of common pairs to be expected in a count of #b1jjj letters of ,spanish military orders and reports4 ,based on ,table ,,viii4 ,,de #ei ,,on #cb ,,ac #bd ,,la #ed ,,ad #ca ,,ec #bd ,,es #eb ,,st #cj ,,ci #bc ,,en #df ,,ed #bi ,,ia #bc ,,ar #dj ,,ra #bi ,,do #bb ,,as #ci ,,te #bh ,,ne #bb ,,el #ci ,,er #bg ,,al #ba ,,re #ch ,,co #bf ,,ll #ba ,,or #cf ,,se #be ,,pa #bj ,,an #cb ,,ue #be ,,po #bj ,alphabetic ,frequency ,tables 7,truesdell7 ,frequency of occurrence in #a1jjj letters of text3 ,letter ,french ,german ,italian ,portuguese ,a #hj #eb #aag #adj ,b #f #ah #f #f ,c #cc #ca #de #cd ,d #dj #ea #ca #dj ,e #aig #agc #abf #adb ,f #i #ba #aj #ab ,g #g #db #ag #aj ,h #f #da #f #aj ,i #fe #ha #aad #ei ,j #c #a #a #e ,k #a #aj #a ,l #di #bh #gb #cb ,m #ca #bj #cj #df ,n #gi #abj #ff #dh ,o #eg #bh #ic #aaj ,p #cb #h #cj #bh ,q #ab #a #c #af ,r #gd #fi #fd #fd ,s #ff #eg #di #hh ,t #fe #fj #fj #dc ,u #fb #ea #bi #df ,v #ba #i #bj #ae ,w #a #ae ,x #c #a #a #a ,y #b #a #a #a ,z #a #ad #ab #d ,order of ,frequency ,french ,e ,a ,n ,r ,s ,i ,u ,o ,l ,d ,c ,p ,m ,v ,q ,f ,g ,b ,j ,y ,z ,t ,h ,x ,german ,e ,n ,i ,r ,t ,s ,a ,d ,g ,h ,c ,l ,f ,m ,b ,w ,z ,k ,v ,p ,j ,q ,x ,y ,u ,o ,italian ,e ,a ,i ,o ,l ,n ,r ,t ,s ,c ,d ,m ,u ,v ,g ,z ,f ,b ,q ,p ,h ,portuguese ,e ,a ,o ,s ,r ,i ,n ,m ,t ,d ,c ,l ,p ,q ,v ,f ,g ,b ,j ,z ,x ,y ,u ,h ,graphic ,frequency ,tables ,frequency of occurrence in #bjj letters of text4 ,french ,a #af #aaaaaaaaaaaaaaaa ,b #b #aa ,c #f #aaaaaa ,d #aj #aaaaaaaaaa ,e #ci #aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa ,f #b #aa ,g #a #a ,h #a #a ,i #ac #aaaaaaaaaaaaa ,j #a #a ,k ,l #aj #aaaaaaaaaa ,m #f #aaaaaa ,n #af #aaaaaaaaaaaaaaaa ,o #aa #aaaaaaaaaaa ,p #f #aaaaaa ,q #b #aa ,r #ae #aaaaaaaaaaaaaaa ,s #ac #aaaaaaaaaaaaa ,t #ac #aaaaaaaaaaaaa ,u #ab #aaaaaaaaaaaa ,v #d #aaaa ,w ,x #a #a ,y ,z ,italian ,a #bc #aaaaaaaaaaaaaaaaaaaaaaa ,b #a #a ,c #i #aaaaaaaaa ,d #f #aaaaaa ,e #be #aaaaaaaaaaaaaaaaaaaaaaaaa ,f #b #aa ,g #c #aaa ,h #a #a ,i #bc #aaaaaaaaaaaaaaaaaaaaaaa ,l #ad #aaaaaaaaaaaaaa ,m #f #aaaaaa ,n #ac #aaaaaaaaaaaaa ,o #ai #aaaaaaaaaaaaaaaaaaa ,p #f #aaaaaa ,q ,r #ac #aaaaaaaaaaaaa ,s #aj #aaaaaaaaaa ,t #ab #aaaaaaaaaaaa ,u #f #aaaaaa ,v #d #aaaa ,x ,y ,z #b #aa ,german ,a #aj #aaaaaaaaaa ,b #d #aaaa ,c #f #aaaaaa ,d #aj #aaaaaaaaaa ,e #cb #aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa ,f #d #aaaa ,g #h #aaaaaaaa ,h #h #aaaaaaaa ,i #af #aaaaaaaaaaaaaaaa ,j ,k #b #aa ,l #f #aaaaaa ,m #d #aaaa ,n #bd #aaaaaaaaaaaaaaaaaaaaaaaa ,o #f #aaaaaa ,p #b #aa ,q ,r #ad #aaaaaaaaaaaaaa ,s #aa #aaaaaaaaaaa ,t #ab #aaaaaaaaaaaa ,u #aj #aaaaaaaaaa ,v #b #aa ,w #c #aaa ,x ,y ,z #c #aaa ,portuguese ,a #bh #aaaaaaaaaaaaaaaaaaaaaaaaaaaa ,b #a #a ,c #g #aaaaaaa ,d #h #aaaaaaaa ,e #bh #aaaaaaaaaaaaaaaaaaaaaaaaaaaa ,f #b #aa ,g #b #aa ,h #b #aa ,i #ab #aaaaaaaaaaaa ,j #a #a ,l #f #aaaaaa ,m #i #aaaaaaaaa ,n #aj #aaaaaaaaaa ,o #bb #aaaaaaaaaaaaaaaaaaaaaa ,p #f #aaaaaa ,q #c #aaa ,r #ac #aaaaaaaaaaaaa ,s #ah #aaaaaaaaaaaaaaaaaa ,t #i #aaaaaaaaa ,u #i #aaaaaaaaa ,v #c #aaa ,x ,y ,z #a #a ,,chapter ,,iii ,,technique ,,of ,,cipher ,,examination ,in time of active operations it is important that captured or intercepted cipher messages reach the examining office with the least possible delay4 ,the text of messages1 captured at a distance from the examining office1 should be sent to the office by telegraph or telephone1 the original messages being forwarded to the office as soon thereafter as possible4 ,the preamble1 place from1 date1 address and signature1 give most important clues as to the language of the cipher1 the cipher method probably used1 and even the subject matter of the message4 ,if the whole of a telegraphic or radio message is in cipher1 it is highly probable that the preamble1 place from1 etc41 are in an operators' cipher and are distinct from the body of the message4 ,as these operators' ciphers are necessarily simple1 an attempt should always be made to discover1 by methods of analysis to be set forth later1 the exact extent of the operator's cipher and then to decipher the parts of the messages enciphered with it4 ,in military messages1 we almost invariably find the language of the text to be that of the nation to which the military force belongs4 ,the language of the text of the message of secret agents is1 however1 another matter and1 in dealing with such messages1 we should use all available evidence1 both external and internal1 before deciding finally on the language used4 ,whenever a frequency table can be prepared1 such a table will give the best evidence for this purpose4 ,all work in enciphering and deciphering messages and in copying ciphers should be done with capital letters4 ,there is much less chance of error when working with capitals and1 with little practice1 it is just about as fast4 ,an additional safeguard is to use black ink or pencil for the plain text and colored ink or pencil for the cipher4 ,a separate color may be used for the key when necessary4 ,the following blank form is suggested as convenient for keeping a record of a cipher under examination4 ,it should accompany the cipher through the examining process and should be filled in as the facts are determined4 ,this record1 the original cipher and all notes of work done during the examination1 should be filed together when the examination is completed1 whether the cipher has been solved or not4 ,it may be that other ciphers solved later will give clues to the solution of such unsolved ciphers4 ,the first column of this blank should be filled out from data furnished by the officer obtaining the cipher from the enemy4 ,a general order1 emphasizing the importance of promptly forwarding captured or intercepted ciphers to an examining office1 could specify that a brief report embodying this data should be forwarded with each cipher4 ,the second column of the blank should be filled out progressively as the work proceeds4 ,the office number should be a serial one1 the first cipher examined being ,no4 #a4 ,the date and hour of receipt at examining office will be a check as to the time required to transmit it from place of capture4 ,the spaces ,from1 ,at1 ,to1 ,at1 ,date1 are for the information concerning sender and addressee of the cipher and are to be obtained from the message4 ,in case an operators' cipher has been used1 these parts of the message will have to be deciphered before the blanks can be filled in4 ,intelligence ,section1 ,general ,staff #ast ,field ,army ---------------------------------------- --------- ,place1 ,date ,record of ,cipher ,examination ,this cipher obtained by ,office ,no4 ----------------------- ,received ------------- ----------- ---------------------------------- 7,date7 7,hour7 ---------------------------------- ,from ----------------------------- at ------------------------------- ,at ------------------------------- on ---------------- -------------- ,to ------------------------------- 7date7 7hour7 ,at ------------------------------- ,how being transmitted when obtained4 7,underscore means used and enter ,date ----------------------------- data on sending and receiving stations74 ,probable language of text -------- ,sending ,receiving ,transposition ---------- ,station ,station ------------------------ ,radio ,class ,telephone ,substitution ----------- ,telegraph ,buzzer ------------------------ ,helio ,lantern ,case ----------------------------- ,flag ,cyclist from to ,remarks3 ,foot ,messenger 11 11 ,mtd4 ,messenger 11 11 ,how obtained4 7,underscore means used74 ,captured before delivery ,solution completed --------- ------ to addressee4 ,captured after 7date7 7hour7 delivery to addressee4 ,intercepted1 not received by addressee4 ,copied1 ,language of text ------------------ but received by addressee4 ,key1 7if determined7 -------------- ,remarks3 ----------------------------------- ,type ---------- ,file ,no4 ---------- ----------------------------------- ----------------------------------- ,examiner4 ,the probable language of the text is assumed from the preceding data and1 if necessary1 from internal evidence4 ,thus a cipher from a ,mexican source and not containing ,k or ,w is probably in ,spanish4 ,the class and case are determined by the rules laid down later4 ,the space for remarks is to permit notation of any special features4 ,when the solution is completed1 the date and hour are noted1 the language of text and key 7if determined7 are entered and a type number1 to identify it with other ciphers prepared by the same method 7but not necessarily the same key71 is given to it4 ,the file number is for convenience in filing and in preparation of a card index4 ,the process of examination in an office with one examiner1 one stenographer and one clerk1 might be as follows3 ,on receipt of a captured cipher with accompanying report1 the stenographer makes four copies of the cipher on the typewriter4 ,the clerk and stenographer then check the work4 ,the stenographer then proceeds to fill out the first column and first two lines of the second column of the record blank from the report of the capturing officer1 keeping the original cipher and two copies with the record4 ,he may also fill out the first seven lines of the second column1 if this data is on the captured cipher in plain text4 ,in the meantime the clerk is counting and setting down the whole number of letters of the cipher and the occurrence of ,,aeiou1 ,,lnrst1 and ,,jkqxz1 while the examining officer is looking over the cipher for possible recurring groups of letters and underlining them when found4 ,this work being completed1 the examining officer is in a position1 ordinarily1 to decide on the class of the cipher and he may have found something in his examination which will lead him to the case under the class4 ,the clerk in this preliminary count should keep track of the total occurrence of each of the fifteen check letters and not of the three groups given above4 ,this takes a little longer but when done1 the data for fifteen letters of the alphabet for a frequency table is completed1 leaving only eleven other letters1 and in ,spanish1 but nine1 to be counted1 in case it is necessary to prepare a frequency table4 ,if the examining officer decides the cipher to be of the transposition class1 no further work with frequency tables is necessary4 ,the clerk should proceed to count and set down the number of vowels in each line and column and the examining officer should look for any occurrence of the letter ,q and try to connect it with ,u and another vowel4 ,the stenographer may be set to work putting the cipher into rectangles of different dimensions4 ,the clerk's work gives data for possible rearrangement1 for if the vowels are much out of proportion at any point1 they must be connected with the proper proportion of consonants as a first step in rearrangement4 ,work with transposition ciphers must necessarily include much of the fit and try method4 ,the details of this work are taken up later4 ,if a cipher seems to be a substitution cipher1 the examining officer should look over the frequency of occurrence of each of the fifteen letters counted4 ,if some letters 7it is of no importance at present which ones7 occur much more frequently than others and some occur rarely or not at all1 we may safely decide on ,case #d1 #e or #f and let the clerk proceed to finish the frequency table for the message4 ,on the other hand1 if all the fifteen letters examined occur with somewhere near the same frequency--for example1 the most common letter occurring not over three or four times as often as the least common letter--we may at once eliminate the first three cases and let the clerk proceed to examine the cipher for recurring pairs and groups1 counting the intervening letters1 so that the examining officer may decide whether ,case #g1 or some more complicated case1 should be chosen4 ,if something more complicated than ,case #g has been used and other ciphers are on hand awaiting examination1 the cipher should go into the unsolved file to be worked on when other work permits1 unless the contents of the cipher are believed to be very important4 ,every opportunity should be taken to clean up the unsolved file and1 whenever a message is solved1 the methods should be tried1 if applicable1 to everything remaining in the file4 ,the first few days or weeks after the establishment of an examining office will be the most trying time4 ,when solved ciphers begin to pile up1 the methods of the enemy will be more and more apparent and it will often be possible to determine the method from knowledge of the name of the sender and receiver4 ,when a cipher has been solved1 the solution should be prepared in triplicate and given the serial number of the cipher4 ,any parts which are not clear1 through errors in enciphering or in transmission1 should be underlined or otherwise made conspicuous1 so that the head of the ,intelligence ,section may note them and1 possibly1 from other sources1 supply the deficiency4 ,one of the copies of the cipher and report of examination1 with a copy of the solution1 should be turned over at once to the head of the ,intelligence ,section or to the ,chief of ,staff4 ,the other copies of the solution should be filed with the original cipher1 the report of examination1 and all work done on the cipher4 ,periodically1 say once a week or even daily at the beginning of active operations1 there should be an interchange between all examining offices of solved messages involving new methods used by the enemy4 ,all the examining offices will thus be kept in touch4 ,it may also be possible to assign certain hostile radio stations to each examining office to prevent duplication of work4 ,,chapter ,,iv ,,classes ,,of ,,ciphers ,there are1 in general1 two classes of ciphers4 ,these are the transposition cipher and the substitution cipher4 ,substitution ciphers may be made up of substituted letters1 numerals1 conventional signs or combinations of all three2 and furthermore1 for a single letter of the original text there may be substituted a single letter1 numeral or sign or two or more of each1 or a whole word or group of figures1 combination of conventional signs1 or combinations of all three of these elements4 ,thus substitution ciphers may vary from those of extreme simplicity to those whose complication defies any ordinary method of analysis and whose solution requires the possession of long messages and much time and study4 ,fortunately the more difficult substitution ciphers are rarely used for military purposes1 on account of the time and care required for enciphering and deciphering4 ,transposition ciphers are limited to the characters of the original text4 ,these characters are rearranged singly1 according to some predetermined method or key 7monoliteral transposition71 or whole words are similarly rearranged 7route cipher74 ,there may also be a combination of transposition and substitution methods in enciphering a message but in this case it will fall into the substitution class on first determination and after solution as a substitution cipher it must be handled as a transposition cipher4 ,examples of this case will be given4 ,we may also find transposition or substitution methods applied to words taken from a code book1 or to numbers which represent these words4 ,thus cipher methods blend into code work1 for a code is1 after all1 only a specialized substitution cipher4 ,we can now lay down the rules for determining whether any given cipher belongs to the substitution class or to the transposition class4 ,count the number of letters in the message1 the number of vowels1 ,,aeiou1 the number of the consonants1 ,,lnrst1 and the number of the consonants1 ,,jkqxz4 ,if the text is ,english and the cipher is a transposition cipher1 this proportion will hold2 vowels ,,aeiou constitute #dj of the whole2 consonants ,,lnrst1 #cj and consonants ,,jkqxz1 #c4 ,if the text be ,spanish the proportions for a transposition cipher will be3 vowels ,,aeiou #de1 consonants ,,lnrst1 #cj2 consonants ,,jkqxz1 #b4 ,if these proportions do not hold within #e1 one way or the other1 the cipher is certainly a substitution cipher4 ,note1 however1 that often the end of a message is filled with letters like ,k1 ,x1 ,z to complete cipher words and it is best to neglect the last word or words in making a count4 ,also1 if the cipher be a long one1 this determination can safely be made by taking #ajj or #bjj consecutive letters of the message1 either from the beginning or1 if nulls at the beginning are suspected1 from the interior of the message4 ,the distinction between the route cipher 7transposition7 and the substitution cipher where whole words are substituted for letters of the original text1 must be made on the basis of the words actually used4 ,it is better to consider such a message as a route cipher when the words used appear to have some consecutive meaning bearing on the situation at hand4 ,a substitution cipher of this variety would only be used for transmission of a short message of great importance and secrecy1 and then the chances are that certain words corresponding to ,a1 ,e1 ,n1 ,o and ,t would appear with such frequency as to point at once to the fact that a substitution cipher was used4 ,watch the initial or terminal letters in such a cipher2 they may spell the message4 ,in general1 the determination of class by proportion of vowels1 common consonants and rare consonants may be safely followed4 ,we will now proceed to the examination of the more common varieties of each class of cipher4 ,,chapter ,v ,,examination ,,of ,,transposition ,,ciphers ,after having decided that a cipher belongs to the transposition class1 it remains to decide on the variety of cipher used4 ,as1 by definition1 a transposition cipher consists wholly of characters of the original message1 rearranged according to some law1 we may1 in general1 say that such a cipher offers fewer difficulties in solution than a substitution cipher4 ,a transposition cipher is like a picture puzzle2 the parts are all there and the solution merely involves their correct arrangement4 ,case #a4--;,geometrical ciphers4 ,this case includes all ciphers in which a certain number of the characters are chosen so that they will form a square or rectangle of predetermined dimensions2 and then these characters are arranged according to a geometrical design4 ,taking the message3 ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x of twenty-four letters and assuming a rectangle of six letters horizontally1 and four letters vertically1 we may have3 7a7 ,simple ,horizontal3 ,a ,b ,c ,d ,e ,f ,f ,e ,d ,c ,b ,a ,s ,t ,u ,v ,w ,x ,x ,w ,v ,u ,t ,s ,g ,h ,i ,j ,k ,l ,l ,k ,j ,i ,h ,g ,m ,n ,o ,p ,q ,r ,r ,q ,p ,o ,n ,m ,m ,n ,o ,p ,q ,r ,r ,q ,p ,o ,n ,m ,g ,h ,i ,j ,k ,l ,l ,k ,j ,i ,h ,g ,s ,t ,u ,v ,w ,x ,x ,w ,v ,u ,t ,s ,a ,b ,c ,d ,e ,f ,f ,e ,d ,c ,b ,a 7b7 ,simple ,vertical3 ,a ,e ,i ,m ,q ,u ,d ,h ,l ,p ,t ,x ,u ,q ,m ,i ,e ,a ,x ,t ,p ,l ,h ,d ,b ,f ,j ,n ,r ,v ,c ,g ,k ,o ,s ,w ,v ,r ,n ,j ,f ,b ,w ,s ,o ,k ,g ,c ,c ,g ,k ,o ,s ,w ,b ,f ,j ,n ,r ,v ,w ,s ,o ,k ,g ,c ,v ,r ,n ,j ,f ,b ,d ,h ,l ,p ,t ,x ,a ,e ,i ,m ,q ,u ,x ,t ,p ,l ,h ,d ,u ,q ,m ,i ,e ,a 7c7 ,alternate ,horizontal3 ,a ,b ,c ,d ,e ,f ,f ,e ,d ,c ,b ,a ,x ,w ,v ,u ,t ,s ,s ,t ,u ,v ,w ,x ,l ,k ,j ,i ,h ,g ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,r ,q ,p ,o ,n ,m ,m ,n ,o ,p ,q ,r ,r ,q ,p ,o ,n ,m ,l ,k ,j ,i ,h ,g ,g ,h ,i ,j ,k ,l ,x ,w ,v ,u ,t ,s ,s ,t ,u ,v ,w ,x ,a ,b ,c ,d ,e ,f ,f ,e ,d ,c ,b ,a 7d7 ,alternate ,vertical3 ,a ,h ,i ,p ,q ,x ,d ,e ,l ,m ,t ,u ,x ,q ,p ,i ,h ,a ,u ,t ,m ,l ,e ,d ,b ,g ,j ,o ,r ,w ,c ,f ,k ,n ,s ,v ,w ,r ,o ,j ,g ,b ,v ,s ,n ,k ,f ,c ,c ,f ,k ,n ,s ,v ,b ,g ,j ,o ,r ,w ,v ,s ,n ,k ,f ,c ,w ,r ,o ,j ,g ,b ,d ,e ,l ,m ,t ,u ,a ,h ,i ,p ,q ,x ,u ,t ,m ,l ,e ,d ,x ,q ,p ,i ,h ,a 7e7 ,simple ,diagonal3 ,a ,b ,d ,g ,k ,o ,g ,k ,o ,s ,v ,x ,o ,k ,g ,d ,b ,a ,x ,v ,s ,o ,k ,g ,c ,e ,h ,l ,p ,s ,d ,h ,l ,p ,t ,w ,s ,p ,l ,h ,e ,c ,w ,t ,p ,l ,h ,d ,f ,i ,m ,q ,t ,v ,b ,e ,i ,m ,q ,u ,v ,t ,q ,m ,i ,f ,u ,q ,m ,i ,e ,b ,j ,n ,r ,u ,w ,x ,a ,c ,f ,j ,n ,r ,x ,w ,u ,r ,n ,j ,r ,n ,j ,f ,c ,a ,a ,c ,f ,j ,n ,r ,j ,n ,r ,u ,w ,x ,r ,n ,j ,f ,c ,a ,x ,w ,u ,r ,n ,j ,b ,e ,i ,m ,q ,u ,f ,i ,m ,q ,t ,v ,u ,q ,m ,i ,e ,b ,v ,t ,q ,m ,i ,f ,d ,h ,l ,p ,t ,w ,c ,e ,h ,l ,p ,s ,w ,t ,p ,l ,h ,d ,s ,p ,l ,h ,e ,c ,g ,k ,o ,s ,v ,x ,a ,b ,d ,g ,k ,o ,x ,v ,s ,o ,k ,g ,o ,k ,g ,d ,b ,a 7f7 ,alternate ,diagonal3 ,a ,b ,f ,g ,n ,o ,g ,n ,o ,u ,v ,x ,o ,n ,g ,f ,b ,a ,x ,v ,u ,o ,n ,g ,c ,e ,h ,m ,p ,u ,f ,h ,m ,p ,t ,w ,u ,p ,m ,h ,e ,c ,w ,t ,p ,m ,h ,f ,d ,i ,l ,q ,t ,v ,b ,e ,i ,l ,q ,s ,v ,t ,q ,l ,i ,d ,s ,q ,l ,i ,e ,b ,j ,k ,r ,s ,w ,x ,a ,c ,d ,j ,k ,r ,x ,w ,s ,r ,k ,j ,r ,k ,j ,d ,c ,a ,a ,c ,d ,j ,k ,r ,j ,k ,r ,s ,w ,x ,r ,k ,j ,d ,c ,a ,x ,w ,s ,r ,k ,j ,b ,e ,i ,l ,q ,s ,d ,i ,l ,q ,t ,v ,s ,q ,l ,i ,e ,b ,v ,t ,q ,l ,i ,d ,f ,h ,m ,p ,t ,w ,c ,e ,h ,m ,p ,u ,w ,t ,p ,m ,h ,f ,u ,p ,m ,h ,e ,c ,g ,n ,o ,u ,v ,x ,a ,b ,f ,g ,n ,o ,x ,v ,u ,o ,n ,g ,o ,n ,g ,f ,b ,a 7g7 ,spiral1 clockwise3 ,a ,b ,c ,d ,e ,f ,l ,m ,n ,o ,p ,a ,i ,j ,k ,l ,m ,n ,d ,e ,f ,g ,h ,i ,p ,q ,r ,s ,t ,g ,k ,v ,w ,x ,q ,b ,h ,u ,v ,w ,x ,o ,c ,r ,s ,t ,u ,j ,o ,x ,w ,v ,u ,h ,j ,u ,t ,s ,r ,c ,g ,t ,s ,r ,q ,p ,b ,q ,x ,w ,v ,k ,n ,m ,l ,k ,j ,i ,i ,h ,g ,f ,e ,d ,f ,e ,d ,c ,b ,a ,a ,p ,o ,n ,m ,l 7h7 ,spiral1 counter clockwise3 ,a ,p ,o ,n ,m ,l ,n ,m ,l ,k ,j ,i ,i ,h ,g ,f ,e ,d ,f ,e ,d ,c ,b ,a ,b ,q ,x ,w ,v ,k ,o ,x ,w ,v ,u ,h ,j ,u ,t ,s ,r ,c ,g ,t ,s ,r ,q ,p ,c ,r ,s ,t ,u ,j ,p ,q ,r ,s ,t ,g ,k ,v ,w ,x ,q ,b ,h ,u ,v ,w ,x ,o ,d ,e ,f ,g ,h ,i ,a ,b ,c ,d ,e ,f ,l ,m ,n ,o ,p ,a ,i ,j ,k ,l ,m ,n ,it is simply a matter of inspection to read a message in a cipher of this type1 once the dimensions of the rectangles have been determined4 ,we place the whole or a portion of the message in such rectangles and read horizontally1 vertically and diagonally forward and backward4 ,parts of words will at once be apparent and the whole message is soon deciphered4 ,two examples will show the process4 ,message ,,ilvgioiaeitsrnmanhmng ,this message contains eight vowels or #ch out of twenty-one letters1 and the letters ,,lnrst occur #g times or #cc1 the letters ,,xqjkz not appearing4 ,it is therefore a transposition cipher4 ,twenty-one letters immediately suggest seven columns of three letters each or three columns of seven letters each4 ,trying the former we have3 ,i ,l ,v ,g ,i ,o ,i ,a ,e ,i ,t ,s ,r ,n ,m ,a ,n ,h ,m ,n ,g and reading down each column in succession 7,case #a-;b7 reveals the message to be ,i am leaving this morning4 ,message ,m ,s ,i ,b ,r ,o ,r ,s ,e ,e ,v ,u ,e ,e ,m ,c ,o ,r ,e ,r ,e ,l ,i ,d ,e ,t ,o ,e ,p ,q ,e ,n ,r ,e ,r ,n ,s ,e ,r ,y ,e ,c ,o ,l ,l ,e ,r ,e ,u ,s ,p ,l ,u ,r ,c ,e ,l ,o ,a ,j ,a ,e ,h ,u ,h ,p ,f ,a ,s ,o ,n ,n ,o ,a ,a ,e ,p ,i ,u ,a ,p ,p ,e ,a ,c ,u ,q ,a ,r ,u ,o ,p ,o ,e ,i ,i ,r ,r ,m ,i ,a ,f ,d ,a ,a ,r ,q ,u ,b ,o ,z ,a ,e ,g ,e ,r ,s ,f ,s ,x ,there are #abj letters in this message with #eg vowels or #dg vowels1 and the letters ,,lnrst occur #ca times or #bf of the whole4 ,non-occurrence of ,k and ,w and vowel proportion leads us to the assumption that it is a transposition cipher of a ,spanish text4 ,the factors of #abj are #e #c #b #b #b4 ,we may then have one rectangle of #d #cj or one of #e #bd or two of #e #ab1 or three of #e #h1 or four of #e #f1 or five of #c #h1 or ten of #c #d1 or twenty of #c #b4 ,the message being in a rectangle of #d #cj1 we can inspect it as it stands and this is clearly not the arrangement if it be a geometrical transposition cipher at all4 ,it is best however to try the largest possible rectangles first so we will put it in the form #e #bd1 thus3 ,m ,s ,i ,b ,r ,o ,r ,s ,e ,e ,v ,u ,e ,e ,m ,c ,o ,r ,e ,r ,e ,l ,i ,d ,e ,t ,o ,e ,p ,q ,e ,n ,r ,e ,r ,n ,s ,e ,r ,y ,e ,c ,o ,l ,l ,e ,r ,e ,u ,s ,p ,l ,u ,r ,c ,e ,l ,o ,a ,j ,a ,e ,h ,u ,h ,p ,f ,a ,s ,o ,n ,n ,o ,a ,a ,e ,p ,i ,u ,a ,p ,p ,e ,a ,c ,u ,q ,a ,r ,u ,o ,p ,o ,e ,i ,i ,r ,r ,m ,i ,a ,f ,d ,a ,a ,r ,q ,u ,b ,o ,z ,a ,e ,g ,e ,r ,s ,f ,s ,x ,here an inspection shows this to be ,case #a-;f1 alternate diagonal1 and the text to be ,,me ,,situo ,,sobre ,,parral ,,porque ,,me ,,presencia ,,fue ,,revelada ,,por ,u2 here the sense breaks but note that ,u is the twelfth letter of the line and continue as if the rectangle were #e #ab and we have ,,na ,,pareja ,,qu4 ,now inspect the second rectangle of #e #ab in the same way and the sense continues ,e ,,se ,,me ,,acerco ,y ,,hubo ,,que ,,rechazar ,,por ,,el ,,fuego ,,alli ,,esrero ,,ordenes ,,finisx4 ,the practical way of examining a cipher of this type is to have several men prepare rectangles of different dimensions1 using the letters of the cipher in the order received4 ,the rectangles can be inspected very rapidly when once prepared4 ,note that the dimensions of any rectangle will rarely be such as to contain more than fifty letters1 on account of the necessity of filling up a rectangle with nulls if the number of letters of the message is just a little greater than a multiple of the rectangle4 ,also large rectangles give1 for all but the diagonal method1 whole words in a line or column and these are easily noted4 ,the following ciphers come under ,case #a3 ,case #a-;i4--,the rail fence cipher1 useful as an operators' cipher but permits of no variation and is therefore read almost as easily as straight text when the method is known4 ,the message3 ,,hostile ,,cavalry ,,has ,,retired is written3 ,o ,t ,l ,c ,v ,l ,y ,a ,r ,t ,r ,d ,h ,s ,i ,e ,a ,a ,r ,h ,s ,e ,i ,e and is sent3 ,,otlcv ,,lyart ,,rdhsi ,,eaarh ,,seiex ,case #a-;j4 ,message ,s ,s ,o ,h ,s ,t ,p ,f ,o ,r ,i ,e ,e ,a ,e ,t ,q ,n ,e ,t ,f ,a ,i ,x ,e ,g ,l ,f ,d ,r ,a ,u ,l ,r ,n ,o ,s ,r ,x ,l ,h ,a ,t ,r ,o ,to solve this cipher1 read down the columns in this order #h1 #a1 #ae1 #b1 #ad1 #c1 #ac1 #d1 #ab1 etc4 ,a variation is to arrange the cipher so the columns are read upwards4 ,another is to arrange the ciphers so the columns are read alternately upward and downward4 ,the factors of the number of letters in this case give the shape of the rectangle as usual4 ,it will be seen that there are a great number of possible transposition ciphers that come under ,case #a but practically all of them are useless from a military standpoint because they do not depend on a key which can be readily and frequently changed4 ,however such ciphers constantly crop up in cipher examination1 being used for special communication between parties who consider the regular military ciphers too complicated4 ,thus some of these expedients have been used4 ,reversed ,writing4--7,special case of ,case #a-;a74 ,,leaving ,,tonight is enciphered ,,thginot ,,gnivael or it may be reversed by words1 thus ,,gnivael ,,thginot or by groups of five letters1 thus ,,ivael ,,notgn ,,xthgi4 ,vertical ,writing4--7,special case of ,case #a-;b74 ,same message is enciphered1 ,,lt ,,eo ,,an ,,vi and is sent1 ,,lteoa ,,nviig ,,nhgtx4 ,,ig ,,nh ,,gt ,case #b4--,this case includes all transposition ciphers in which lines and columns of the text are rearranged according to some key word or key number4 ,there are many varieties of this case but their solution usually is arrived at through the methods suggested for ,case #a1 that is1 arrangement into appropriate rectangles and examination of lines and columns for words or syllables4 ,rearrangement of columns or lines follows until the solution is completed4 ,case #b-;a4 ,message ,,hiigf ,,tnghi ,,ntcvn ,,ieiot ,,cyify ,,lhaea ,,esnba ,,eeeen ,,rwgbn ,,ydelr ,,oaesg ,,rnebo ,,vnlda ,,icaoa ,,lcndt ,,irgva ,,cdoie ,,serec ,,dvpei ,,afifl ,,rineh ,,ett ,there are #ajh letters in this message and examination shows it to be a transposition cipher1 ,english text4 ,the number of letters1 #ajh1 immediately suggests a rectangle of #ab #i or #i #ab letters4 ,put into this form we have3 ,vowels ,vowels ,h ,i ,i ,g ,f ,t ,n ,g ,h ,i ,n ,t #c ,h ,i ,i ,g ,f ,t ,n ,g ,h #b ,c ,v ,n ,i ,e ,i ,o ,t ,c ,y ,i ,f #e ,i ,n ,t ,c ,v ,n ,i ,e ,i #d ,y ,l ,h ,a ,e ,a ,e ,s ,n ,b ,a ,e #f ,o ,t ,c ,y ,i ,f ,y ,l ,h #b ,e ,e ,e ,n ,r ,w ,g ,b ,n ,y ,d ,e #d ,a ,e ,a ,e ,s ,n ,b ,a ,e #f ,l ,r ,o ,a ,e ,s ,g ,r ,n ,e ,b ,o #e ,e ,e ,e ,n ,r ,w ,g ,b ,n #c ,v ,n ,l ,d ,a ,i ,c ,a ,o ,a ,l ,c #e ,y ,d ,e ,l ,r ,o ,a ,e ,s #d ,n ,d ,t ,i ,r ,g ,v ,a ,c ,d ,o ,i #d ,g ,r ,n ,e ,b ,o ,v ,n ,l #b ,e ,s ,e ,r ,e ,c ,d ,v ,p ,e ,i ,a #f ,d ,a ,i ,c ,a ,o ,a ,l ,c #e ,f ,i ,f ,l ,r ,i ,n ,e ,h ,e ,t ,t #d ,n ,d ,t ,i ,r ,g ,v ,a ,c #b ,d ,o ,i ,e ,s ,e ,r ,e ,c #e ,d ,v ,p ,e ,i ,a ,f ,i ,f #d ,l ,r ,i ,n ,e ,h ,e ,t ,t #c ,the vowel count of the lines shows the first arrangement to be the more likely4 ,we will now number the columns and try pairing off certain ones which in no line would give impossible combinations of letters4 #a #b #c #d #e #f #g #h #i #aj #aa #ab ,h ,i ,i ,g ,f ,t ,n ,g ,h ,i ,n ,t ,c ,v ,n ,i ,e ,i ,o ,t ,c ,y ,i ,f ,y ,l ,h ,a ,e ,a ,e ,s ,n ,b ,a ,e ,e ,e ,e ,n ,r ,w ,g ,b ,n ,y ,d ,e ,l ,r ,o ,a ,e ,s ,g ,r ,n ,e ,b ,o ,v ,n ,l ,d ,a ,i ,c ,a ,o ,a ,l ,c ,n ,d ,t ,i ,r ,g ,v ,a ,c ,d ,o ,i ,e ,s ,e ,r ,e ,c ,d ,v ,p ,e ,i ,a ,f ,i ,f ,l ,r ,i ,n ,e ,h ,e ,t ,t ,these combinations appear among others3 #a #f #b #d #e #b ,h ,t ,i ,g ,f ,i ,c ,i ,v ,i ,e ,v ,y ,a ,l ,a ,e ,l ,e ,w ,e ,n ,r ,e ,l ,s ,r ,a ,e ,r ,v ,i ,n ,d ,a ,n ,n ,g ,d ,i ,r ,d ,e ,c ,s ,r ,e ,s ,f ,i ,i ,l ,r ,i ,the word ,,fight stares at us from the first line2 let us arrange the columns thus3 #e #b #d #a #f #c ,f ,i ,g ,h ,t ,i ,e ,v ,i ,c ,i ,n ,e ,l ,a ,y ,a ,h ,r ,e ,n ,e ,w ,e ,e ,r ,a ,l ,s ,o ,a ,n ,d ,v ,i ,l ,r ,d ,i ,n ,g ,t ,e ,s ,r ,e ,c ,e ,r ,i ,l ,f ,i ,f ,we have the words ,,fighti7,,ng71 ,,vicin7,,ity71 ,,renewe7,d71 ,,andvil7,,la71 ,,rdingt7,o71 ,,rece7,,ived74 ,with this to go on1 we must choose column #aa as the next one and then in order1 columns #h1 #aj1 #g1 #ab1 #i4 ,but note that the order #aa1 #h1 #aj1 #g1 #ab1 #i1 is the same as the order #e1 #b1 #d1 #a1 #f1 #c4 ,the message was written in twelve columns and the columns have been transposed in that order4 ,we may1 although it is entirely unnecessary1 speculate on the key word used4 ,it was probably ,m ,e ,x ,i ,c ,o #d #b #f #c #a #e meaning that the #dth column of the plain text was transferred in enciphering so it became our #ast1 the #b;d column remained the #b;d2 the #fth column became our #c;d1 etc4 ,actually1 this cipher was solved because the word ,,villa was suspected and all the necessary letters were found in line six of the arrangement in twelve columns4 ,the order #a1 #f1 #c1 #aa1 #h was tried and gave this result4 #a #f #c #aa #h ,h ,t ,i ,n ,g ,c ,i ,n ,i ,t ,y ,a ,h ,a ,s ,e ,w ,e ,d ,b ,l ,s ,o ,b ,r ,v ,i ,l ,l ,a ,n ,g ,t ,o ,a ,e ,c ,e ,i ,v ,f ,i ,f ,t ,e ,the remainder of the solution followed the lines already laid down and1 naturally1 offered no difficulties1 in view of the large number of connected syllables available4 ,case #b-;b4 ,message ,,slcof ,,weetn ,,ebrdo ,,orvym ,,ffedi ,,nmtec ,,roiar ,,perho ,,esets ,,rfbhl ,,tenah ,,optau ,,somtl ,,rtett ,,ascbh ,,niodc ,,renen ,,aaprd ,,lacye ,,eciie ,,sgufn ,this is a transposition cipher1 ,english text1 and contains #aje letters4 ,the factors of #aje are #e #c #g so that we must investigate the following rectangles2 #e #ba1 #ae #g1 three of #e #g1 five of #c #g and seven of #e #c4 #ba #e ,vowels ,s ,l ,c ,o ,f ,w ,e ,e ,t ,n ,e ,b ,r ,d ,o ,o ,r ,v ,y ,m ,f #f ,f ,e ,d ,i ,n ,m ,t ,e ,c ,r ,o ,i ,a ,r ,p ,e ,r ,h ,o ,e ,s #i ,e ,t ,s ,r ,f ,b ,h ,l ,t ,e ,n ,a ,h ,o ,p ,t ,a ,u ,s ,o ,m #g ,t ,l ,r ,t ,e ,t ,t ,a ,s ,c ,b ,h ,n ,i ,o ,d ,c ,r ,e ,n ,e #f ,n ,a ,a ,p ,r ,d ,l ,a ,c ,y ,e ,e ,c ,i ,i ,e ,s ,g ,u ,f ,n #i ,vowels #a #b #a #b #a #j #a #d #j #a #c #c #a #c #c #c #a #a #c #b #a ,the vowel count of the columns of the rectangle #e #ba is very satisfactory4 ,let us consider it as three blocks of #e #g each1 since we must do this ultimately1 and make a vowel count of columns for these blocks4 #e #ba ,vowels ,s ,l ,c ,o ,f #a ,w ,e ,e ,t ,n #b ,e ,b ,r ,d ,o #b ,o ,r ,v ,y ,m #a ,f ,f ,e ,d ,i #b ,n ,m ,t ,e ,c #a ,r ,o ,i ,a ,r #c ,p ,e ,r ,h ,o #b ,e ,s ,e ,t ,s #b ,r ,f ,b ,h ,l #j ,t ,e ,n ,a ,h #b ,o ,p ,t ,a ,u #c ,s ,o ,m ,t ,l #a ,r ,t ,e ,t ,t #a ,a ,s ,c ,b ,h #a ,n ,i ,o ,d ,c #b ,r ,e ,n ,e ,n #b ,a ,a ,p ,r ,d #b ,l ,a ,c ,y ,e #b ,e ,c ,i ,i ,e #d ,s ,g ,u ,f ,n #a ,vowels #g #i #h #g #f ,column #a #b #c #d #e ,vowels1 #ast block #b #b #c #b #b ,vowels1 #b;d block #b #c #b #b #b ,vowels1 #c;d block #c #d #c #b #b ,this is also excellent1 so we will try three blocks #e #g and see if rearrangement of horizontal lines will give results reading the columns vertically4 #a ,s ,l ,c ,o ,f ,p ,e ,r ,h ,o ,a ,s ,c ,b ,h #b ,w ,e ,e ,t ,n ,e ,s ,e ,t ,s ,n ,i ,o ,d ,c #c ,e ,b ,r ,d ,o ,r ,f ,b ,h ,l ,r ,e ,n ,e ,n #d ,o ,r ,v ,y ,m ,t ,e ,n ,a ,h ,a ,a ,p ,r ,d #e ,f ,f ,e ,d ,i ,o ,p ,t ,a ,u ,l ,a ,c ,y ,e #f ,n ,m ,t ,e ,c ,s ,o ,m ,t ,l ,e ,c ,i ,i ,e #g ,r ,o ,i ,a ,r ,r ,t ,e ,t ,t ,s ,g ,u ,f ,n ,among other combinations are3 #c ,e ,b ,r ,d ,o ,r ,f ,b ,h ,l ,r ,e ,n ,e ,n #b ,w ,e ,e ,t ,n ,e ,s ,e ,t ,s ,n ,i ,o ,d ,c #a ,s ,l ,c ,o ,f ,p ,e ,r ,h ,o ,a ,s ,c ,b ,h #e ,f ,f ,e ,d ,i ,o ,p ,t ,a ,u ,l ,a ,c ,y ,e #g ,r ,o ,i ,a ,r ,r ,t ,e ,t ,t ,s ,g ,u ,f ,n ,the addition of line #f above line #c and line #d below line #g will complete this cipher4 ,the successive columns should be read downward4 ,case #b-;c4 ,in this case1 both lines and columns are rearranged by means of a key word or key words4 ,the method of solution is the same as ,case #b-;a and #b-;b except that the lines must be rearranged after the columns have been correctly arranged1 or in some cases1 vice versa4 ,this cipher is not infrequently met with because it seems to offer safety by use of two key words and by the great but only apparent complexity of the method4 ,message ,,wvgae ,,egenl ,,tftoh ,,teief ,,rbtse ,,ineng ,,onwrm ,,gxixn ,,goitn ,,romro ,,espal ,,hneac ,,udnnh ,,derme ,this is a transposition cipher1 ,english text and the number of letters1 #gj1 leads us to try rectangles of #aj #g and #g #aj4 ,vowels ,vowels ,w ,v ,g ,a ,e ,e ,g ,e ,n ,l #d ,w ,v ,g ,a ,e ,e ,g #c ,t ,f ,t ,o ,h ,t ,e ,i ,e ,f #c ,e ,n ,l ,t ,f ,t ,o #b ,r ,b ,t ,s ,e ,i ,n ,e ,n ,g #c ,h ,t ,e ,i ,e ,f ,r #c ,o ,n ,w ,r ,m ,g ,x ,i ,x ,n #b ,b ,t ,s ,e ,i ,n ,e #c ,g ,o ,i ,t ,n ,r ,o ,m ,r ,o #d ,n ,g ,o ,n ,w ,r ,m #a ,e ,s ,p ,a ,l ,h ,n ,e ,a ,c #d ,g ,x ,i ,x ,n ,g ,o #b ,u ,d ,n ,n ,h ,d ,e ,r ,m ,e #c ,i ,t ,n ,r ,o ,m ,r #b ,o ,e ,s ,p ,a ,l ,h #c ,n ,e ,a ,c ,u ,d ,n #c ,n ,h ,d ,e ,r ,m ,e #b ,the first form looks the more likely from the vowel count4 ,we proceed to number the columns and lines and try rearrangement of columns so as to obtain possible letter combinations from every line4 #a #b #c #d #e #f #g #h #i #aj #a ,w ,v ,g ,a ,e ,e ,g ,e ,n ,l #b ,t ,f ,t ,o ,h ,t ,e ,i ,e ,f #c ,r ,b ,t ,s ,e ,i ,n ,e ,n ,g #d ,o ,n ,w ,r ,m ,g ,x ,i ,x ,n #e ,g ,o ,i ,t ,n ,r ,o ,m ,r ,o #f ,e ,s ,p ,a ,l ,h ,n ,e ,a ,c #g ,u ,d ,n ,n ,h ,d ,e ,r ,m ,e ,among other combinations we have these3 #c #e #a #d #b #h #aj #f #i #g #a ,g ,e ,w ,a ,v ,e ,l ,e ,n ,g #b ,t ,h ,t ,o ,f ,i ,f ,t ,e ,e #c ,t ,e ,r ,s ,b ,e ,g ,i ,n ,n #d ,w ,m ,o ,r ,n ,i ,n ,g ,x ,x #e ,i ,n ,g ,t ,o ,m ,o ,r ,r ,o #f ,p ,l ,e ,a ,s ,e ,c ,h ,a ,n #g ,n ,h ,u ,n ,d ,r ,e ,d ,m ,e ,a very casual inspection of the lines shows that they should be rearranged in order #f1 #a1 #b1 #g1 #c1 #e1 #d1 as follows3 #c #e #a #d #b #h #aj #f #i #g #f ,p ,l ,e ,a ,s ,e ,c ,h ,a ,n #a ,g ,e ,w ,a ,v ,e ,l ,e ,n ,g #b ,t ,h ,t ,o ,f ,i ,f ,t ,e ,e #g ,n ,h ,u ,n ,d ,r ,e ,d ,m ,e #c ,t ,e ,r ,s ,b ,e ,g ,i ,n ,n #e ,i ,n ,g ,t ,o ,m ,o ,r ,r ,o #d ,w ,m ,o ,r ,n ,i ,n ,g ,x ,x ,although of no particular importance1 it may be stated that the column key in this case was ,,grand and the line key was ,,central1 both used as in enciphering ,case #b-;a4 ,case #c4 ,route ciphers4 ,in this case1 whole words of the message are transposed according to some of the methods of ,case #a or #b or their equivalents4 ,the route cipher is little used at present4 ,its development and use during the ,civil ,war was caused by the inability of the telegraphers of that day to handle regular cipher matter correctly and rapidly4 ,it was1 even in those days1 frankly only a delaying cipher and1 to be of any value1 had to be filled with meaningless words to conceal the message proper4 ,an example from the ,signal ,book will suffice to show the general character of route ciphers4 ,to one familiar with monoliteral transposition ciphers1 even the best of route ciphers offers but little difficulty4 ,to encipher the message ',,move ,,daylight4 ,,enemy ,,approaching ,,from ,,north4 ,,prisoners ,,say ,,strength ,,one ,,hundred ,,thousand4 ,,meet ,,him ,,as ,,planned4' arrange as follows3 ,,move ,,strength ,,planned ,,say ,,daylight ,,one ,,as ,,prisoners ,,enemy ,,hundred ,,him ,,north ,,approaching ,,thousand ,,meet ,,from ,here the route is down the first column1 up the fourth1 down the second and up the third4 ,this cipher was often complicated by the introduction of nulls for every fifth word4 ,thus the above message might be sent3 ,,move ,,strength ,,planned ,,say ,,never ,,daylight ,,one ,,as ,,prisoners ,,leaving ,,enemy ,,hundred ,,him ,,north ,,unchanged ,,approaching ,,thousand ,,meet ,,from ,,come4 ,the words in italics are nulls and not a part of the message and the receiver eliminates them before arranging his message in columns to get the sense of it4 ,as an additional complication1 it was customary for each correspondent to have a dictionary or code in which the names of all prominent generals and places and many of the prominent verbs1--as to march1 to sail1 to encamp1 to attack1 to retreat1--were represented by other words4 ,a route cipher using the code words of the ,war ,department code might have some advantages over the method of enciphering code messages as prescribed in that ,code4 ,general ,remarks on ,transposition ,ciphers ,it is the consensus of opinion of experts that the transposition cipher is not the best one for military purposes4 ,it does not fulfill the first1 second1 and third of ,kerckhoffs' requirements as to indecipherability1 safety when apparatus and method fall into the hands of the enemy1 and dependability on a readily changeable key word4 ,however1 transposition ciphers are often encountered4 ,they are favorites with those who find the substitution ciphers too difficult and too tedious to handle and who believe that their transposition methods are either absolutely indecipherable or sufficiently so for the purpose of concealing the text of a message for the time being4 ,they seem to be particularly popular with secret agents and spies1 presumably because special apparatus is rarely necessary in enciphering and deciphering4 ,although the number of transposition methods is legion1 they can practically all be considered under one of the three cases already discussed4 ,it is surprising how often transposition ciphers prepared by complicated rules1 will1 on analysis1 be seen to be very simple4 ,to be successful in solving transposition ciphers1 one should constantly practice reading backward and up and down columns1 so that the common combinations of letters are as quickly identified when seen thus as when encountered in straight text4 ,combinations like ,,eht1 ,,lliw1 ,,rof1 ,,dna1 etc41 should be appreciated immediately as common words written backward4 ,a study of the table of frequency of digraphs or pairs is also excellent practice and such a table should be at hand when a transposition cipher is under consideration4 ,it assists greatly if ,case #b be encountered and is of considerable use in solving ,case #a4 ,the solution of route ciphers is necessarily one of try and fit1 with the knowledge that such ciphers usually are read up and down columns4 ,it is not believed that route ciphers will often be met with at the present day4 ,,chapter ,,vi ,,examination ,,of ,,substitution ,,ciphers ,when an unknown cipher has been put into the substitution class by the methods already described we may proceed to decide on the variety of substitution cipher which has been used4 ,there are a few purely mechanical ways of solving some of the simple cases of substitution ciphers but as a general rule some or all of the following determinations must be made3 #a4 ,by preparation of a frequency table for the message we determine whether one or more substitution alphabets have been used and1 if one only has been used1 this table leads to the solution4 #b4 ,by certain rules we determine how many alphabets have been used1 if there are more than one1 and then isolate and analyze each alphabet by means of a frequency table4 #c4 ,if the two preceding steps give no results we have to deal with a cipher with a running key1 a cipher of the ,playfair type1 or a cipher where two or more characters are substituted for each letter of the text4 ,some special cases under this third head will be given but1 in general1 military ciphers of the substitution class will usually be found to come under the first two heads1 on account of the time and care required in the preparation and deciphering of messages by the last named methods and the necessity1 in many cases1 of using complicated machines for these processes4 ,case #d-;a4 ,message ,,obqfo ,,bpbrp ,,qbaml ,,obhif ,,pilfq ,,fjbox ,,oflnr ,,bixoz ,,el ,from the recurrence of ,b1 ,f and ,o1 we may conclude that a single substitution alphabet was used for this message4 ,if so and if the alphabet runs in the same order and direction as the regular alphabet1 the simplest way to discover the meaning of the message is to take the first two words and write alphabets under each letter as follows1 until some line makes sense3 ,o ,b ,q ,f ,o ,b ,p ,b ,r ,p ,p ,c ,r ,g ,p ,c ,q ,c ,s ,q ,q ,d ,s ,h ,q ,d ,r ,d ,t ,r ,r ,e ,t ,i ,r ,e ,s ,e ,u ,s ,the word ,,retirese occurs in the fourth line1 and1 if the whole message be handled in this way we find the rest of the fourth line to read ,,usted ,,por ,,el ,,mismo ,,itinerario ,,que ,,marcho4 ,the message was enciphered using an alphabet where ,a ,x1 ,b ,y1 ,c ,z1 ,d ,a1 etc4 noting that as this message is in ,spanish the letters ,k and ,w do not appear in the alphabet4 ,case #d-;b4 ,message ,,hujzh ,,uiupn ,,ozyts ,,vqxmi ,,smomx ,,mqhud ,,umrei ,,sesju ,,ag ,this is a message in ,spanish4 ,we will handle it as in case #d-;a1 setting down the whole message4 ,,hujzhuiu ,,pnozy ,,tsv ,,qx ,,mismo ,,mxmqhudumr ,,eis ,,esjuag ,,ivlaivjv ,,qopaz ,,utx ,,ry ,a,a ,,nynrivevns ,,fjt ,,ftlvbh ,,jxmbjxlx ,,rpqba ,,vuy ,,sz ,,ozosjxfxot ,,glu ,,gumxci ,,lynclymy ,,sqrcb ,,xvz ,,ta ,,paptlygypu ,,hmv ,,hvnydj ,,mzodmznz ,,trsdc ,,yxa ,,ub ,,qbqumzhzqv ,,inx ,,ixozel ,,napenaoa ,,usted ,,zyb ,,vc ,,rcrvnaiarx ,,joy ,,jypafm ,,obqfobpb ,a,u ,,azc ,,xd ,,sdsxobjbsy ,,lpz ,,lzqbgn ,,pcrgpcqc ,,bad ,,ye ,,tetypclctz ,,mqa ,,marcho ,,qdshqdrd ,,cbe ,,zf ,,ufuzqdmdua ,,nrb ,a,s ,,retirese ,,dcf ,,ag ,,vgvarenevb ,,osc ,a,q ,,edg ,,bh ,,xhxbsfofxc ,,ptd ,,feh ,,ci ,,yiyctgpgyd ,,que ,,gfi ,,dj ,,zjzduhqhze ,a,o ,,hgj ,,el ,,alaeviriaf ,,ihl ,a,m ,,bmbfxjsjbg ,,jim ,,cncgyltlch ,,ljn ,,dodhzmumdi ,,mlo ,,epeianvnej ,,nmp ,,fqfjboxofl ,,onq ,,grglcpypgm ,,por ,,hshmdqzqhn ,a,e ,,itinerario ,a,d ,here each word of the message comes out on a different line1 and noting in each case the letter corresponding to ,a1 we have the word ,,quemados which is the key4 ,the cipher alphabet changed with each word of the message4 ,a variation of this case is where the cipher alphabet changes according to a key word but the change comes every five letters or every ten letters of the message instead of every word4 ,the text of the message can be picked up in this case with a little study4 ,note in using case #d that if we are deciphering a ,spanish message we use the alphabet without ,k or ,w as a rule1 altho if the letters ,k or ,w appear in the cipher it is evidence that the regular ,english alphabet is used4 ,case #e-;a4 ,message ,,dnwlw ,,mxyqj ,,anrsa ,,rlpte ,,cabcq ,,rlnec ,,lmiwl ,,xzqtt ,,qiwry ,,zwnsm ,,bknwr ,,ymapl ,,asdan ,this message contains ,k and ,w and therefore we expect the ,english alphabet to be used4 ,the frequency of occurrence of ,a1 ,l1 ,n1 ,r and ,w has lead us to examine it under case #d but without result4 ,let us set down the first two words and decipher them with a cipher disk set ,a to ,a and then proceed as in case #d4 ,cipher message ,,dnwlwmxyqj ,deciphered ,a to ,a ,,xnepeodckr ,b ,,yofqfpedls ,c ,,zpgrgqfemt ,d ,,aqhshrgfnu ,e ,,britishgov ,the message is thus found to be enciphered with a cipher disk set ,a to ,e and the text is3 ,,british ,,government ,,placed ,,contracts ,,with ,,following ,,firms ,,during ,,september4 ,case #e-;b4 ,same as case #d-;b except that the cipher message must be deciphered by means of a cipher disk set ,a to ,a before proceeding to make up the columns of alphabets4 ,the words of the deciphered message will be found on separate lines1 the lines being indicated as a rule by a key word which can be determined as in case #d-;b4 ,the question of alphabetic frequency has already been discussed in considering the mechanism of language4 ,it is a convenient thing to put the frequency tables in a graphic form and to use a similar graphic form in comparing unknown alphabets with the standard frequency tables4 ,for instance the standard ,spanish frequency table put in graphic form is here presented in order to compare with it the frequency table for the message discussed in case #d-;a4 ,standard ,spanish ,table for ,message frequency table ,case #d-;a ,a #aaaaaaaaaaaaaaaaaaaaaaaaaaa #bg ,a #a #a ,b #aa #b ,b #aaaaaaa #g ,c #aaaaaaaaa #i ,c ,d #aaaaaaaaaa #aj ,d ,e #aaaaaaaaaaaaaaaaaaaaaaaaaaaa #bh ,e #a #a ,f #aa #b ,f #aaaaa #e ,g #aaa #c ,g ,h #aa #b ,h #a #a ,i #aaaaaaaaaaaa #ab ,i #aaa #c ,j #a #a ,j #a #a ,l #aaaaaaaaaa #aj ,l #aaa #c ,m #aaaaaa #f ,m #a #a ,n #aaaaaaaaaaaa #ab ,n #a #a ,o #aaaaaaaaaaaaaaaa #af ,o #aaaaaa #f ,p #aaaaa #e ,p #aaa #c ,q #aa #b ,q #aaa #c ,r #aaaaaaaaaaaaaaa #ae ,r #aa #b ,s #aaaaaaaaaaaaaa #ad ,s ,t #aaaaaaaa #h ,t ,u #aaaaaaa #g ,u ,v #aa #b ,v ,x ,x #aa #b ,y #aa #b ,y ,z #a #a ,z #a #a ,our first assumption might be that ,b ,a and ,f ,e but it is evident at once that in that case1 ,s1 ,t1 ,u and ,v 7equal to ,r1 ,s1 ,t and ,u7 do not occur and a message even this short without ,r1 ,s1 ,t or ,u is practically impossible4 ,by trying ,b ,e we find that the two tables agree in a general way very well and this is all that can be expected with such a short message4 ,the longer the message the nearer would its frequency table agree with the standard table4 ,note that if a cipher disk has been used1 the alphabet runs the other way and we must count upward in working with a graphic table4 ,note also that if1 in a fairly long message1 it is impossible to cordinate the graphic table1 reading either up or down1 with the standard table and yet some letters occur much more frequently than others and some do not occur at all1 we have a mixed alphabet to deal with4 ,the example chosen for case #f-;a is of this character4 ,an examination of the frequency table given under that case shows that it bears no graphic resemblance to the standard table4 ,however1 as will be seen in case #g-;b1 the preparation of graphic tables enables us to state definitely that the same order of letters is followed in each of a number of mixed alphabets4 ,general ,remarks ,any substitution cipher1 enciphered by a single alphabet composed of letters1 figures or conventional signs1 can be handled by the methods of case #f4 ,for example1 the messages under case #d-;a and #e-;a are easily solved by these methods4 ,but note that the messages under case #d-;b and #e-;b cannot so be solved because several alphabets are used4 ,we will see later that there are methods of segregating the different alphabets in some cases where several are used and then each of the alphabets is to be handled as below4 ,case #f-;a4 ,message ,,qdbyp ,,bxhys ,,oxpcp ,,yshcs ,,edrbs ,,zptpb ,,bscsb ,,pshsz ,,ajhcd ,,osexv ,,hpoda ,,pbpsz ,,bsvxy ,,xshcd ,this message was received from a source which makes us sure it is in ,spanish4 ,the occurrence of ,b1 ,h1 ,p and ,s has tempted us to try the first two words as in case #d and #e but without result4 ,we now prepare a frequency table1 noting at the same time the preceding and following letter4 ,this latter proceeding takes little longer than the preparation of an ordinary frequency table and gives most valuable information4 ,frequency ,table ,prefix ,suffix ,a #aa #b ,,zd ,,jp ,b #aaaaaaaa #h ,,dprpbspz ,,yxsbspps ,c #aaaaa #e ,,phshh ,,pssdd ,d #aaaaa #e ,,qecoc ,,broa ,e #aa #b ,,ss ,,dx ,f ,g ,h #aaaaaa #f ,,xssjvs ,,ycscpc ,i ,j #a #a ,a ,h ,l ,m ,n ,o #aaa #c ,,sdp ,,xsd ,p #aaaaaaaaa #i ,,yxcztbhab ,,bcytbsobs ,q #a #a ,d ,r #a #a ,d ,b ,s #aaaaaaaaaaaa #ab ,,yycbbcphopbx ,,ohezcbhzezvh ,t #a #a ,p ,p ,u ,v #aa #b ,,xs ,,hx ,x #aaaaa #e ,,boevy ,,hpvys ,y #aaaa #d ,,bhpx ,,pssx ,z #aaa #c ,,sss ,,pab ,it is clear from an examination of this table that we have to deal with a single alphabet but one in which the letters do not occur in their regular order4 ,we may assume that ,p and ,s are probably ,a and ,e1 both on account of the frequency with which they occur and the variety of their prefixes and suffixes4 ,if this is so1 then ,b and ,h1 are probably consonants and may represent ,r and ,n respectively4 ,d and ,x are then vowels by the same method of analysis4 ,noting that ,,hc occurs three times and taking ,h as ,n we conclude that ,c is probably ,t4 ,substitute these values in the last three words of the message because the letters assumed occur rather frequently there4 ,,pbpszbsvxyxshcd ,i ,i ,i ,,arae,,re ,,ent ,o ,o ,o ,now ,z is always prefixed by ,s and may be ,l4 ,taking ,x,i and ,d,o1 7they are certainly vowels71 ,v,g and ,y,m1 we have ,,ara ,,el ,,regimiento ,substituting these values in the rest of the message we have ,q ,,dbypbxh ,,ysoxpcp ,,yshcsed ,,rbszptpb ,,ormarin ,,me,,iata ,,mente,o ,,rela,,ar ,,bscsb ,,pshsz ,,ajhcd ,,osexvhpoda ,,reter ,,aenel ,,nto ,e,,igna,o ,we may now take ,q,f1 ,o,d1 ,e,s1 ,r,b1 ,t,c1 ,a,p and ,j,u and the message is complete4 ,we are assisted in our last assumption by noting that ,s,e and ,e,s1 etc41 and we may on that basis reconstruct the entire alphabet4 ,the letters in parenthesis do not occur in the message but may be safely assumed to be correct4 ,ordinary ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,x ,y ,z ,cipher ,p ,r ,t ,o ,s 7,q7 7,v7 ,n 7,x7 7,u7 7,z7 7,y7 7,h7 ,d ,a ,f ,b ,e ,c ,j ,g ,i ,m ,l ,it is always well to attempt the reconstruction of the entire alphabet for use in case any more cipher messages written in it are received4---- ,case #f-;b4 ,message ,lt4 ,j4 ,b4 ,smith1 ,royal ,flying ,corps1 ,calais1 ,france4 ,,dacft ,,rrbha ,,mooue ,,aenoi ,,ztiet ,,asmos ,,eohie ,,yockf ,,nohoe ,,nouth ,,omeah ,,nilgo ,,osahu ,,ohoue ,,apchs ,,tlnda ,,cften ,,intwn ,,bafoh ,,groht ,,aeioh ,,abris ,,odacf ,,trren ,,ostsm ,,aybis ,,dften ,,efaph ,,osmni ,,ztiea ,,hlill ,,twsou ,,gdeno ,,uthom ,,eahbh ,,amoou ,,eayoe ,,qisuu ,,oleha ,,denoe ,,nhooq ,,obbor ,,tslho ,,baheo ,,ubhob ,,ihtsw ,,enoho ,,pahih ,,ituas ,,bihtl ,graham-,white4 ,the address and signature indicate that this message is in ,english4 ,there are #bej letters in the cipher2 the vowels ,,aeiou occur #aji times or #dc4f1 the letters ,,lnrst occur #fb times or #bd4h1 and the letters ,,kqvxz occur #e times or #b4 ,the proportion in the case of the vowels is somewhat too large and1 in the case of the letters ,,lrnst1 it is too small4 ,it is then questionable whether this is a transposition cipher altho1 at first glance it might appear to be one4 ,on examination for parts of possible words we are at once struck by the occurrence at irregular intervals of recurring groups1 viz3 ,,dacftrr ,,eno ,,bhamoouea ,,dacften ,,enouthomeah ,,bhamoouea ,,eno ,,dacftrr ,,denouthomeah ,,iztie ,,ften ,,deno ,,iztie ,,eno ,this is a strong indication that the cipher is a substitution cipher1 so1 to make an examination a frequency table will be constructed4 ,frequency ,table ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m #bc #aa #g #f #bd #g #c #bf #af #j #a #h #h ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z #ae #cf #c #b #h #ad #ag #aa #a #c #j #c #b ,superficially1 this looks like a normal frequency table1 but ,o is the dominant letter1 followed by ,h1 ,e1 ,a1 ,t1 ,i1 ,n1 ,s1 in the order named4 ,it is certainly ,case #f if it is a substitution cipher at all4 ,let us see what can be done by assuming ,o,e2 the triplet ,,eno1 occurring six times might well be ,,the and ,e,t and ,n,h4 ,a glance at the frequency table shows this to be reasonable4 ,now substitute these letters in some likely groups4 ,,fnohoeno becomes ,,he,,ethe2 ,,ften becomes ,,th2 ,,enoenho becomes ,,theth,e2 ,,enoho becomes ,,the,e4 ,a bit of study will show that ,f,w1 ,t,i and ,h,r and the frequency table bears this out except that ,h7,r7 seems to occur too frequently4 ,the recurring groups containing ,,dac 7see above7 occur in such a way that we may be sure ,,dac is one word1 ,,ftrr is another and ,,ften7,,with7 is a third4 ,now ,,ftrr becomes ,,wi1 which can only be completed by a double letter4 ,,ll fills the bill and we may say ,r,l4 ,as ,,dac starts the message and is followed by ,,ftrr 7,,will7 it is reasonable to try ,,dac,,you4 ,looking up ,,dac in the frequency table it is evident that we strain nothing by this assumption4 ,we now have3 ,letters of cipher ,,ontahecfd ,letters of message ,,ehiortuwy ,now take the group ,,enouthomeah which occurs twice4 ,this becomes ,,the,,ire,,tor and if we substitute ,u,d and ,m,c we have ,,the ,,director4 ,next the group 7,,ftrr7,,bhamoouea becomes 7,,will7 ,,roceedto and the context gives word with missing letter as ,,proceed1 from which ,b,p4 ,next the group 7,,eno7 ,,iztietasmoseohieyock7,,fnoho7 becomes 7,,the7,i,,tio,,ce,,ter,t,,eu7,,where7 and the group 7,,ften7,,efaphosmniztieahl becomes 7,,with7,,two,,re,,ch,i,,tor4 ,the substitution of ,a for ,i1 ,v for ,z1 ,n for ,s and ,f for ,p makes the latter group read 7,,with ,,two ,,french ,,aviators and the former read 7,,the7,,aviation ,,center ,,at ,,eu7,,where74 ,now the word ,,yock 7,,eu7 is the name of a place1 evidently4 ,we find another group containing ,y1 viz3 ,,enostsmaybisd which becomes ,,theninco,,pany so that evidently we should substitute ,m for ,y4 ,the other occurrence of ,y 7,m7 is in the group ,,eayoeqisu which becomes ,,tomet,,and4 ,a reasonable knowledge of geography gives us the words ,,meux and ,,metz so that ,x should be substituted for ,k and ,z for ,q4 ,we now have sufficient letters for a complete deciphering of the message4 ,letters of cipher ,,abcdefghiklmnopqrstuvwyz ,letters of message ,,opuytw,,raxschefzlnid,,mv ,the message deciphers3 ,,you ,,will ,,proceed ,,to ,,the ,,aviation ,,center ,,at ,,meux ,,where ,,the ,,director ,,has ,,een ,,ordered ,,to ,,furnish ,,you ,,with ,a ,,hi,h ,,power ,,leriot ,,aeroplane4 ,,you ,,will ,,then ,,in ,,company ,,with ,,two ,,french ,,aviators ,,assi,,ned ,y ,,the ,,director ,,proceed ,,to ,,metz ,,and ,,destroy ,,the ,,three ,,zeppelins ,,reported ,,preparin ,,there ,,for ,a ,,raid ,,on ,,paris4 ,the substitution of ,b for ,g1 ,g for ,w and ,k for ,v completes the cipher4 ,this cipher is difficult only because the cipher alphabet is made up1 not haphazard1 but scientifically with proper consideration for the natural frequency of occurrence of the letters4 ,in cipher work it is dangerous to neglect proper analysis and jump at conclusions4 ,in the study of ,mexican substitution ciphers1 several alphabets have been found which are made up in a general way1 like the one discussed in this case4 ,case #f-;c4--,it is a convenience in dealing with ciphers made up of numbers or conventional signs to substitute arbitrary letters for the numbers and signs4 ,suppose we have the message3 88#b #dex#ae 7#h #ax#d #d #fx8 #h99x#d #f99 #d ,by arbitrary substitution of letters this is made ,,abbcd ,,efghf ,,ijkdl ,,ddhge ,,mdedm ,,ngbda ,,kdoge ,,npopd ,,maeda ,this message is now in convenient shape to handle as ,case #f-;a and on solution is found to read3 ,,all ,,persons ,,have ,,been ,,ordered ,,to ,,leave ,,fortified ,,area4 ,in the same way the message #agbc #cbbc #bhbe #ahbh #cfcj #bccf #adbc #bhbg #bcbd #cabj #bcag #cabc #cjcf #babj #bdae #cjbi #aeab #bhca #agba #bgae #bhaa #bgae #aibc #cjcj #abae #aacj #babh #cfbc is found to be made up entirely of numbers between #aa and #cf with the numbers #bc1 #bh and #cj occurring most frequently4 ,this immediately suggests an alphabet made up of the numbers from #aa to #cf inclusive and each cipher group of figures represents two letters4 ,by arbitrary substitution of letters for groups of two numbers we obtain3 ,,ab ,,cb ,,de ,,fd ,,gh ,,bg ,,ib ,,dj ,,bk ,,lm ,,ba ,,lb ,,hg ,,nm ,,op ,,hq ,,pr ,,dl ,,an ,,jp ,,ds ,,jp ,,tb ,,hh ,,rp ,,sh ,,nd ,,gb and this message is also in shape to handle as ,case #f-;a4 ,it reads1 on solution1 ,,seven ,,hundred ,,men ,,left ,,yesterday ,,for ,,points ,,on ,,lower ,,rio ,,grande4 ,,chapter ,,vii ,we will now consider the class of substitution ciphers where a number of alphabets are used1 the number and choice of alphabets depending on a key word or equivalent and being used periodically throughout the message4 ,in this class belong the methods of ,vigenere1 ,porta1 ,beaufort1 ,st4 ,cyr1 and many others4 ,these methods date back several hundred years1 but variations of them are constantly appearing as new ciphers4 ,the ,larrabee cipher1 used for communication between government departments1 is the ,vigenere cipher of the #agth ,century4 ,the cipher disk method is practically the ,vigenere cipher with reversed alphabets4 ,in using these ciphers1 there is provided a number of different cipher alphabets1 usually twenty-six1 and each cipher alphabet is identified by a different letter or number4 ,a key word or phrase 7or key number7 is agreed upon by the correspondents4 ,the message to be enciphered is written in lines containing a number of letters which is a multiple of the number of letters of the key4 ,the key is written as the first line4 ,then each column under a letter of the key is enciphered by the cipher alphabet pertaining to that letter of the key4 ,for example1 let us take the message1 ,all radio messages must hereafter be put in cipher1 with the key ,grant1 using the ,vigenere cipher alphabets given below4 ,each of these alphabets is identified by the first or left hand letter which represents ,a of the text4 ,we thus will use in turn the alphabets beginning with ,g1 with ,r1 with ,a1 with ,n1 and with ,t4 ,g ,r ,a ,n ,t ,g ,r ,a ,n ,t ,a ,l ,l ,r ,a ,d ,i ,o ,m ,e ,s ,s ,a ,g ,e ,s ,m ,u ,s ,t ,h ,e ,r ,e ,a ,f ,t ,e ,r ,b ,e ,p ,u ,t ,i ,n ,c ,i ,p ,h ,e ,r ,using the alphabet indicated by ,g1 we get ,g ,j ,y ,y ,n ,l ,k ,t ,k ,continuing for the other alphabets1 we get ,g ,c ,l ,e ,t ,j ,z ,o ,z ,x ,y ,j ,a ,t ,x ,y ,d ,u ,f ,m ,n ,v ,r ,r ,t ,l ,k ,e ,e ,u ,k ,g ,u ,g ,b ,t ,t ,i ,c ,a ,k ,i ,this method of arranging the message into lines and columns and then enciphering whole columns with each cipher alphabet is much shorter than the method of handling each letter of the message separately4 ,the chance of error is also greatly reduced4 ,all these cipher methods can be operated by means of squares containing the various alphabets1 cipher disks or arrangements of fixed and sliding alphabets4 ,for example1 this was the original cipher of ,vigenere3 ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,s ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,t ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,u ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,v ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,w ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,x ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,y ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,z ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,the first horizontal alphabet is the alphabet of the plain text4 ,each substitution alphabet is designated by the letter at the left of a horizontal line4 ,for example1 if the key word is ,,bad1 the second1 first and fourth alphabets are used in turn and the word ,,will is enciphered ,,xiom4 ,the ,larrabee cipher is merely a slightly different arrangement of the ,vigenere cipher and is printed on a card in this form3 ---------------------------------- ,a ,,abcdefghijklmnopqrstuvwxyz abcdefghijklmnopqrstuvwxyz ---------------------------------- ,b ,,abcdefghijklmnopqrstuvwxyz bcdefghijklmnopqrstuvwxyza ---------------------------------- ,c ,,abcdefghijklmnopqrstuvwxyz cdefghijklmnopqrstuvwxyzab ---------------------------------- etc4 ---------------------------------- ,y ,,abcdefghijklmnopqrstuvwxyz yzabcdefghijklmnopqrstuvwx ---------------------------------- ,z ,,abcdefghijklmnopqrstuvwxyz zabcdefghijklmnopqrstuvwxy ---------------------------------- ,the large letters at the left are the letters of the key word4 ,it will be noted that these letters correspond to the first letters of the cipher alphabets 7in small letters7 as in the ,vigenere cipher4 ,a much simpler arrangement of the ,vigenere cipher is the use of a fixed and sliding alphabet4 ,either the fixed or sliding alphabet must be double in order to get coincidence for every letter when ,a is set to the letter of the key word4 ,fixed ,alphabet of ,text ,,abcdefghijklmnopqrstuvwxyzabcdefghijkl mnopqrstuvwxyz ---------------------------------------- ------------- ,,abcdefghijklmnopqrstuvwxyz ,movable ,alphabet of ,cipher ---------------------------------------- --- ,as shown here1 ,a of the fixed or text alphabet coincides with ,t of the movable cipher alphabet4 ,this is the setting where ,t is the letter of the key word in use4 ,the lower movable alphabet is moved for each letter of the message and the ,a of the fixed alphabet is made to coincide in turn with each letter of the key before the corresponding letter of the text is enciphered4 ,it is obviously only a step from this arrangement to that of a cipher disk1 where the fixed alphabet1 7a single one will now serve7 is printed in a circle and the movable alphabet1 also in a circle1 is on a separate rotatable disk4 ,coincidence of any letter on the disk with ,a of the fixed alphabet is obtained by rotating the disk4 ,the well known ,u4 ,s4 ,army ,cipher ,disk has just such an arrangement of the fixed alphabet but the alphabet of the disk is reversed4 ,this has several advantages in simplicity of operation but none in increasing the indecipherability of the cipher prepared with it4 ,the arrangement of fixed and sliding alphabets which is equivalent to the ,u4 ,s4 ,army cipher disk is this3 ,fixed ,alphabet ,,abcdefghijklmnopqrstuvwxyzabcdefghijkl mnopqrstuvwxyz ---------------------------------------- -------------- ,,zyxwvutsrqponmlkjihgfedcba ,movable ,alphabet ---------------------------------------- -- ,it will be noticed that with this arrangement of running the alphabets in opposite directions1 it becomes immaterial which alphabet is used for the text and which for the cipher for if ,a ,g then ,g ,a4 ,this is not true of the ,vigenere cipher4 ,it is perfectly feasible to substitute a card for the ,u4 ,s4 ,army cipher disk4 ,it would have this form3 ,,abcdefghijklmnopqrstuvwxyz #a ,,azyxwvutsrqponmlkjihgfedcb #b ,,bazyxwvutsrqponmlkjihgfedc #c ,,cbazyxwvutsrqponmlkjihgfed etc4 #be ,,yxwvutsrqponmlkjihgfedcbaz #bf ,,zyxwvutsrqponmlkjihgfedcba ,the first horizontal line is the alphabet of the text4 ,the other twenty-six lines are the cipher alphabets each corresponding to the letter of the key word which is at the left of the line4 ,one of the ciphers of ,porta was prepared with a card of this kind3 ----------------------------- ,,ab ,,abcdefghijklm ,,nopqrstuvwxyz ----------------------------- ,,cd ,,abcdefghijklm ,,znopqrstuvwxy ----------------------------- ,,ef ,,abcdefghijklm ,,yzabcdefghijk ----------------------------- etc4 ----------------------------- ,,wx ,,abcdefghijklm ,,pqrstuvwxyzno ----------------------------- ,,yz ,,abcdefghijklm ,,opqrstuvwxyzn ----------------------------- ,in this cipher the large letters at the left correspond to the letters of the key and1 in each alphabet1 the lower letter is substituted for the upper and vice versa4 ,for example1 with key ,,bad to encipher ,,will we would get ,,jvxy4 ,note that with either ,b or ,a as the key letter1 the first alphabet would be used4 ,a combination of the ,vigenere and ,porta ciphers is this3 ---------------------------------- ,a ,,abcdefghijklmnopqrstuvwxyz ,,abcdefghijklmnopqrstuvwxyz ---------------------------------- ,,bc ,,abcdefghijklmnopqrstuvwxyz ,,bcdefghijklmnopqrstuvwxyza ---------------------------------- ,,de ,,abcdefghijklmnopqrstuvwxyz ,,cdefghijklmnopqrstuvwxyzab ---------------------------------- etc4 ---------------------------------- ,,vw ,,abcdefghijklmnopqrstuvwxyz ,,lmnopqrstuvwxyzabcdefghijk ---------------------------------- ,,xy ,,abcdefghijklmnopqrstuvwxyz ,,mnopqrstuvwxyzabcdefghijkl ---------------------------------- ,z ,,abcdefghijklmnopqrstuvwxyz ,,nopqrstuvwxyzabcdefghijklm ---------------------------------- ,here again the large letters at the left correspond to the letters of the key and1 in each pair of alphabets1 the upper one is that of the plain text and the lower is that of the cipher4 ,this cipher can also be operated by a fixed and sliding alphabet4 ,fixed ,alphabet of ,text3 ,,abcdefghijklmnopqrstuvwxyzabcdefghijkl mnopqrstuvwxyz ---------------------------------------- -------------- ,,abcdefghijklmnopqrstuvwxyz ,sliding ,alphabet of ,cipher ,index ---------------------------------------- -- ,,bdfhjlnprtvx ,a ,z ,letters of ,key4 ,,cegikmoqsuwy ,the other ciphers mentioned are merely variations of these that have been discussed4 ,it is immaterial1 in the following analysis1 which variety has been used4 ,the analysis is really based on what can be done with a cipher made up with a mixed cipher alphabet which may be moved with reference to the fixed alphabet of the text1 7,see ,case #g-;b74 ,clearly this is a much more difficult proposition than dealing with a cipher in which the cipher alphabets run in their regular sequence1 either backward or forward4 ,in fact1 in the analysis of ,case #g1 we may consider any cipher prepared by the method of ,vigenere or any of its variations as a special and simple case4 ,it was long ago discovered that1 in any cipher of this class1 7#a7 two like groups of letters in the cipher are most probably the result of two like groups of letters of the text enciphered by the same alphabets and 7#b7 the number of letters in one group plus the number of letters to the beginning of the second group is a multiple of the number of alphabets used4 ,it is evident1 of course1 that we may have similar groups in the cipher which are not the result of enciphering similar groups of the text by the same alphabets but if we take all recurring groups in a message and investigate the number of intervening letters1 we will find that the majority of such cases will conform to these two principles4 ,changing the key word and message to illustrate more clearly the above points1 the following is quoted from the ,signal ,book1 #aiad1 with reference to the use of the cipher disk in preparing a message with a key word4 #b --,this simple disk can be used with a cipher word or1 preferably1 cipher words1 known only to the correspondents4444 ,using the key word 'disk' to encipher the message ',artillery commander will order all guns withdrawn1' we will proceed as follows3 ,write out the message to be enciphered and above it write the key word 444 letter over letter1 thus3 ,,disk,,disk,,disk,,disk,,disk,,disk,,di sk,,disk,,disk,,disk,,dis ,,arti,,ller,,ycom,,mand,,erwi,,llor,,de ra,,llgu,,nswi,,thdr,,awn ,,drzc,,sxot,,fgey,,rifh,,zrwc,,sxet,,ae bk,,sxmq,,qqwc,,xbpt,,dmp ,now bring the 'a' of the upper disk under the first letter of the key word on the lower disk1 in this case ',d'4 ,the first letter of the message to be enciphered is ',a'3 'd' is found to be the letter connected with ',a'1 and it is put down as the first cipher letter4 ,the letter 'a' is then brought under ',i' which is the second letter of the key word4 ',r' is to be enciphered and 'r' is found to be the second cipher letter4444 ,proceed in this manner until the last letter of the key word is used and beginning again with the letter ',d'1 so continue until all letters of the message have been enciphered4 ,divided into groups of five letters1 it will be as follows3 ,,drzcs ,,xotfg ,,eyrif ,,hzrwc ,,sxeta ,,ebksx ,,mqqqw ,,ckbpt ,,dmf4 ,so much for the ,signal ,book2 now let us examine the above message for pairs or similar groups and count the intervening letters to demonstrate principles 7#a7 and 7#b72 ,,csx--,,csx #af #dd ,,sx--,,sx #af #dd ,,sx--,,sx #h #bd ,,wc--,,wc #af #dd ,the key word might contain #b1 #d or #h letters from the evidence but we may eliminate #b as unlikely and preparation of frequency tables of each of the four alphabets would soon show that #d is the correct number4 ,a later and more extensive example 7,case #g-;a7 will show pairs not separated by multiples of the number of alphabets used1 but the evidence in nearly every case will be practically conclusive4 ,especially is this so if chance assists us by giving groups of three or more letters like the group ,,csx in the above example4 ,the number of alphabets having been determined each alphabet is handled by the methods of ,case #f already discussed4 ,case #g-;a4--,the following message appeared in the personal column of a ,london paper3 ,m4 ,b4 ,will deposit #bg #ads #e;d tomorrow1 and the next day we find this one3 ,m4,b4 ,,ct ,,osb ,,uhgi ,,tp ,,ipewf ,h ,,cewil ,,nsttle ,,fjnvx ,,xtyls ,,fwkkhi ,,bjlsi ,,sq ,,voi ,,bksm ,,xmkul ,,sk ,,nvponpn ,,gsw ,,ol4 ,,ieag ,,npsi ,,hyjisfz ,,cyy ,,npuxqg ,,tprja ,,vxmxi ,,ap ,,ehvppr ,,th ,,wppnel4 ,,uvzua ,,mmyvsf ,,knts ,,zsz ,,uajpq ,,dlmmjxl ,,jr ,,ra ,,portelogj ,,csultwni ,,xmkuhw ,,xgln ,,elcpowy ,,ol4 ,,uljtl ,,bvj ,,tlbwtpz ,,xld ,k ,,zisznk ,,osy ,,dl ,,ryjuajssgk4 ,,tlfns ,,uvd ,,vv ,,fqgcyl ,,fjhvsi ,,yjl ,,nexv ,,po ,,wtol ,,pyyyhsh ,,gqboh ,,agztiq ,,eyfax ,,ypmp ,,sqa ,,ci ,,xeyvxnppaii ,,uv ,,tlftwmc ,,fu ,,wbwxguhiwu4 ,,aiiwg ,,hsi ,,yjvti ,,bjv ,,xmqn ,,sfx ,,dqb ,,lrty ,,tz ,,qtxlnisvz4 ,,gift ,,aii ,,uqsjgj ,,ohz ,,xfowfv ,,bkai ,,ctwy ,,dswtltttpkfrhg ,,ivx ,,qcafv ,,tp ,,diis ,,jbf ,,esf ,,jsc ,,mccf ,,hngk ,,esbp ,,djpq ,,nlu ,,ctw ,,rosb ,,csm4 ,the messages in question appeared in an ,english newspaper4 ,it is fair to presume then that the cipher is in ,english4 ,this is checked negatively by the fact that it contains the letter ,w which is not used in any of the ,latin languages and that the last fifteen words of the message consist of from two to four letters each1 an impossible thing in ,german4 ,it contains #ajh groups which are probably words1 as there are #dgc letters or an average of #d4d letters per group1 while we normally expect an average of about #e letters per group4 ,the vowels ,,aeiou number #ij and the letters ,,jkqxz number #gh4 ,it is thus a substitution cipher 7#bj of #dgcid4f74 ,recurring words and similar groups are ,,aiiwg1 ,,aii2 ,,bksm1 ,,bkai2 ,,ct1 ,,ctwy1 ,,ctw2 ,,dlmmjxl1 ,,dl2 ,,esf1 ,,esbp2 ,,fjnvx1 ,,fjhvsi2 ,,npsi1 ,,npuxqg2 ,,osb1 ,,osy1 ,,rosb2 ,,ol1 ,,ol2 ,,portelogj1 ,,po2 ,,sq1 ,,sqa2 ,,tp1 ,,tp2 ,,tlbwtpz1 ,,tlfns1 ,,tlftwmc2 ,,uvzua1 ,,uvd1 ,,uv2 ,,xmkul1 ,,xmkuhw2 ,,yjl1 ,,yjvti4 ,frequency ,table for the ,message ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z #ae #ac #ae #h #ac #bj #af #af #cj #ba #ac #bg #ad #ai #ae #bf #ac #i #cc #cj #ag #ab #ai #bj #ai #aa ,this clearly eliminates ,cases #d1 #e and #f4 ,referring to the recurring words and groups above noted1 we figure the number of letters between each4 ,,aii 444 ,,aii #de #cce ,,bk 444 ,,bk #cde #bcce ,,ct 444 ,,ct #djc ,no factors ,,ctw 444 ,,ctw #fj #bbce ,,dl 444 ,,dl #ge #cee ,,es 444 ,,es #ad #bg ,,fj 444 ,,fj #ahg ,no factors ,,np 444 ,,np #ad #bg ,,ol 444 ,,ol #abj #bbbce ,,os 444 ,,os #bbj #aabbe ,,osb 444 ,,osb #dfe #cace ,,po 444 ,,po #aje #gce ,,sq 444 ,,sq #bej #beee ,,tlf 444 ,,tlf #hj #bbbbe ,,tp 444 ,,tp #dje #cccce ,,uv 444 ,,uv #aae #bce ,,xmku 444 ,,xmku #abj #bbbce ,,uv 444 ,,uv #gc ,no factors ,,yj 444 ,,yj #he #age ,the dominant factor is clearly #e1 so we may consider that five alphabets were used1 indicating a keyword of five letters4 ,writing the message in lines of five letters each and making a frequency table for each of the five columns so formed1 we find the following3 ,frequency ,tables ,colum #a ,column #b ,column #c ,column #d ,column #e ,a #aa ,a #aaaaaaaaa ,a #a ,a #a ,a #aa ,b ,b #aaa ,b #aaa ,b ,b #aaaaaaa ,c #aaaaaaa ,c #a ,c #aaa ,c #aaaa ,c ,d #aa ,d #aa ,d #a ,d ,d #aaa ,e #aaaa ,e ,e #aa ,e #aaaaaaa ,e ,f #aaa ,f ,f #aaaaaaaaa ,f #aaa ,f #aaaaa ,g #aaaaaaaaa ,g ,g #aaa ,g #aa ,g #aa ,h #aaa ,h #aaaaa ,h #aaa ,h #aaa ,h #aa ,i #aa ,i #aa ,i #aaaaaaa ,i #aaaaaaaaaaaaaaaaa ,i #aa ,j #aaaaa ,j #a ,j #aaaaaa ,j ,j #aaaaaaaaa ,k #aaaaaa ,k #aaaaa ,k ,k #a ,k #a ,l ,l #aaaaaaaaaaaaaaaaaaa ,l #aa ,l #aaaaa ,l #a ,m ,m ,m #aaaaaaa ,m #aaaa ,m #aaa ,n #aaaaaaa ,n #aaa ,n #aaaa ,n ,n #aaaaa ,o #aaaaa ,o ,o #aaaaaaaaa ,o #a ,o ,p #aaaaaaa ,p #aaaaaaa ,p #aaaaaaaa ,p #aaaa ,p ,q #aaaaa ,q ,q ,q #aa ,q #aaaaaa ,r ,r #a ,r #a ,r #aaaaaa ,r #a ,s ,s #aaaaaaaa ,s #aaaaaa ,s #aaaaaaaaaaaa ,s #aaaaaaa ,t #aaaaaaa ,t #aaa ,t #aaaaa ,t #a ,t #aaaaaaaaaaaaaa ,u #aaaaaaa ,u #aaa ,u #aaaaaa ,u ,u #a ,v #aaaaa ,v ,v #aa ,v #aaaaa ,v ,w #aaa ,w #aaaa ,w ,w #aaaaa ,w #aaaaaaa ,x #aa ,x ,x #aaaa ,x #aaaaaaaa ,x #aaaaaa ,y #aaaa ,y #aaaaa ,y ,y #aaa ,y #aaaaaaa ,z ,z #aaaaa ,z #aaa ,z ,z #aaa ,in the table for ,column #a1 the letter ,g occurs #i times4 ,let us consider it tentatively as ,e4 ,then if the cipher alphabet runs regularly and in the direction of the regular alphabet1 ,c 7#g times7,a and the cipher alphabet bears a close resemblance to the regular frequency table4 ,note ,,tuv 7,,rst7 occurring respectively #g1 #g1 and #e times and the non-occurrence of ,b1 ,l1 ,m1 ,r1 ,s1 ,z1 7,z1 ,j1 ,k1 ,p1 ,q1 and ,x respectively47 ,in the next table1 ,l occurs #ai times and taking it for ,e with the alphabet running in the same way1 ,a,h4 ,the first word of our message1 ,,ct1 thus becomes ,,am when deciphered with these two alphabets and the first two letters of the key are ,c ,h4 ,similarly in the third table we may take either ,f or ,o for ,e1 but a casual examination shows that the former is correct and ,a,b 7even if we were looking for a vowel for the next letter of the keyword74 ,in the fourth table1 ,i is clearly ,e and ,a,e4 ,the fifth table shows ,t#ad and ,j#i4 ,if we take ,t,e we find that we would have many letters which should not occur4 ,on the other hand1 if we take ,j,e then ,t,o and in view of the many ,e's already accounted for in the other columns1 this may be all right4 ,it checks as correct if we apply the last three alphabets to the second word of our message1 ,,osb1 which deciphers ,,now4 ,using these alphabets to decipher the whole message1 we find it to read3 ,m4 ,b4 ,am now safe on board a barge moored below ,tower ,bridge where no one will think of looking for me4 ,have good friends but little money owing to action of police4 ,trust1 little girl1 you still believe in my innocence although things seem against me4 ,there are reasons why ,i should not be questioned4 ,shall try to embark before the mast in some outward bound vessel4 ,crews will not be scrutinized so sharply as passengers4 ,there are those who will let you know my movements4 ,fear the police may tamper with your correspondence but later on when hue and cry have died down will let you know all4 ,the key to this message is ,,chbef which is not intelligible as a word but if put into figures indicating that the #b;d1 #gth1 #ast1 #dth1 and #eth letter beyond the corresponding letter of the message has been used the key becomes #bgade and we may connect it with the personal which appeared in the same paper the day before reading3 ,m4 ,b4 ,will deposit #bg #ads #e;d tomorrow4 ,case #g-;b4 ,message ,,ddlrm ,,erglm ,,ujtll ,,chers ,,lsoee ,,smeju ,,zjimu ,,daees ,,dutdb ,,gugpn ,,rchob ,,eqeie ,,ooacd ,,eioog ,,coljl ,,pduvm ,,igiyx ,,qqtot ,,djcpj ,,oisly ,,duasi ,,upfne ,,aecob ,,oesho ,,betnd ,,qxucy ,,luqoy ,,ehydu ,,lxpeq ,,fixze ,,pdcnz ,,enelq ,,mjtsq ,,ecfie ,,arndn ,,etscf ,,ifqse ,,tddnp ,,uuzhq ,,cdtxq ,,irmer ,,glxbe ,,iqrxj ,,fbsqd ,,ldsvi ,,xumtb ,,aeqeb ,,yleco ,,iycud ,,qtpys ,,voqbl ,,ulyro ,,yhefm ,,oymuy ,,roymu ,,eqblv ,,ubrey ,,ghytq ,,cmubr ,,eqtof ,,vsddu ,,daffs ,,cebsv ,,tioye ,,tclqx ,,dvnlq ,,xytsi ,,mzulx ,,baxqr ,,ecvtd ,,etgob ,,ccuyf ,,ttnxl ,,unefs ,,ivijr ,,zhsby ,,lltsi ,on the preliminary determination1 we have the following count of letters out of a total of #che3 ,a #h ,l #bc ,j #i ,e #ch ,n #aa ,q #bb ,i #ai ,r #ad ,v #i ,o #ba ,s #bj ,x #ac ,u #bd ,t #ba ,z #f ,total #aaj ,total #hi ,total #ei #bh #bc #ae ,every letter except ,k and ,w occurs at least six times4 ,we may say then that it is a substitution cipher1 ,spanish text1 and certainly not ,case #d1 #e or #f4 ,we will now analyze it for recurring pairs or groups to determine1 if it be ,case #g1 how many alphabets were used4 ,the following is a complete list of such recurring groups and pairs with the number of letters intervening and the factors thereof4 ,in work of this kind1 the groups of three or more letters are always much more valuable than single pairs4 ,for example1 the groups1 ,,hobe1 ,,oymu1 ,,rmergl and ,,ubre show1 without question1 that six alphabets were used4 ,it is not necessary1 as a rule1 to make a complete list like the following3 ,,ae #gdbcg ,,ie #aajbeaa ,,re #ejbee ,,ae #abjbbbce ,,im #cjbbaea ,,rmergl #aihbccaa ,,be #hhbbbaa ,,io #bejbeee ,,sc #acbbbcaa ,,cd #acbbbcaa ,,ix #ghbcac ,,sd #bfbbaca ,,cfi #abbbc ,,ly #aehbgi ,,si #bcjbebc ,,ch #cfbbcc ,,jt #aejbcee ,,si #cdbag ,,co #dbbcg ,,ll #cfg ,no factors ,,si #bfdbbbcaa ,,co #abfbccg ,,lq #afdbbda ,,si #abbbc ,,cu #aadbcai ,,lqx #fbc ,,sl #ghbcac ,,dd #ahfbcca ,,lu #abdbbca ,,sq #edbccc ,,dd #aafbbbi ,,lu #aajbeaa ,,sv #bgccc ,,de #bheeeg ,,lu #bcdbccac ,,sv #fcccg ,,dl #bahbaji ,,lx #ffbcaa ,,sv #ijbcce ,,dn #adbg ,,lxb #acbbbcaa ,,td #dg ,no factors ,,dq #abjbbbce ,,ly #aehbgi ,,td #afeceaa ,,du #cfbbcc ,,me #bbbaa ,,td #ifbbbbbc ,,du #bdbbbc ,,mu #bdbbbc ,,tn #bci ,no factors ,,du #chbai ,,mu #bdjbbbbce ,,ts #adbg ,,du #afeceaa ,,mu #ahbcc ,,ts #aefbbcac ,,ea #cjbce ,,nd #dg ,no factors ,,tsi #ejbee ,,eb #ghbcac ,,ne #dhbbbbc ,,ubre #abbbc ,,ec #ahjbbcce ,,ne #ahbcc ,,ud #fjbbce ,,eco #abfbccg ,,ne #aibbbbbbbc ,,uda #bgjbccce ,,ees #adbg ,,ob #fbc ,,ul #aadbcai ,,ef #ajeceg ,,ob #bcdbccac ,,ulx #aihbccaa ,,ei #hbbb ,,oe #iccca ,,uy #hi ,no factors ,,ei #aebbbbai ,,oi #addbbbbcc ,,uz #afbbcccc ,,eq #hhbbbaa ,,oo #g ,no factors ,,vi #adhbbcg ,,eq #bfdbbbcaa ,,oy #fbc ,,vt #cccaa ,,eq #ddbbaa ,,oy #dfbbc ,,xq #aadbcai ,,eqe #agfbbbbaa ,,oymu #fbc ,,xq #addbbbbcc ,,er #abbbc ,,pd #gecee ,,xu #iiccaa ,,es #ghbcac ,,qbl #bdbbbc ,,ye #ahdbbbbc ,,et #acecce ,,qc #ieeai ,,yl #ajfbec ,,et #icc ,,qe #ajhbbccc ,,yl #addbbbbcc ,,et #edbccc ,,qe #fhbbag ,,ym #fbc ,,et #ca ,no factors ,,qr #acbbbcaa ,,yro #abbbc ,,he #bdeegg ,,qto #bajbceg ,,ze #fbc ,,hobe #ffbcaa ,,qx #aihbccaa ,,zh #ahccfa ,out of one hundred and one recurring pairs we have fifty with the factors #bcf2 out of twelve recurring triplets1 nine have these factors2 and the four recurring groups of four or more letters all have these factors4 ,the percentages are respectively #di4e1 #ge and #ajj and we may be certain from this that six alphabets were used4 ,but1 before the six frequency tables are made up1 there is one more point to be considered2 why are there so many recurring groups which do not have six as a factor8 ,the answer is that one or more of the alphabets is repeated in each cycle2 that is1 a key word of the form ,,havana has been used4 ,if this were the key word1 the second1 fourth and sixth alphabets would be the same4 ,we will see later that in this example the second and sixth alphabets are the same and this introduces the great number of recurring groups without the factor #f4 ,we will now proceed to make a frequency table for each alphabet4 ,as the message is written in thirty columns1 we take the first1 seventh1 thirteenth1 etc41 as constituting the first alphabet2 the second1 eighth1 fourteenth1 etc41 as constituting the second alphabet and so on4 ,the prefix and suffix letter is noted for each occurrence of each letter4 ,the importance of this will be appreciated when the form of the frequency tables is examined4 ,none bears any resemblance to the normal frequency table except that each is evidently a mixed up alphabet4 ,the numbers after ,prefix and ,suffix refer to the alphabet to which these belong1 for convenience in future reference4 ,frequency ,tables ,first ,alphabet ,letter ,prefix 7#f7 ,suffix 7#b7 ,a #aaa #c ,,dud ,,esf ,b #aaaaaaaa #h ,,ooofeeos ,,eoesyscy ,c #j ,d #aaaa #d ,,tyt ,,djud ,e #a #a ,e ,s ,f #j ,g #j ,h #j ,i #aaaaaaaa #h ,,eoffeovs ,,osefqyj ,j #j ,l #a #a ,o ,j ,m #a #a ,f ,o ,n #aaaa #d ,,fedu ,,eeee ,o #a #a ,e ,o ,p #aa #b ,,ge ,,nd ,q #aaaa #d ,,ueoe ,,ofbb ,r #aaaaaaa #g ,,eeeyybb ,,gsgooee ,s #a #a ,d ,v ,t #aaaaaaaa #h ,,jujmqyvf ,,ldsbpqdt ,u #j ,v #aa #b ,,uf ,,ms ,x #aaaaaa #f ,,yqtqqa ,,quqdyq ,y #a #a ,o ,e ,z #aaa #c ,,uum ,,jhu ,second ,alphabet ,letter ,prefix 7#a7 ,suffix 7#c7 ,a #j ,b #aaa #c ,,tqq ,,all ,c #a #a ,b ,c ,d #aaaaaa #f ,,dtpdxt ,,lbcnve ,e #aaaaaaaaaaa #a #a ,,abnbninrryn ,,eoatlatyqtf ,f #aaa #c ,,qia ,,iqf ,g #aa #b ,,rr ,,ll ,h #a #a ,z ,o ,i #j ,j #aaaa #d ,,zldi ,,ilcr ,l #a #a ,t ,l ,m #a #a ,v ,i ,n #a #a ,p ,r ,o #aaaaaaa #g ,,oibqrmr ,,aoeyyyy ,p #a #a ,t ,y ,q #aaaaa #e ,,xxitx ,,oircr ,r #j ,s #aaaaaaaa #h ,,reiatbvb ,,lmliqqdv ,t #a #a ,t ,n ,u #aaa #c ,,xdz ,,cll ,v #a #a ,s ,i ,x #j ,y #aaaa #d ,,bixb ,,lctl ,z #j ,third ,alphabet ,letter ,prefix 7#b7 ,suffix 7#d7 ,a #aaaa #d ,,oeeb ,,cere ,b #a #a ,d ,g ,c #aaaaaa #f ,,judyqc ,,pynumu ,d #a #a ,s ,d ,e #aaa #c ,,eod ,,sst ,f #aa #b ,,fe ,,ss ,g #j ,h #j ,i #aaaaaa #f ,,jmsfqv ,,mguxrx ,j #j ,l #aaaaaaaaaaaaaa #ad ,,dglsjsuegybbuy ,,rmcspyxqxeuvxl ,m #a #a ,s ,e ,n #aa #b ,,dt ,,px ,o #a #a ,o ,g ,p #j ,q #aaaaaaa #g ,,eqsfhse ,,etescdt ,r #aaaa #d ,,nqqj ,,cxez ,s #j ,t #aaaa #d ,,eeey ,,nscs ,u #j ,v #aa #b ,,sd ,,tn ,x #j ,y #aaaaaa #f ,,opoooe ,,eshmmg ,z #j ,fourth ,alphabet ,letter ,prefix 7#c7 ,suffix 7#e7 ,a #j ,b #j ,c #aaaaa #e ,,lraqt ,,hhddl ,d #aa #b ,,qd ,,lu ,e #aaaaaaaa #h ,,mqayqalr ,,jichcqcc ,f #j ,g #aaaa #d ,,boiy ,,ucih ,h #a #a ,y ,e ,i #j ,j #j ,l #a #a ,l ,t ,m #aaaaa #e ,,liyyc ,,uuuuu ,n #aaa #c ,,tcv ,,dzl ,o #j ,p #aaa #c ,,lcn ,,dju ,q #a #a ,l ,m ,r #aaa #c ,,lai ,,mnm ,s #aaaaaaaaa #i ,,leetqyftf ,,odhcevcii ,t #aaaa #d ,,qqve ,,ooig ,u #aaaa #d ,,iclc ,,pdly ,v #a #a ,l ,u ,x #aaaaaaa #g ,,lilriln ,,pzbubl ,y #aa #b ,,lc ,,dlj ,z #a #a ,r ,h ,fifth ,alphabet ,letter ,prefix 7#d7 ,suffix 7#f7 ,a #j ,b #aa #b ,,xx ,,ea ,c #aaaaaaa #g ,,gddsdsd ,,ooffoev ,d #aaaaaa #f ,,scpyncu ,,ueuuqtq ,e #aa #b ,,sh ,,tp ,f #j ,g #a #a ,u ,t ,h #aaaaaa #f ,,ccsdgz ,,eooyys ,i #aaaaa #e ,,egtss ,,eyomv ,j #aaa #c ,,epx ,,uop ,l #aaaaaa #f ,,yducnx ,,udyqqu ,m #aaa #c ,,rqr ,,eje ,n #a #a ,r ,d ,o #aaa #c ,,stt ,,etf ,p #aa #b ,,ux ,,fe ,q #a #a ,e ,e ,r #j ,s #j ,t #a #a ,l ,s ,u #aaaaaaaaaa #aj ,,mmgpxmmvmd ,,jdgumyebbd ,v #a #a ,s ,o ,x #j ,y #a #a ,u ,f ,z #aa #b ,,xn ,,ee ,sixth ,alphabet ,letter ,prefix 7#e7 ,suffix 7#a7 ,a #a #a ,b ,x ,b #aa #b ,,uu ,,rr ,c #j ,d #aaaa #d ,,unlu ,,ansa ,e #aaaaaaaaaaaaa #ac ,,mhoidpzzmbquc ,,rreoiqpnribqb ,f #aaaaaaa #g ,,pccjeoc ,,niibmvt ,g #a #a ,u ,p ,h #j ,i #j ,j #aa #b ,,um ,,tt ,l #j ,m #aa #b ,,ui ,,tz ,n #j ,o #aaaaaaaaa #i ,,hcjchcvig ,,blibbiqyb ,p #j ,q #aaaa #d ,,ddll ,,xtxx ,r #j ,s #aa #b ,,ht ,,bi ,t #aaa #c ,,oed ,,ddx ,u #aaaaaaa #g ,,jdddlul ,,ztvaqzn ,v #aa #b ,,ci ,,ti ,x #a #j ,i ,y #aaaaa #e ,,ihluh ,,xdrrt ,z #j ,we will now set down some of the determinations which can be made at once from these frequency tables4 ,clearly several mixed alphabets have been used4 ,as was to be expected from the analysis of the recurring groups1 we note that the frequency tables for alphabets #b and #f are of so nearly the same general form that certainly these two alphabets are one and the same4 ,if a ,spanish word has been used as a key word1 this means that ,a is probably represented by a vowel in these two alphabets and probably equals ,a or ,o1 because these two letters are such common finals in ,spanish4 #ast ,alphabet4 ,probable vowels ,t1 ,x2 probable common consonants1 ,b1 ,i1 ,n1 ,r4 ,we conclude this because of the frequency of occurrence of ,t and ,x and the variety of their prefixes and suffixes4 ,on the other hand1 ,b1 ,i1 ,n1 and ,r have for prefixes and suffixes1 in a majority of cases1 ,e1 ,f1 ,o and ,s which are the probable vowels in the #b;d and #fth alphabets4 #b;d and #fth ,alphabets4--,probable vowels ,e1 ,f1 ,o1 ,s2 probable common consonants1 ,d1 ,j1 ,q1 ,u1 ,y4 #c;d ,alphabet4--,probable vowels ,c1 ,i1 ,l2 probable common consonants ,a1 ,q1 ,t1 ,y4 #dth ,alphabet4--,probable vowels1 ,e1 ,g1 ,s1 ,t2 probable common consonants1 ,c1 ,m1 ,n1 ,p1 ,u1 ,x4 #eth ,alphabet4--,probable vowels1 ,d1 ,l1 ,u2 probable common consonants1 ,c1 ,h1 ,i4 ,now this cipher may have been made up from five distinct alphabets with letters chosen at random but it is much more likely to have been prepared with a cipher disk or equivalent1 having the regular alphabet on the fixed disk and the mixed alphabet on the movable disk4 ,an equivalent form of apparatus 7not using the mixed alphabet in question7 is one like this3 ,fixed ,alphabet of ,text ,,abcdefghijlmnopqrstuvxyzabcdefghijlmno pqrstuvxyz ---------------------------------------- -------------- ,,pcjvrqzbaodfsutmxiyhlgen ,movable ,alphabet of ,cipher ---------------------------------------- --- ,here ,a of the plain text is enciphered by ,s and the other letters come as they will4 ,if we move the cipher alphabet one space to the left1 ,a will be enciphered by ,u and the whole sequence of the alphabet will be changed4 ,we will therefore use some such form as the above and see if we can insert our letters1 as they are determined1 in such a way as to have each of the cipher slips identical4 ,we may start thus3 ,,abcdefghijlmnopqrstuvxyzabcdefghijlmno pqrstuvxyz #ast ,alphabet t x #b;d ol qei ms d c u #c;d ol qei ms d c u #dth ol qei ms d c u #eth d c u ol qei ms #fth ol qei ms d c u ,in the #ast alphabet1 ,t and ,x are placed as ,a and ,e respectively on the basis of frequency4 ,in the #b;d and #fth alphabets1 ,o and ,e are placed as ,a and ,e respectively on the basis of frequency4 ,in the #dth alphabet1 ,e and ,s are placed as ,a and ,e1 and in the #eth1 ,d1 ,u and ,l are placed as ,a1 ,e and ,o for the same reason4 ,we now have an excess of ,e's and a deficiency of ,a's1 which will be corrected if1 in the #c;d alphabet1 we place ,l1 ,i and ,c as ,a1 ,e and ,o respectively4 ,as a check1 this gives us ,,toledo as the key word4 ,in the second alphabet1 ,o is four letters to the left of ,e2 we may place ,o four letters to the left of ,e in the fourth and it comes under ,v4 ,note that in the fourth frequency table ,o 7,v7 does not occur4 ,in the same way in the fourth alphabet1 ,s is four letters to the right of ,e2 placing it in the same position with respect to ,e in the second and sixth1 we have ,s under ,i4 ,we have already noted that ,s probably represents a vowel in these two alphabets4 ,in this way1 we may add ,d and ,u to the third alphabet from their position in the fifth with respect to ,l and we may add ,i and ,o to the fifth from their position in the third with respect to ,l4 ,in every case we check results from the frequency tables and find nothing unlikely in the results4 ,now in the second and sixth1 let us try ,q1 ,d and ,u as ,d1 ,n and ,r respectively4 ,we may add these letters to the third1 fourth and fifth alphabets by the method of observing the number of letters to the right or left of some letter already fixed4 ,we now add ,l to the second1 third1 fourth and sixth from its position with reference to ,d and ,u in the fifth4 ,m is probably ,d in the fourth and we may add it to each of the alphabets1 except the first1 in the same way4 ,the table is now complete as shown4 ,let us try these letters on the first line of the message and see if some other letters will be self-evident4 ,alphabet #a #b #c #d #e #f #a #b #c #d #e #f #a #b #c #d #e #f #a #b #c #d #e #f #a #b #c #d #e #f ,message ,d ,d ,l ,r ,m ,e ,r ,g ,l ,m ,u ,j ,t ,l ,l ,c ,h ,e ,r ,s ,l ,s ,o ,e ,e ,s ,m ,e ,j ,u ,deciphered ,n ,a ,u ,e ,a ,d ,e ,a ,b ,a ,l ,e ,i ,a ,e ,n ,e ,i ,g ,a ,r ,referring to our frequency tables as a check on suppositions1 we find everything agrees well enough if we assume the first line to read3 ,,unafuerza ,,de ,,caballeria ,,enemiga ,we will now put the newly found letters in the table4 ,the letters previously found are in capitals and the new letters in small letters4 ,the addition of ,d 7,u7 to the first alphabet permits us to add all the letters of the other alphabets to the first by the methods already discussed4 ,each of the other letters may then be added to every alphabet by these methods3 ,,abcdefghijlmnopqrstuvxyzabcdefghijlmno pqrstuvxyz #ast ,t xhgoljqei msr d c u #b;d t xhg,o,lj,q,e,i ,m,sr ,d ,c ,u #c;d t xhg,o,lj,q,e,i ,m,sr ,d ,c ,u #dth t xhg,o,lj,q,e,i ,m,sr ,d ,c ,u #eth t xhg,o,lj,q,e,i ,m,sr ,d ,c ,u #fth t xhg,o,lj,q,e,i ,m,sr ,d ,c ,u ,one alphabet checks another in this way and we find everything to fit so far4 ,we will decipher a few words more of the cipher message by the above alphabets and see if we can determine some new letters4 ,alphabet #efabcdefabcdefabcdefabcdefabcdefabcdefa bcdefabcdefabcdefab ,message ,,juzjimudaeesdutdbgugpnrchobeqeieooacde ioogcoljlpduvmigiyxq ,deciphered ,,pr,,ceden,,edearau,,uez,,illa,,ecaseha ,,laenazucaica,,ar,,heus,,ed ,again referring to the frequency tables the first word is evidently ,,procedente4 ,we have also ,,halla and ,,marcheusted4 ,the letter ,b may be determined from another cipher group1 ,,jfbsqdld 7#efabcdef7 ,,posicion4 ,the letter ,n may be determined from ,,betndqxuc 7#abcdefabc7 ,,serradero4 ,the letters ,f and ,y may be determined from ,,jcpjoislyduasiupf 7#bcdefabcdefabcdef7 ,,compania ,,partiendo4 ,the completed alphabets1 arranged as before1 are3 ,,abcdefghijlmnopqrstuvxyzabcdefghijlmno pqrstuvxyz #ast ,,tyvnxhgoljqeizmsrbadfcpu #b;d ,,tyvnxhgoljqeizmsrbadfcpu #c;d ,,tyvnxhgoljqeizmsrbadfcpu #dth ,,tyvnxhgoljqeizmsrbadfcpu #eth ,,tyvnxhgoljqeizmsrbadfcpu #fth ,,tyvnxhgoljqeizmsrbadfcpu ,the key word is ,,toledo and the completely deciphered message is3 ,una fuerza de caballeria enemiga procedente de ,aranjuez y ,villaseca se halla en ,azucaica4 ,marche usted con su compania partiendo de la casa de la serradero por las alturas de lo este y norte de ,azucaica con el fin de reconocer su numero y clase de fuerzas y en disposicion que se halla4 7,q7 ,esta acantonada 7,q7 ,se hallan otras tropas detras de ella 7,q74 ,el resultado del reconocimiento necesito saberlo dentro de tres horas y media cuando mas4 ,pongo a sus ordenes un ciclista 7,x7 ,fin4 ,special ,solution for ,case #g ,when a short message is enciphered with a long key word1 the methods of analysis already discussed may fail2 first1 because there will be no recurring pairs to indicate the number of alphabets used and1 second1 because there will be so few letters in each alphabet that the methods of ,case #f will not be easily applied4 ,however1 if we know or correctly assume one word1 preferably a fairly long one1 in the cipher text1 a solution is very simple4 ,for example1 the following message is believed to refer to renforcements and to contain that word4 ,,yanzv ,,znlpp ,,kqfxi ,,jbpwa ,,nruqp ,,eplom ,,ccwhm ,i ,let us assume that ,,reinforcements is the first word and that it is represented by the cipher group ,,yanzvznlppkqfx4 ,we may put the test in this tabular form1 using a cipher disk and a ,larrabee cipher card to determine the value of ,a for each letter under these two systems4 ,any other alphabets suspected may be tried out at the same time4 ,if ,y ,a ,n ,z ,v ,z ,n ,l ,p ,p ,k ,q ,f ,x equals ,r ,e ,i ,n ,f ,o ,r ,c ,e ,m ,e ,n ,t ,s then1 with cipher disk1 ,a equals ,p ,e ,r ,m ,a ,n ,e ,n ,t ,b ,o ,d ,y ,p and1 in ,vigenere cipher1 ,a equals ,h ,w ,f ,m ,q ,l ,w ,j ,l ,d ,g ,d ,m ,f ,it is evident that the guess as to the appearance of the word ,,reinforcements was correct1 that it is the first word of the message1 that the cipher disk was used in preparing the cipher and that the key words are ,,permanent ,,body4 ,this is1 of course1 an especially favorable case and we will take one less favorable to show how this method can be applied4 ,two ,mexican chieftains1 ,a and ,b1 have been communicating with the following cipher alphabet3 ,plain text ,,abcdefghijlmnopqrstuvxyz ,cipher ,,pcjvrqzbaodfsutmxiyhlgen ,this alphabet has been determined from many radio messages from ,a1 the superior1 to ,b1 his sub-ordinate1 who has a force of about #b1jjj men near the border4 ,a uses the form ,,ordeno ,,que instead of the more familiar ,,mando ,,que in all his messages giving orders to ,b4 ,the following message is received from ,a by ,b's radio station 7and other listening stations7 and about an hour later there is a good deal of noise and movement as if ,b's force were breaking camp4 ,,iihah ,,ydxrp ,,egqgv ,,jjeee ,,hobgv ,,gjcag ,,xaesa ,,vvxle ,,iilhm ,,psqag ,,bdgav ,,gsqaz ,this is a substitution cipher1 but it is not ,case #f using the usual alphabet of the communications from ,a to ,b and1 in fact1 is not ,case #f at all4 ,the recurring pairs and triplets point to a key word of ten letters and this would give us but six letters per alphabet if it is ,case #g4 ,the preparations for a move lead us to believe that ,a has given an order to ,b and he has1 in that case1 probably used the expression ,,ordeno ,,que in the message4 ,we will try the first nine letters of the message as in the other example1 first preparing a cipher disk or equivalent sliding arrangement having on it the alphabet usually used between these chieftains or ,a-,b cipher4 ,fixed ,cipher ,alphabet ,,pcjvrqzbaodfsutmxiyhlgenpcjvrqzbaodfsu tmxiyhlgen ---------------------------------------- -------------- ,,abcdefghijlmnopqrstuvxyz ,sliding ,plain ,text ,alphabet ---------------------------------------- -- ,a-,b ,cipher ,if ,i equals ,o then ,a equals ,r ,i ,r ,c ,h ,d ,x ,a ,e ,r ,h ,n ,b ,y ,o ,q ,clearly there is nothing here and the assumed words1 if they occur1 are in the middle of the message4 ,we may jump to the combination ,,pegqgv at once since the preceding letters do not make ,,ordeno ,,que4 ,we try this without result and proceed to ,,egqgvj1 ,,gqgvjj1 ,,qgvjje1 ,,gvjjee1 ,,vjjeee1 ,,jjeeeh1 ,,jeeeho1 ,,eeehob1 ,,eehobg1 ,,ehobgv1 ,,hobgvg1 ,,obgvgj1 ,,bgvgjc1 ,,gvgjca1 ,,vgjcag1 all without result4 ,this work requires less time than might be imagined and is the kind of work which can be divided among a number of operators4 ,now let us come to the next combination ,,gjcagx4 ,we add the next three letters1 ,,aes1 against ,,que4 ,if ,g ,j ,c ,a ,g ,x ,a ,e ,s equals ,o ,r ,d ,e ,n ,o ,q ,u ,e ,then1 in the ,a-,b cipher1 ,a equals ,a ,d ,e ,r ,o ,v ,i ,v ,a ,the key is found2 ,,viva,,adero and a trial of ,m in the blank space shows correct results4 ,this checks with our theory that a ten letter key word was used and deciphering the message we have3 ,,para ,,el ,,ataque ,,contra ,,torreon ,,ordeno ,,que ,,sus ,,tropas ,,marchen ,,este ,,noche ,x4 ,the reason for breaking camp is now evident4 ,this method may be used1 with some labor1 on short words like ,,the1 ,,and1 etc4 ,parts of the key will appear whenever an assumed word is found in the message and the whole key may be assembled if enough of the parts are available4 ,even if only part of the key may be so recovered1 it will always lead to the ultimate solution of the cipher by trial of the partially recovered key on the message letter by letter4 ,as an example of recovery of a key by use of short common words1 let us refer to the message of ,case #g-;a4 ,there are twenty-four groups of three letters each in this message and we will try them against ,,the1 ,,are and ,,you1 assuming that the ,vigenere cipher is used4 #a #b #c #d #e #f #g #h #i #aj #aa #ab ,if ,,osb ,,voi ,,gsw ,,cyy ,,zsz ,,bvj ,,xld ,,osy ,,uvd ,,yjl ,,sqa ,,hsi equals ,,the ,,the ,,the ,,the ,,the ,,the ,,the ,,the ,,the ,,the ,,the ,,the or ,,are ,,are ,,are ,,are ,,are ,,are ,,are ,,are ,,are ,,are ,,are ,,are or ,,you ,,you ,,you ,,you ,,you ,,you ,,you ,,you ,,you ,,you ,,you ,,you then ,a equals ,,vlx ,,che ,,nls ,,jru ,,glv ,,iof ,,eez ,,vlu ,,boz ,,fch ,,zjw ,,ole or ,,obx ,,vxe ,,gbs ,,chu ,,zbv ,,bef ,,xuz ,,obu ,,uez ,,ysh ,,szw ,,hbe or ,,qeh ,,xao ,,iec ,,eke ,,bef ,,dhp ,,zxj ,,qee ,,whj ,,avr ,,ucg ,,jeo #ac #ad #ae #af #ag #ah #ai #bj #ba #bb #bc #bd ,if ,,bjv ,,sfx ,,dqb ,,aii ,,ohz ,,ivx ,,jbf ,,esf ,,jsc ,,nlu ,,ctw ,,csm equals ,,the ,,the ,,the ,,the ,,the ,,the ,,the ,,the ,,the ,,the ,,the ,,the or ,,are ,,are ,,are ,,are ,,are ,,are ,,are ,,are ,,are ,,are ,,are ,,are or ,,you ,,you ,,you ,,you ,,you ,,you ,,you ,,you ,,you ,,you ,,you ,,you then ,a equals ,,icr ,,zyt ,,kjx ,,hbe ,,vav ,,pot ,,qub ,,llb ,,qly ,,ueq ,,jms ,,jli or ,,bsr ,,sot ,,dzx ,,are ,,oqv ,,iet ,,jkb ,,ebb ,,jby ,,nuq ,,ccs ,,cbi or ,,dvb ,,urd ,,fch ,,yuo ,,qtf ,,khd ,,lnl ,,gel ,,lei ,,pxa ,,efc ,,ees ,in column #e1 we have1 for ,,you1 the key ,,bef2 column #f gives the same key for ,,are2 column #aj gives the key ,,fch for ,,the and column #ae gives the same key for ,,you2 column #ab gives the key ,,hbe for ,,are and column #af gives the same key for ,,the2 column #bc gives the key ,,efc for ,,you4 ,the only possible key for the message is a five-letter one made up of the letters ,,befch or ,,efchb or ,,fchbe or ,,chbef or ,,hbefc4 ,if the key in this case were a word1 we would have no difficulty in determining it2 as it is1 there is no real difficulty in the matter as we may now divide the message into blocks of five letters and note that ,,zsz 7,,you7 form the #c;d1 #dth and #eth letters of a group4 ,the corresponding key letters1 ,,bef1 are then the #c;d1 #dth and #eth letters of the key which must be ,,chbef4 ,this special solution for ,case #g depends so largely on the intuition of the operator in choice of a word that it is not1 in general1 advisable to use it unless the message is very short and the regular methods of analysis have been tried unsuccessfully4 ,it is1 however1 a wonderfully short cut in difficult cases where the other methods fail4 ,,chapter ,,viii ,case #h4 ,the ,playfair cipher4 ,this is the ,english military field cipher2 as the method is published in ,english military manuals and as it is a cipher of proven reliability1 it may be met with in general cipher work4 ,the ,playfair cipher operates with a key word2 two letters are substituted for each two letters of the text4 ,the ,playfair cipher may be recognized by the following points3 7a7 ,it is a substitution cipher1 7b7 it always contains an even number of letters1 7c7 when the cipher is divided into groups of two letters each1 no group consists of the repetition of the same letter as ,,ss or ,,bb1 7d7 there will be recurrence of pairs throughout the message1 following in a general way1 the frequency table of digraphs of pairs1 7e7 in short messages there may be recurrence of cipher groups representing words or even phrases1 and these will always be found in long messages4 ,in preparing a cipher by this method1 a key word is chosen by the correspondents4 ,a large square1 divided into twenty-five smaller squares1 is constructed as shown below and the letters of the key word are written in1 beginning at the upper left hand corner4 ,if any letter recurs in the key word1 it is only used on the first occurrence4 ,the remaining letters of the alphabet are used to fill up the square4 ,it is customary to consider ,i and ,j as one letter in this cipher and they are written together in the same square4 ,if the key word chosen is ,,leavenworth1 then the square would be constructed as follows3 ,l ,e ,a ,v ,n ,w ,o ,r ,t ,h ,b ,c ,d ,f ,g ,,ij ,k ,m ,p ,q ,s ,u ,x ,y ,z ,the text of the message to be sent is then divided up into groups of two letters each1 and equivalents are found for each pair4 ,every pair of letters in the square must be3 ,either 7#a7 in the same vertical line4 ,thus in the above example each letter is represented in cipher by that which stands next below it1 and the bottom letter by the top one of the same column2 for instance1 ,,ty is represented by ,,fv4 ,or 7#b7 in the same horizontal line4 ,each letter in this case is represented by that which stands next on its right1 and the letter on the extreme right by that on the extreme left of the same horizontal line with it2 for instance ,,rh is represented by ,,tw4 ,or 7#c7 at opposite corners of a rectangle4 ,each letter of the pair is represented by the letter in the other corner of the rectangle in the same horizontal line with it2 for instance ,,ts is represented by ,,wy4 ,if1 on dividing the letters of the text into pairs1 it is found that a pair consists of the same letter repeated1 a dummy letter1 as ,x1 ,y1 or ,z1 should be introduced to separate the similar letters4 ,if the message to be sent were ,the enemy moves at dawn1 it would be divided into pairs3 ,,th ,,ex ,,en ,,em ,,ym ,,ov ,,es ,,at ,,da ,,wn and enciphered3 ,,hw ,,au ,,al ,,ak ,,xp ,,te ,,lu ,,vr ,,mr ,,hl ,the message is then broken up into groups of five letters for transmission4 ,to decipher such a cryptogram1 7knowing the key word71 the receiver divides it into pairs1 and from his table finds the equivalent of these pairs1 taking the letter immediately above each1 when they are in the same vertical line2 those immediately on the left1 when in the same horizontal line2 and those at opposite angles of the rectangle when this is formed4 ,it is evident1 from the foregoing description1 that any letter of the plain text may be represented in cipher by one of five letters1 viz3 ,the one next below it and the other four letters in the same horizontal line with it in the square4 ,take1 for example1 the letter ,d of the plain text1 in combination with each of the other letters of the alphabet4 ,we have1 using the key ,,leavenworth3 ,,da ,,db ,,dc ,,de ,,df ,,dg ,,dh ,,di ,,dk ,,dl ,,dm ,,dn ,,do ,,dp ,,dq ,,dr ,,ds ,,dt ,,du ,,dv ,,dw ,,dx ,,dy ,,dz ,,mr ,,fc ,,fd ,,ca ,,fg ,,fb ,,gr ,,bm ,,cm ,,ba ,,mx ,,ga ,,cr ,,fm ,,gm ,,md ,,bx ,,fr ,,cx ,,fa ,,br ,,ma ,,fx ,,gx ,this gives ,d represented by ,b ,c ,f ,g ,m #d #d #h #d #d times1 and1 connected with these five letters representing ,d1 we have ,a ,r ,d ,m ,x ,b ,c ,g #e #e #b #d #e #a #a #a times4 ,note that these letters are those of the vertical column containing ,d plus the letters ,b1 ,c and ,g1 of the horizontal line containing ,d4 ,lieut4 ,frank ,moorman1 ,u4 ,s4 ,army1 has developed a method for determining the letters which make up the key word in a ,playfair cipher4 ,in the first place1 a key word necessarily contains vowels in the approximate proportion of two vowels to three consonants and it is also likely that a key word will contain other common letters4 ,this key word is placed in the first row or rows4 ,now if a table is made1 showing what letters in the cipher occur with every letter1 it will be found that the letters having the greatest number of other letters in combination with them are very likely to be letters of the key word1 or in other words1 letters occurring in the first or second lines4 ,an example will make this clear3 ,message ,,db ,,fn ,,ex ,,tz ,,mf ,,to ,,vb ,,qb ,,qt ,,ob ,,xa ,,of ,,pr ,,tz ,,eq ,,rh ,,qk ,,qv ,,dx ,,ok ,,ab ,,pr ,,qi ,,el ,,tv ,,ke ,,ex ,,xs ,,fs ,,bp ,,wd ,,bo ,,by ,,bf ,,ro ,,ea ,,bo ,,rh ,,qk ,,qv ,,tx ,,gu ,,el ,,ab ,,th ,,tr ,,xn ,,on ,,ea ,,ay ,,xh ,,bo ,,hn ,,ex ,,bs ,,hr ,,qb ,,zm ,,se ,,xp ,,hf ,,gz ,,ug ,,kc ,,bd ,,po ,,ea ,,ay ,,xh ,,bo ,,xp ,,hf ,,kr ,,qi ,,ab ,,pr ,,qi ,,el ,,bx ,,fz ,,bi ,,se ,,fx ,,pb ,,ra ,,pr ,,qi ,,wc ,,br ,,xd ,,yg ,,tb ,,qt ,,ea ,,ay ,,xh ,,bo ,,hn ,,ex ,,bs ,,hr ,,qb ,,pr ,,qi ,,el ,,bx ,,bt ,,hb ,,qb ,,nf ,,si ,,se ,,bx ,,nu ,,xp ,,bu ,,rb ,,xb ,,qr ,,ox ,,ba ,,tb ,,rh ,,bp ,,wd ,,rp ,,ro ,,gu ,,gx ,,qr ,,se ,,zy ,,ox ,,ba ,,el ,,ax ,,cw ,,by ,,ba ,,sx ,,rk ,,ro ,,pr ,,hb ,,op ,,bd ,,pi ,,cn ,,ox ,,em ,,rp ,,kr ,,xt ,,el ,,ax ,,cw ,,eq ,,fz ,,sx ,,el ,,rh ,,ro ,,pr ,,hb ,,ux ,,da ,,se ,,xn ,,zn ,,gu ,,el ,,bx ,,fs ,,dg ,,db ,,tb ,,zl ,,ve ,,rh ,,bo ,,rq4 ,from this message1 we make up the following table1 considering the letters of each pair3 ,first ,letters of ,pairs ,a ,b ,c ,d ,e ,f ,g ,h ,i ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x ,y ,z ,a #c #a #d #a #a ,b #c #b #c #a #a #d #a #c #a #a ,c #a #a ,d #b #b #a ,e #a #e #a ,f #a #b #a #a #a ,g #a #a #a #a ,h #e #a #c ,i #a #a #e #a ,k #a #b #a ,l #h #a ,m #a #a ,n #a #a #b #a #b #a ,o #f #a #d #a ,p #b #a #b #c ,q #b ,r #a #b #b #g #b #a ,s #b #b #a ,t #a #b #a ,u #a #c #a ,v #b ,w #b ,x #a #e #a #d #a #a #c #b #a #a ,y #e #a ,z #b #a #b ,from this table we pick out the letters ,b1 ,e1 ,f1 ,o1 ,r1 ,t1 ,x1 as tentative letters of the key word on account of the variety of other letters with which they occur4 ,as there are but two vowels for seven letters1 we will add ,a to the list on account of its occurrences with ,b1 ,d1 ,e1 ,r1 and ,x4 ,this leaves the letters for the bottom lines of the square as follows3 -------------------- 4 4 4 4 4 -------------------- 4 4 4 ,c ,d -------------------- ,g ,h ,,ij ,k ,l -------------------- ,m ,n ,p ,q ,s -------------------- ,u ,v ,w ,y ,z -------------------- ,referring to the table again we find the most frequent combination to be ,,el1 occurring #h times1 with no occurrence of ,,le4 ,now1 ,,th is the commonest pair in plain text1 and ,,ht is not common4 ,the fact that ,h occurs in the same horizontal line with ,l and that ,e and ,t are probably in the key1 will lead us to put ,e in the first line over ,h and ,t in the first line over ,l1 so as to make ,,el equal ,,th4 ,the next most frequent combination is ,,pr occurring #g times1 with ,,rp occurring twice4 ,in the square as partially arranged1 ,,pr equals ,m or ,n or ,q or ,i4 ,we may eliminate all these except ,n1 and this ,n could only be ,,no or ,,na1 so that we will put1 tentatively the ,r in the second line over ,h and the ,o and ,a in the same line over ,,ij4 ,we have then3 -------------------- 4 ,e 4 4 ,t -------------------- 4 ,r ,,ao ,c ,d -------------------- ,g ,h ,,ij ,k ,l -------------------- ,m ,n ,p ,q ,s -------------------- ,u ,v ,w ,y ,z -------------------- ,let us now check this by picking out the combinations beginning with ,,el and seeing if the table will solve them4 ,we find1 ,,eltv1 ,,elab1 ,,elbxfz1 ,,elbxbt1 ,,elaxcwby1 ,,elaxcweq1 ,,elrh1 ,,elbxfs4 ,now1 on the assumption that the letter after ,,el represents ,e1 we have it represented by ,a three times1 ,b three times1 ,r once and ,t once4 ,this requires that ,a and ,b be put in the same horizontal line with ,e1 since ,t is already there1 and ,r is tentatively under ,e4 ,the combination ,,eltv now equals ,,thez4 ,if the ,t were moved one place to the left1 it would be ,,they1 a more likely combination1 but this requires the ,l to be moved one place to the left also1 by putting ,i or ,k in the key word and taking out ,o1 ,r or ,x and returning it to its place in the alphabetical sequence4 ,the most frequent pairs containing ,o are ,b ,o six times1 ,r ,o four times1 and ,o ,x three times4 ,now these pairs equal respectively ,e ,n1 ,e ,s and ,h ,e1 if ,o is put between ,n and ,p in the fourth line4 ,we will therefore cease to consider it as a letter of the the key word4 ,the combination ,,elab can only be ,,the on the assumption that ,a is the first letter to the right of ,e4 ,the combination ,,elbx occurs three times4 ,if it represents ,,the1 the ,b must be the first letter of the first line and the ,x must now be placed under ,e where the ,r was tentatively put4 ,we can get ,,the out of ,,elrh by putting ,r in the first line or leaving it where it is1 but the preponderance of the ,,bx combination should suggest the former alternative4 ,a new square showing these changes will look like this3 -------------------- ,b ,e ,a ,t ,r -------------------- 4 ,x 4 4 4 -------------------- ,g ,h 4 ,l ,m -------------------- ,n ,o ,p ,q ,s -------------------- ,u ,v ,w ,y ,z -------------------- ,as ,i put in the space under ,b will give the word ,,beatrix and as a vowel is clearly necessary there1 we will so use the ,,ij and leave ,k between ,h and ,l4 ,this leaves ,c1 ,d and ,f to be placed4 ,it appeared at first that ,f was in the key but if it is in the second line1 in proximity to the letters of the first line1 it will give the same indications4 ,completing the square then1 we have -------------------- ,b ,e ,a ,t ,r -------------------- ,,ij ,x ,c ,d ,f -------------------- ,g ,h ,k ,l ,m -------------------- ,n ,o ,p ,q ,s -------------------- ,u ,v ,w ,y ,z -------------------- ,with this square1 the message is deciphered without difficulty4 ,it is very frequently neces7x7sary to employ ciphers and they have for many centuries been employed in the relations betwe7x7en governments1 for com7x7munication betwe7x7en com7x7manders and their subordinates and particularly betwe7x7en governments and their agents in foreign countries2 there are many cases in history where the capture of a message not in cipher has made the captors of the message victorious in their military movements4 ,it will be seen that the method of ,lieut4 ,moorman enabled us to pick out six letters of the key word out of eight letters chosen tentatively4 ,the reason for the appearance of ,f has already been noted2 the letter ,o occurred with many other letters because it happened to remain in the same line with ,n and ,s and to be under ,h4 ,it thus was likely to represent any of these three letters which occur very frequently in any text4 ,two-character ,substitution ,ciphers ,case #i4--,two-character substitution ciphers4 ,in ciphers of this type1 two letters1 numerals1 or conventional signs1 are substituted for each letter of the text4 ,there are many ways of obtaining the characters to be substituted but1 in general1 these ciphers may be considered as special varieties of ,case #f or ,case #g4 ,the ciphers which come under this case are not well suited to telegraphic correspondence because the cipher message will contain twice as many letters as the plain text4 ,however they are so used2 an example is at hand in which two numerals are substituted for each letter and this makes transmission by telegraph very slow4 ,case #i can be recognized by some or all of the following points2 the number of characters in the cipher is always an even number2 often only a few1 say five to ten1 of the letters of the alphabet appear2 either a frequency table for pairs of the cipher text resembling the normal single letter frequency table can be made1 or groups of four letters will show a regular recurrence1 from which the cipher can be solved as in ,case #g4 ,case #i;a4-- ,message ,,rntgn ,,raagr ,,narna ,,gtgra ,,tgaan ,,nangg ,,rarat ,,naanr ,,nnnrn ,,aaagg ,,aangr ,,nggnn ,,nrnaa ,,aanra ,,tnann ,,nggrn ,,rnnrg ,,ttgrg ,,tggrn ,,arntg ,,nnart ,,ggrnr ,,grnnt ,,gtgaa ,,nnarn ,,arnrt ,,tgagg ,,gaaaa ,,nanna ,,rnaga ,,ngnat ,,nnnat ,this message contains #afj letters and it will be noted that the only letters used are ,a1 ,g1 ,n1 ,r and ,t4 ,we may expect a simple two-letter substitution cipher at once4 ,it will simplify the work if we divide the cipher into groups of two letters and then1 if we find there are #bf or less recurring groups1 to assign an arbitrary letter to each group and work out the cipher by the method of ,case #f4 ,,rn ,,tg ,,nr ,,aa ,,gr ,,na ,,rn ,,ag ,,tg ,,ra ,,tg ,,aa ,,nn ,,an ,,gg ,,ra ,,ra ,,tn ,,aa ,,nr ,,nn ,,nr ,,na ,,aa ,,gg ,,aa ,,ng ,,rn ,,gg ,,nn ,,nr ,,na ,,aa ,,an ,,ra ,,tn ,,an ,,nn ,,gg ,,rn ,,rn ,,nr ,,gt ,,tg ,,rg ,,tg ,,gr ,,na ,,rn ,,tg ,,nn ,,ar ,,tg ,,gr ,,nr ,,gr ,,nn ,,tg ,,tg ,,aa ,,nn ,,ar ,,na ,,rn ,,rt ,,tg ,,ag ,,gg ,,aa ,,aa ,,na ,,nn ,,ar ,,na ,,ga ,,ng ,,na ,,tn ,,nn ,,at ,with arbitrary letters substituted1 we have ,a ,b ,c ,d ,e ,f ,a ,g ,b ,h ,b ,d ,i ,j ,k ,h ,h ,l ,d ,c ,i ,c ,f ,d ,k ,d ,m ,a ,k ,i ,c ,f ,d ,j ,h ,l ,j ,i ,k ,a ,a ,c ,n ,b ,o ,b ,e ,f ,a ,b ,i ,p ,b ,e ,c ,e ,b ,b ,d ,i ,p ,f ,a ,q ,b ,g ,k ,d ,d ,f ,i ,p ,f ,r ,m ,f ,l ,i ,s ,now1 preparing a frequency table1 with note of prefixes and suffixes we have3 ,frequency ,prefix ,suffix ,a #g #aaaaaaa ,,fmkaff ,,bgkacbq ,b #aj #aaaaaaaaaa ,,aghnoapibq ,,chdoeiebdg ,c #f #aaaaaa ,,bdiiae ,,diffne ,d #i #aaaaaaaaa ,,cblfkfbkd ,,eickmjidf ,e #d #aaaa ,,dbbc ,,ffci ,f #h #aaaaaaaa ,,eccepdpm ,,addaairl ,g #b #aa ,,ab ,,bk ,h #d #aaaa ,,bkjh ,,bhll ,i #i #aaaaaaaaa ,,dckjbedfl ,,jcckpbpp ,j #c #aaa ,,idl ,,khi ,k #e #aaaaa ,,jdaig ,,hdiad ,l #c #aaa ,,hhf ,,dji ,m #b #aa ,,dr ,,af ,n #a #a ,c ,b ,o #a #a ,b ,b ,p #c #aaa ,,iii ,,bff ,q #a #a ,a ,b ,r #a #a ,f ,m ,s #a #a ,i ,a brief study of this table and the distribution in the cipher leads to the conclusion that ,b1 ,f and ,c are certainly vowels and are1 if the normal frequency holds1 equal to ,e1 ,o1 and ,a or ,i4 ,similarly ,d and ,i are consonants and we may take them as ,n and ,t4 ,i is taken as ,t because of the combination ,,ip 7possibly ,,th7 occurring three times4 ,the next letter in order of frequency is ,a2 it is certainly a consonant and may be taken as ,r on the basis of its frequency4 ,let us now try these assumptions on the first two lines of the message4 ,we have ,a ,a ,a ,r ,e ,n ,o ,r ,e ,e ,n ,t ,n ,t ,o ,n ,n ,i ,i ,i ,this is clearly the word ,,reinforcements and1 using the letters thus found1 the rest of the line becomes ,,ammunitionand4 ,we have then the following letters determined3 ,arbitrary letters ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,k ,l ,m ,plain ,text ,r ,e ,i ,n ,f ,o ,c ,m ,t ,s ,a ,u ,d ,if these be substituted we have for the message3 ,,reinforcements ,,ammunition ,,and ,,rations ,,must ,,arri,e ,,efore ,t,e ,,fifteent ,,or ,e ,,cannot ,o,d ,,out4 ,from this the remainder of the letters are determined3 ,arbitrary letters ,n ,o ,p ,q ,r ,s ,plain text ,v ,b ,h ,w ,l ,x ,now let us substitute the two-letter groups for the arbitrary letters3 ,arbitrary letters ,k ,o ,g ,m ,b ,e ,p ,c ,r ,h ,d ,f ,a ,j ,i ,l ,n ,q ,s ,two-letter groups ,,gg ,,rg ,,ag ,,ng ,,tg ,,gr ,,ar ,,nr ,,ga ,,ra ,,aa ,,na ,,rn ,,an ,,nn ,,tn ,,gt ,,rt ,,at ,plain text ,a ,b ,c ,d ,e ,f ,h ,i ,l ,m ,n ,o ,r ,s ,t ,u ,v ,w ,x ,it is evident that the cipher was prepared with the letters of the word ,,grant chosen by means of a square of this kind3 ,g ,r ,a ,n ,t ,g ,a ,b ,c ,d ,e ,r ,f ,g ,h ,i ,k ,a ,l ,m ,n ,o ,p ,n ,q ,r ,s ,t ,u ,t ,v ,w ,x ,y ,z ,thus ,,tg,e1 ,,an,s1 etc41 as we have already found4 ,case #i-;b ,message #aiejdibieh #cabcbebhae #ddahdebhae #bjdhaaejda #bbebaaecde #ehdiacdabd #ejbheebebf #eiccaiebbb #ebdeaacbae #fbaeehdadc #bhfacfabfe #bideefejae #bcdbdeehej #fcdeedbjai #aeejahecaa #baaedaehbh #aabdagdeec #deedbjeiej #beebdedacb #aeccdibjdh #ejahaebcfd ,an examination of the groups of two numerals each which make up this message1 shows that we have #aa to #cf and #da to #fe with eleven groups missing4 ,now the #aa to #cf combination is a very familiar one in numeral substitution ciphers 7,see ,case #f-;c7 and it will be noted that #da to #ff would give us a similar alphabet4 ,let us make a frequency table in this form3 ,group ,frequency ,group ,frequency #aa #aaaaa #da #aaaaa #ab #a #db #a #ac #a #dc #a #ad #dd #a #ae #aaaaaaaaa #de #aaaaaaaaa #af #df #ag #a #dg #ah #aaa #dh #aa #ai #aaa #di #aaa #bj #aaaa #ej #aaaaaaaa #ba #a #ea #bb #aa #eb #aaaa #bc #aaa #ec #aaa #bd #aa #ed #aa #be #aaa #ee #a #bf #a #ef #a #bg #eg #bh #aaaaa #eh #aaaaa #bi #aa #ei #aa #cj #fj #ca #a #fa #a #cb #aa #fb #a #cc #aa #fc #a #cd #fd #a #ce #fe #a #cf #a #ff ,each of these tables looks like the normal frequency table except for the position of #bj and #ej which should represent ,t1 by all our rules1 and should be apparently #cj and #fj4 ,but suppose we put the alphabet and corresponding numerals in this form3 #a #b #c #d #e #f #g #h #i #j #a or #d ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j #b or #e ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t #c or #f ,u ,v ,w ,x ,y ,z ,then ,a#aa or #da1 ,j#aj or #dj and ,t#bj or #ej as we found4 ,using the above alphabet1 the message may easily be read4 ,note that this cipher is made up of ten characters only1 the ,arabic numerals4 ,case #i;c-- ,message #aaefbedfgf #bedbbiddcb #aidibidjae #adbcbagbaa #bigigjcaae #dibdbaceaa #gdbdadghge #gfdfbebddd #eadcbedhde #cagigdbecc #djeedfaeab #gegcbbgide #afbgdhaeaa #gjdbceaidd #acghbebadi #beadgfdeec #aedhcdbabf #gbaebedjge #afaabeghde #dfdbbagdae #diebaigibi #gjaebdbadc #bibedddicc #aigjahgeca #djgibedhbi #deeadiadaa #gcbaagaeed ,an examination of this message shows it to consist of forty-four different two-figure groups running from #aa to #gi4 ,let us prepare a frequency table of these groups4 ,group ,frequency #aa #aaaaaa #ab #a #ac #a #ad #aaaa #ae #aaaaaaaaa #af #aa #ag #a #ah #a #ai #aaaa #bj #ba #aaaaaaa #bb #a #bc #a #bd #aaaa #be #aaaaaaaaaaa #bf #a #bg #a #bh #bi #aaaaaa #cj #ca #aaa #cb #a #cc #aa #cd #a #ce #aa #cf #cg #ch #ci #dj #aaaa #da #db #aaa #dc #aa #dd #aaaa #de #aaaaa #df #aaaa #dg #dh #aaaa #di #aaaaaa #ej #ea #aa #eb #a #ec #a #ed #a #ee #a #ef #a #eg #eh #ei #gj #aaaa #ga #gb #aa #gc #aa #gd #aaa #ge #aaaa #gf #aaa #gg #gh #aaa #gi #aaaaa ,we at once note the resemblance between the frequency tables for the groups #aa to #ai and #ba to #bi2 for the groups #cj to #cf and #ej to #ef2 and for the groups #dj to #di and #gj to #gi4 ,also the groups #aa to #ai and #ba to #bi have a frequency fitting well with the normal frequency table of the letters ,a to ,i2 the groups #da to #di and #ga to #gi have a frequency fitting well with the normal frequency table of the letters ,k to ,s2 and the groups #ca to #cf and #ea to #ef have a frequency fitting well with the normal frequency table of the letters ,u to ,z4 ,we have ,j and ,t unaccounted for1 but note what occurred in ,case #i-;b and that #dj and #gj would correspond well with ,t if they followed respectively #di and #gi4 ,we may now make up a cipher table as follows3 #a #b #c #d #e #f #g #h #i #j #a or #b ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j #d or #g ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t #c or #e ,u ,v ,w ,x ,y ,z and this table will solve the cipher message4 ,in ciphers coming under case #i-;b and #i-;c1 it is not uncommon to assign some of the unused numbers such as #he1 #ic1 etc41 to whole words in common use or to names of persons or places4 ,in case such groups are found1 the meaning must be guessed at from the context2 but if many messages in the same cipher are available1 the meaning of these groups will soon be obtained4 ,the appearance of such odd groups of figures in a message does not interfere materially with the analysis1 and it will be apparent at once on deciphering the message that they represent whole words instead of letters4 ,,chapter ,,ix ,,other ,,substitution ,,methods ,the foregoing cases by no means exhaust the possibilities of the substitution cipher but they cover practically all methods which are satisfactory for military purposes1 having in mind conservation of time1 the minimizing of mental strain1 and the requirements that complicated apparatus and rules be avoided1 and that the resulting cipher should be adapted to telegraphic correspondence4 ,a message may be re-enciphered two or more times using a different key word each time or it may be enciphered by one method and re-enciphered by another method1 using the same or a different key word4 ,complicated cipher systems requiring the memorizing of1 or reference to1 numerous rules have been devised for special purposes4 ,such systems usually fail utterly if there are any errors in transmission and it will be seen later that such errors are very common4 ,there are several ingenious cipher machines by which complicated ciphers can be formed1 but if the apparatus is available and fairly long messages are at hand for examination1 it is usually possible to solve them4 ,such machines are not1 as a rule1 simple and small enough for field use2 and it must always be remembered that a machine cipher operates on certain mechanical cycles1 which can be determined if the machine is available4 ,a book by ,commandant ,bazeries1 entitled ,etude sur la ,cryptographie ,militaire1 and a series of articles by ,a4 ,collon1 entitled ,etude sur la ,cryptographie1 which appeared in the ,revue de ,l',arme ,belge1 #ahii-aijb1 give illustrations and details of operation of several of these cipher machines and the latter goes into the methods of deciphering messages enciphered with them4 ,these methods of analysis require long messages1 and as each one is adapted only to the product of a certain machine or apparatus1 it is not considered advisable to include a discussion of them here4 ,those interested in such advanced cipher work must refer to these and other ,european authors on the subject4 ,the requirement that cipher messages should be adapted to telegraphic transmission1 practically excludes ciphers in which three or more letters or whole words are substituted for each letter of the plain text4 ,such ciphers might be used for the transmission of very short messages but in no other case4 ,the cipher of ,case #g1 with a key word or phrase longer than one-fourth of the message1 the cipher after the method of ,case #g1 using a certain page of a book as a key1 and the cipher with a running key1 where each letter of the cipher is the key for enciphering the next letter1 all look safe and desirable1 theoretically1 but1 practically1 the work of enciphering and deciphering is hopelessly slow1 and errors in enciphering or transmission make deciphering very difficult4 ,incidentally the first and second of these ciphers can be solved by the special solution for ,case #g1 and the third can be solved by trying each of the twenty-six letters of the alphabet as the first key letter1 and then continuing the work for five or six letters of the cipher4 ,when the proper primary key letter is found1 the solution of the next five or six letters of the cipher will make sense1 and thereafter the cipher offers no difficulty4 ,there are numerous other methods of preparing what is virtually a very long1 or even an indefinitely long key from a short key word1 but all such cipher methods have the same practical disadvantages of slowness of operation and difficulty in deciphering1 if errors of enciphering or transmission have been made4 ,the ciphers of ,napoleon were long series of numbers representing letters1 syllables and words4 ,they were really codes2 and a code based on these principles1 but using letters instead of numerals1 might be evolved very easily4 ,the ,war ,department ,code1 the ,western ,union ,code1 and1 in fact1 all codes are nothing but specialized substitution ciphers in which each code word represents a letter1 word or phrase of the plain text4 ,combined ,transposition and ,substitution ,methods ,it is evident that a message can be enciphered by any transposition method1 and the result enciphered again by any substitution method1 or vice versa4 ,but this takes time and leads to errors in the work1 so that1 if such a process is employed1 the substitution and transposition ciphers used are likely to be very simple ones which can be operated with fair rapidity4 ,on preliminary determination1 a cipher prepared by such a combination of methods will appear to be a substitution cipher to be solved as such4 ,the frequency table of the result will resemble the normal frequency table1 although the message will still be unintelligible and we will know at once that it is a transposition cipher for further solution4 ,the substitution methods usually found in combination ciphers are those of ,case #d1 #e and #f1 and the transposition method is nearly always ,case #a1 and particularly the simple varieties of this case like the fence rail 7,case #a-;i71 reversed writing or vertical writing4 ,a few examples will show some of the possible combinations4 ,the first line of the message of ,case #d-;a is3 ,,obqfobpbrp ,we might write it ,,bfbbpoqopr 7,case #a-;i71 or ,,prbpbofqbo 7,case #a1 reversed writing71 or ,,ofqboprbpb 7,case #a1 reversed by groups of five74 ,the first line of the message of ,case #b-;b is3 ,,slcof ,,weetn ,,ebrdo ,,orvym ,,ffedi ,we might write it ,,tmdpg ,,xffuo ,,fcsep ,,pswzn ,,ggfej1 or ,,rkbne ,,vddsm ,,daqcn ,,nquxl ,,eedch 7,case #d-;a1 going forward one letter or back one letter74 ,these examples give an idea of the use of combination methods4 ,it is very rare to find both complicated transposition and substitution methods used in combination4 ,if one is complicated1 the other will usually be very simple2 and ordinarily both are simple1 the sender depending on the combination of the two to attain indecipherability4 ,it is evident how futile this idea is4 ,methods of ,enciphering ,numerals ,it is frequently desirable to send numerals in the body of a cipher message4 ,several cipher systems prescribe that all numerals in the body of a message must be spelled out2 and1 while there is no doubt but that this insures greater accuracy1 it also greatly increases the length of such messages4 ,in most systems in which it is permissible to send numerals1 the following system is used4 ,an indicator1 one of the little used letters and especially ,x1 is interpolated before and after the numeral or numerals to be enciphered1 and then1 for each numeral1 a letter is substituted using this or a similar table3 #a #b #c #d #e #f #g #h #i #j ,a ,b ,c ,d ,e ,f ,g ,h ,i ,j ,the enciphering of the message then proceeds1 dealing with the indicator and substituted letters as if they were the letters of a word4 ,the decipherer arriving at an ,x1 a series of the letters of the above table and another ,x1 casts out the ,x's and substitutes numbers for the letters4 ,sometimes no indicator is used1 but the system of substitution of a certain letter for each numeral is followed4 ,again1 the indicator ,,nr may be used instead of a single letter4 ,conventional letters may also be substituted for special characters like 81 1 1 -1 and periods and commas1 but this is rarely done except for the period and question mark4 ,the context will usually determine the meaning of such letters when found4 ,in this connection1 the use of ,x to represent end of a sentence and ,q to represent a question mark is quite common4 ,,chapter ,x ,,errors ,,in ,,enciphering ,,and ,,transmission ,one of the most difficult tasks before the cipher expert1 is the correction of errors which creep into cipher texts in the process of enciphering and transmission by telegraph or radio4 ,in some cipher methods a mistake in enciphering one letter1 or the omission of one letter1 will so mix up the deciphering process that only one familiar with such errors can apply the necessary corrections4 ,the transmission of cipher text over the telegraph or by radio is a slow process1 and many fairly good operators cannot receive such matter satisfactorily1 because they listen for words and guess at letters at times4 ,the spaced letters in ,american ,morse are the cause of so many errors in code transmission that the ,war ,department ,code does not employ any groups using them4 ,in fact1 this code is limited to the letters ,a ,b ,d ,e ,f ,g ,i ,k ,m ,n ,s ,t ,u ,x so that there may be a minimum of such confusion4 ,in cipher work it is necessary1 under ordinary circumstances1 to use any or all of the letters of the alphabet4 ,to assist operators in keeping the text straight1 it is customary to divide cipher text into groups of four1 five1 six or ten letters1 and usually groups of five letters are used4 ,the receiving operator may then expect five letters per group1 and if he receives more or less he is sure that either he or the sending operator has made an error4 ,this division into groups of a constant number of letters eliminates word forms and1 in the mind of the non-expert1 increases the difficulty of solving the cipher4 ,but the increase in difficulty is more apparent than real2 particularly1 as a cipher examiner habitually finds himself dealing with ciphers without word forms1 and the occurrence of a cipher with word forms usually means that he has an easy one to handle4 ,messages are occasionally encountered which consist partly of plain text and partly of cipher4 ,the cipher part may or may not retain its word forms1 but1 when this method is used1 it is clearly impossible to have a fixed number of letters in each cipher group if the word forms are not used4 ,it is almost impossible to prevent errors of transmission in such messages1 and it often requires considerable skill and labor to correct them4 ,for those unfamiliar with the telegraph alphabets1 they are given below4 ,messages sent by commercial or military telegraphs or buzzer lines will be transmitted with the ,american ,morse alphabet4 ,those sent by radio1 visual signalling or submarine cable will be transmitted by ,continental ,morse1 known also as the ,international ,code4 ,messages may be transmitted by both alphabets in course of transmission4 ,for example1 a cablegram from the ,philippines to ,nome1 ,alaska1 will be transmitted by ,continental ,morse 7commercial cable7 from ,manila to ,san ,francisco1 by ,american ,morse 7commercial land line7 from ,san ,francisco to ,seattle1 by ,continental ,morse 7military cable7 from ,seattle to ,valdez1 by ,american ,morse 7military land line7 from ,valdez to ,nulato and by ,continental ,morse 7military radio7 from ,nulato to ,nome4 ,prior to ,february1 #aiad1 the ,mexican government telegraph lines used an alphabet differing slightly from the ,american and ,continental ,morse4 ,however1 at that time1 the ,continental ,morse alphabet was prescribed for use on these lines and it is believed that the use of the old alphabet has entirely ceased on ,mexican lines4 ,however1 skilled ,american operators would have no difficulty in picking up this alphabet if it were found to be in use4 ,radio communication is1 by ,international ,convention1 invariably in ,continental ,morse4 ,telegraph ,alphabets ,character ,american ,morse ,continental ,morse or ,international ,code ,a 4 - 4 - ,b - 4 4 4 - 4 4 4 ,c 4 4 4 - 4 - 4 ,d - 4 4 - 4 4 ,e 4 4 ,f 4 - 4 4 4 - 4 ,g - - 4 - - 4 ,h 4 4 4 4 4 4 4 4 ,i 4 4 4 4 ,j - 4 - 4 4 - - - ,k - 4 - - 4 - ,l -- 4 - 4 4 ,m - - - - ,n - 4 - 4 ,o 4 4 - - - ,p 4 4 4 4 4 4 - - 4 ,q 4 4 - 4 - - 4 - ,r 4 4 4 4 - 4 ,s 4 4 4 4 4 4 ,t - - ,u 4 4 - 4 4 - ,v 4 4 4 - 4 4 4 - ,w 4 - - 4 - - ,x 4 - 4 4 - 4 4 - ,y 4 4 4 4 - 4 - - ,z 4 4 4 4 - - 4 4 #a 4 - - 4 4 - - - - #b 4 4 - 4 4 4 4 - - - #c 4 4 4 - 4 4 4 4 - - #d 4 4 4 4 - 4 4 4 4 - #e - - - 4 4 4 4 4 #f 4 4 4 4 4 4 - 4 4 4 4 #g - - 4 4 - - 4 4 4 #h - 4 4 4 4 - - - 4 4 #i - 4 4 - - - - - 4 #j ---- - - - - - ,period 4 4 - - 4 4 4 - 4 - 4 - ,question ,mark - 4 4 - 4 4 4 - - 4 4 ,comma 4 - 4 - - - 4 4 - - ,the following example will show some of the errors that creep into messages prepared with the cipher disk and transmitted by radio3 ,message ,radio ,douglas de ,el ,paso1 #b ,h #ga1 twenty-fifth1 #i3jj a4m41 ,govt4 ,to ,c4,o41 ,sixth ,brigade1 ,douglas1 ,arizona3 ,,jprzi ,,rdjsg ,,xtrmj ,,usfpc ,,recla ,,bcpcb ,,oaxpk ,,qeqkf ,,ppzae ,,bkutt ,,jhweu ,,ahpze ,,ezolt ,,hkxph ,,kihav ,,drodn ,,iapzc ,,lvump ,,kfubv ,,vtvnv ,,efvzv ,,tlvqs ,,bkahq ,,nvkvf ,,mgjth ,,owbgn ,,wwepo ,,ljkfp ,,hexkw ,,cpdlz ,,jwsqc ,,jvkig ,,htjht ,,egaha ,,gdxxk ,,bsppk ,,diavz ,,vqonc ,,hovda ,,vzqkw ,,fnvon ,,rpvgh ,,cufpv ,,sfpie ,,tozod ,,wgyfe ,,awnjy ,,koedw ,,umeld ,,nobuh ,,mupql ,,gyopp ,,odbab ,,ufuuc ,,aeojw ,,rdipk ,,wmokv ,,omicw ,,ckpih ,,lumsy ,,yosbg ,,wophv ,,pkomo ,,phger ,smith4 ,the key word is ,,atchison1 the cipher disk being used and the setting changed for every letter of the message4 ,the letter ,x indicates a period where it is evidently not a letter of a word4 ,deciphering the message with this key and method we have3 ,,relia ,,blein ,,forgf ,,tionf ,,romca ,,sasgr ,,andes ,,recei ,,ledhe ,,retha ,,tamou ,,ntedd ,,etach ,,msktl ,,eftth ,,erela ,,stnig ,,httoe ,,scort ,,shymp ,,entof ,,armsa ,,ndamm ,,uniti ,,ontob ,,esmug ,,gleda ,,crjxs ,,borde ,,rnext ,,frida ,,ynigh ,,tatap ,,ointt ,,welve ,,mienx ,,fkosb ,beyond this point the message1 if we continue the deciphering process1 is unintelligible4 ,the sense fails at the first ,p of the cipher group ,,bsppk4 ,we have translated ,b as ,m with disk ,a to ,n and ,s as ,i with disk ,a to ,a4 ,the last words that make sense are ,a ,,point ,,twelve ,,mi2 clearly the rest of the last word is ,,les and this is represented by ,,ppk4 ,putting ,p,l then ,a,a and putting ,p,e then ,a,t4 ,in other words1 the encipherer forgot to change his disk setting1 ,a to ,a1 after enciphering ,i into ,s and enciphered ,l into ,p with the same setting1 ,a to ,a4 ,continuing the deciphering on this basis1 we have3 ,,les ,,easto ,,fdoug ,,las4,t ,,hisis ,,inyou ,,rdist ,,rict4 ,,willy ,,outak ,,enece ,,ssarv ,,steps ,,topre ,,ventt ,,hissh ,,ipmen ,,tfrom ,,going ,,skzrx ,,leade ,,rofsm ,,uggle ,,rssal ,,dtobe ,,juanh ,,ernan ,,dezof ,,naco4 ,the minor errors underlined above are not difficult to correct except the sixth word in the eighth line4 ,they will be taken up however for analysis of cause of error4 ,line #a1 ,,gf should be ,,ma4 ,putting the latter into cipher we find the letters of the cipher should have been ,,go instead of ,,mj4 ,this is clearly a telegrapher's error1 --4 --- becoming -- 4--- ,line #b1 ,l should be ,v4 ,the corresponding cipher letter should be ,f instead of ,p4 ,this is an error of the encipherer in copying4 ,line #b1 ,,sk should be ,,en4 ,the corresponding cipher letters should be ,,yu instead of ,,kx4 ,another telegrapher's error1 -4-- 44- becoming -4- -44- ,line #c1 ,y should be ,i4 ,the corresponding cipher letter should be ,l instead of ,v4 ,another error in copying by the encipherer4 ,line #d1 ,,jx should be ,,os4 ,the corresponding cipher letters should be ,,fk instead of ,,kf2 an error on the part of the encipherer in copying4 ,line #g1 ,v should be ,y4 ,a mistake in copying4 ,line #h1 ,,skzrx4 ,if we take ,x as a period1 then this line might be ,,over1 the ,r being correct and ,,skz being in question4 ,the corresponding cipher letters are ,,aeo and if we encipher ,,ove we get ,,etj4 ,here again we have a telegrapher's error1 4 - 4--- becoming 4- 4 --- ,line #i1 ,l should be ,i4 ,the corresponding cipher letter should be ,k instead of ,h2 an error in copying by the encipherer4 ,the errors by the encipherer above noted are fairly common ones4 ,these and similar errors are usually found when a cipher message1 prepared as a rough draft by the encipherer1 is copied by a clerk and a careful check of the copy is not made4 ,the letters mistaken depend1 of course1 on the encipherer's hand writing or printing4 ,other errors1 besides those noted1 are the confusion of ,c1 ,g1 and ,q2 ,i1 and ,j2 ,b and ,r1 etc4 ,the error by the encipherer1 in not changing his disk setting for one letter and thus throwing out the whole process of deciphering1 would not have occurred had he put the message into eight columns or a multiple thereof and enciphered each column with one disk setting4 ,this latter method is also very much faster4 ,telegraphers' errors in cipher transmission are common and often very confusing4 ,note should be taken as to whether ,continental or ,american ,morse was used for transmission4 ,an analysis along the lines indicated will usually develop the error and correction4 ,if not1 a repetition should be demanded1 calling attention1 if possible1 to the particular groups that are not clear4 ,the deciphered and corrected message is3 ,reliable information from ,casas ,grandes received here that a mounted detachment left there last night to escort shipment of arms and ammunition to be smuggled across border next ,friday night1 at a point twelve miles east of ,douglas4 ,this is in your district4 ,will you take necessary steps to prevent this shipment going over8 ,leader of smugglers said to be ,juan ,hernandez of ,naco4 ,another remarkable example of errors in transmission by ,american ,morse is the following3 ,a message1 partly in cipher and partly in plain text1 contained the cipher words ,,ga ,,gtxieit ,,eidisxq ,this1 deciphered as far as possible by the alphabet determined by analysis of the rest of the cipher1 read ,,su ,,sme,y,m ,y,o,,ges ,it was finally decided that the context required a single word like ,,suspendio or ,,suspendioles for this cipher group4 ,an examination along this line showed that the cipher words should have been received ,g ,a ,g ,l ,x ,c ,u ,r ,d ,p ,x ,g and were received ,g ,a ,g ,t ,x ,,ie ,,it ,,ei ,d ,,is ,x ,q and that there were five errors in transmission in these three cipher groups alone4 ,,notes #a ,occurrence rare1 usually in proper names4 #b ,the method used is not the most satisfactory one for several reasons and a better method is that of writing the message in multiples of the key and enciphering the columns as already described4