Frequency TablesFirst AlphabetSecond AlphabetLetterPrefix (6)Suffix (2)LetterPrefix (1)Suffix (3)A1113DUDESFA0B111111118OOOFEEOSEOESYSCYB1113TQQALLC0C11BCD11114TYTDJUDD1111116DTPDXTLBCNVEE11ESE11111111111 11ABNBNINRRYNEOATLATYQTFF0F1113QIAIQFG0G112RRLLH0H11ZOI111111118EOFFEOVSOSEFQYJI0J0J11114ZLDIILCRL11OJL11TLM11FOM11VIN11114FEDUEEEEN11PRO11EOO11111117OIBQRMRAOEYYYYP112GENDP11TYQ11114UEOEOFBBQ111115XXITXOIRCRR11111117EEEYYBBGSGOOEER0S11DVS111111118REIATBVBLMLIQQDVT111111118JUJMQYVFLDSBPQDTT11TNU0U1113XDZCLLV112UFMSV11SIX1111116YQTQQAQUQDYQX0Y11OEY11114BIXBLCTLZ1113UUMJHUZ0Third AlphabetFourth AlphabetLetterPrefix (2)Suffix (4)LetterPrefix (3)Suffix (5)A11114OEEBCEREA0B11DGB0C1111116JUDYQCPYNUMUC111115LRAQTHHDDLD11SDD112QDLUE1113EODSSTE111111118MQAYQALRJICHCQCCF112FESSF0G0G11114BOIYUCIHH0H11YEI1111116JMSFQVMGUXRXI0J0J0L1111111111111114DGLSJSUEGYBBUYRMCSPYXQXEUVXLL11LTM11SEM111115LIYYCUUUUUN112DTPXN1113TCVDZLO11OGO0P0P1113LCNDJUQ11111117EQSFHSEETESCDTQ11LMR11114NQQJCXEZR1113LAIMNMS0S1111111119LEETQYFTFODHCEVCIIT11114EEEYNSCST11114QQVEOOIGU0U11114ICLCPDLYV112SDTNV11LUX0X11111117LILRILNPZBUBLY1111116OPOOOEESHMMGY112LCDLJZ0Z11RHFifth AlphabetSixth AlphabetLetterPrefix (4)Suffix (6)LetterPrefix (5)Suffix (1)A0A11BXB112XXEAB112UURRC11111117GDDSDSDOOFFOEVC0D1111116SCPYNCUUEUUQTQD11114UNLUANSAE112SHTPE111111111111113MHOIDPZZMBQUCRREOIQPNRIBQBF0F11111117PCCJEOCNIIBMVTG11UTG11UPH1111116CCSDGZEOOYYSH0I111115EGTSSEYOMVI0J1113EPXUOPJ112UMTTL1111116YDUCNXUDYQQUL0M1113RQREJEM112UITZN11RDN0O1113STTETFO1111111119HCJCHCVIGBLIBBIQYBP112UXFEP0Q11EEQ11114DDLLXTXXR0R0S0S112HTBIT11LST1113OEDDDXU111111111110MMGPXMMVMDJDGUMYEBBDU11111117JDDDLULZTVAQZNV11SOV112CITIX0X10IY11UFY111115IHLUHXDRRTZ112XNEEZ0We will now set down some of the determinations which can be made at once from these frequency tables. Clearly several mixed alphabets have been used. As was to be expected from the analysis of the recurring groups, we note that the frequency tables for alphabets 2 and 6 are of so nearly the same general form that certainly these two alphabets are one and the same. If a Spanish word has been used as a key word, this means thatAis probably represented by a vowel in these two alphabets and probably equalsAorO, because these two letters are such common finals in Spanish.1st Alphabet. Probable vowelsT,X; probable common consonants,B,I,N,R. We conclude this because of the frequency of occurrence ofTandXand the variety of their prefixes and suffixes. On the other hand,B,I,N, andRhave for prefixes and suffixes, in a majority of cases,E,F,OandSwhich are the probable vowels in the 2d and 6th alphabets.2d and 6th Alphabets.—Probable vowelsE,F,O,S; probable common consonants,D,J,Q,U,Y.3d Alphabet.—Probable vowelsC,I,L; probable common consonantsA,Q,T,Y.4th Alphabet.—Probable vowels,E,G,S,T; probable common consonants,C,M,N,P,U,X.5th Alphabet.—Probable vowels,D,L,U; probable common consonants,C,H,I.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 equivalent, having the regular alphabet on the fixed disk and the mixed alphabet on the movable disk. An equivalent form of apparatus (not using the mixed alphabet in question) is one like this:Fixed Alphabet of TextABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZPCJVRQZBAODFSUTMXIYHLGENMovable Alphabet of CipherHereAof the plain text is enciphered bySand the other letters come as they will. If we move the cipher alphabet one space to the left,Awill be enciphered byUand the whole sequence of the alphabet will be changed.We will therefore use some such form as the above and see if we can insert our letters, as they are determined, in such a way as to have each of the cipher slips identical. We may start thus:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stAlphabett x2dol qei ms d c u3dol qei ms d c u4thol qei ms d c u5thd c u ol qei ms6thol qei ms d c uIn the 1st alphabet,TandXare placed asAandErespectively on the basis of frequency. In the 2d and 6th alphabets,OandEare placed asAandErespectively on the basis of frequency. In the 4thalphabet,EandSare placed asAandE, and in the 5th,D,UandLare placed asA,EandOfor the same reason. We now have an excess of E’s and a deficiency of A’s, which will be corrected if, in the 3d alphabet, we placeL,IandCasA,EandOrespectively. As a check, this gives usTOLEDOas the key word.In the second alphabet,Ois four letters to the left ofE; we may placeOfour letters to the left ofEin the fourth and it comes underV. Note that in the fourth frequency tableO(=V) does not occur. In the same way in the fourth alphabet,Sis four letters to the right ofE; placing it in the same position with respect toEin the second and sixth, we haveSunderI. We have already noted thatSprobably represents a vowel in these two alphabets. In this way, we may addDandUto the third alphabet from their position in the fifth with respect toLand we may addIandOto the fifth from their position in the third with respect toL. In every case we check results from the frequency tables and find nothing unlikely in the results.Now in the second and sixth, let us tryQ,DandUasD,NandRrespectively. We may add these letters to the third, fourth and fifth alphabets by the method of observing the number of letters to the right or left of some letter already fixed. We now addLto the second, third, fourth and sixth from its position with reference toDandUin the fifth.Mis probablyDin the fourth and we may add it to each of the alphabets, except the first, in the same way. The table is now complete as shown.Let us try these letters on the first line of the message and see if some other letters will be self-evident.Alphabet123456123456123456123456123456MessageDDLRMERGLMUJTLLCHERSLSOEESMEJUDeciphered_NA_UE__ADE_ABAL_E_IAENE_IGA_RReferring to our frequency tables as a check on suppositions, we find everything agrees well enough if we assume the first line to read:UNAFUERZA DECABALLERIA ENEMIGAWe will now put the newly found letters in the table. The letters previously found are in capitals and the new letters in small letters. The addition ofD(=U) to the first alphabet permits us to add all the letters of the other alphabets to the first by the methods already discussed. Each of the other letters may then be added to every alphabet by these methods:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stT xhgoljqei msr d c u2dt xhgOLjQEI MSr D C U3dt xhgOLjQEI MSr D C U4tht xhgOLjQEI MSr D C U5tht xhgOLjQEI MSr D C U6tht xhgOLjQEI MSr D C UOne alphabet checks another in this way and we find everything to fit so far. We will decipher a few words more of the cipher message by the above alphabets and see if we can determine some new letters.Alphabet5612345612345612345612345612345612345612345612345612345612MessageJUZJIMUDAEESDUTDBGUGPNRCHOBEQEIEOOACDEIOOGCOLJLPDUVMIGIYXQDecipheredPR_CEDEN_EDEARAU__UEZ_ILLA_ECASEHA_LAENAZUCAICA_AR_HEUS_EDAgain referring to the frequency tables the first word is evidentlyPROCEDENTE. We have alsoHALLAandMARCHEUSTED. The letterBmay be determined from another cipher group,JFBSQDLD(56123456) =POSICION. The letterNmay be determined fromBETNDQXUC(123456123) =SERRADERO. The lettersFandYmay be determined fromJCPJOISLYDUASIUPF(23456123456123456)=COMPANIA PARTIENDO. The completed alphabets, arranged as before, are:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stTYVNXHGOLJQEIZMSRBADFCPU2dTYVNXHGOLJQEIZMSRBADFCPU3dTYVNXHGOLJQEIZMSRBADFCPU4thTYVNXHGOLJQEIZMSRBADFCPU5thTYVNXHGOLJQEIZMSRBADFCPU6thTYVNXHGOLJQEIZMSRBADFCPUThe key word isTOLEDOand the completely deciphered message is:“Una fuerza de caballeria enemiga procedente de Aranjuez y Villaseca se halla en Azucaica. 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 halla. (Q) Esta acantonada (Q) Se hallan otras tropas detras de ella (Q). El resultado del reconocimiento necesito saberlo dentro de tres horas y media cuando mas. Pongo a sus ordenes un ciclista (X) Fin.”
Frequency TablesFirst AlphabetSecond AlphabetLetterPrefix (6)Suffix (2)LetterPrefix (1)Suffix (3)A1113DUDESFA0B111111118OOOFEEOSEOESYSCYB1113TQQALLC0C11BCD11114TYTDJUDD1111116DTPDXTLBCNVEE11ESE11111111111 11ABNBNINRRYNEOATLATYQTFF0F1113QIAIQFG0G112RRLLH0H11ZOI111111118EOFFEOVSOSEFQYJI0J0J11114ZLDIILCRL11OJL11TLM11FOM11VIN11114FEDUEEEEN11PRO11EOO11111117OIBQRMRAOEYYYYP112GENDP11TYQ11114UEOEOFBBQ111115XXITXOIRCRR11111117EEEYYBBGSGOOEER0S11DVS111111118REIATBVBLMLIQQDVT111111118JUJMQYVFLDSBPQDTT11TNU0U1113XDZCLLV112UFMSV11SIX1111116YQTQQAQUQDYQX0Y11OEY11114BIXBLCTLZ1113UUMJHUZ0Third AlphabetFourth AlphabetLetterPrefix (2)Suffix (4)LetterPrefix (3)Suffix (5)A11114OEEBCEREA0B11DGB0C1111116JUDYQCPYNUMUC111115LRAQTHHDDLD11SDD112QDLUE1113EODSSTE111111118MQAYQALRJICHCQCCF112FESSF0G0G11114BOIYUCIHH0H11YEI1111116JMSFQVMGUXRXI0J0J0L1111111111111114DGLSJSUEGYBBUYRMCSPYXQXEUVXLL11LTM11SEM111115LIYYCUUUUUN112DTPXN1113TCVDZLO11OGO0P0P1113LCNDJUQ11111117EQSFHSEETESCDTQ11LMR11114NQQJCXEZR1113LAIMNMS0S1111111119LEETQYFTFODHCEVCIIT11114EEEYNSCST11114QQVEOOIGU0U11114ICLCPDLYV112SDTNV11LUX0X11111117LILRILNPZBUBLY1111116OPOOOEESHMMGY112LCDLJZ0Z11RHFifth AlphabetSixth AlphabetLetterPrefix (4)Suffix (6)LetterPrefix (5)Suffix (1)A0A11BXB112XXEAB112UURRC11111117GDDSDSDOOFFOEVC0D1111116SCPYNCUUEUUQTQD11114UNLUANSAE112SHTPE111111111111113MHOIDPZZMBQUCRREOIQPNRIBQBF0F11111117PCCJEOCNIIBMVTG11UTG11UPH1111116CCSDGZEOOYYSH0I111115EGTSSEYOMVI0J1113EPXUOPJ112UMTTL1111116YDUCNXUDYQQUL0M1113RQREJEM112UITZN11RDN0O1113STTETFO1111111119HCJCHCVIGBLIBBIQYBP112UXFEP0Q11EEQ11114DDLLXTXXR0R0S0S112HTBIT11LST1113OEDDDXU111111111110MMGPXMMVMDJDGUMYEBBDU11111117JDDDLULZTVAQZNV11SOV112CITIX0X10IY11UFY111115IHLUHXDRRTZ112XNEEZ0We will now set down some of the determinations which can be made at once from these frequency tables. Clearly several mixed alphabets have been used. As was to be expected from the analysis of the recurring groups, we note that the frequency tables for alphabets 2 and 6 are of so nearly the same general form that certainly these two alphabets are one and the same. If a Spanish word has been used as a key word, this means thatAis probably represented by a vowel in these two alphabets and probably equalsAorO, because these two letters are such common finals in Spanish.1st Alphabet. Probable vowelsT,X; probable common consonants,B,I,N,R. We conclude this because of the frequency of occurrence ofTandXand the variety of their prefixes and suffixes. On the other hand,B,I,N, andRhave for prefixes and suffixes, in a majority of cases,E,F,OandSwhich are the probable vowels in the 2d and 6th alphabets.2d and 6th Alphabets.—Probable vowelsE,F,O,S; probable common consonants,D,J,Q,U,Y.3d Alphabet.—Probable vowelsC,I,L; probable common consonantsA,Q,T,Y.4th Alphabet.—Probable vowels,E,G,S,T; probable common consonants,C,M,N,P,U,X.5th Alphabet.—Probable vowels,D,L,U; probable common consonants,C,H,I.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 equivalent, having the regular alphabet on the fixed disk and the mixed alphabet on the movable disk. An equivalent form of apparatus (not using the mixed alphabet in question) is one like this:Fixed Alphabet of TextABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZPCJVRQZBAODFSUTMXIYHLGENMovable Alphabet of CipherHereAof the plain text is enciphered bySand the other letters come as they will. If we move the cipher alphabet one space to the left,Awill be enciphered byUand the whole sequence of the alphabet will be changed.We will therefore use some such form as the above and see if we can insert our letters, as they are determined, in such a way as to have each of the cipher slips identical. We may start thus:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stAlphabett x2dol qei ms d c u3dol qei ms d c u4thol qei ms d c u5thd c u ol qei ms6thol qei ms d c uIn the 1st alphabet,TandXare placed asAandErespectively on the basis of frequency. In the 2d and 6th alphabets,OandEare placed asAandErespectively on the basis of frequency. In the 4thalphabet,EandSare placed asAandE, and in the 5th,D,UandLare placed asA,EandOfor the same reason. We now have an excess of E’s and a deficiency of A’s, which will be corrected if, in the 3d alphabet, we placeL,IandCasA,EandOrespectively. As a check, this gives usTOLEDOas the key word.In the second alphabet,Ois four letters to the left ofE; we may placeOfour letters to the left ofEin the fourth and it comes underV. Note that in the fourth frequency tableO(=V) does not occur. In the same way in the fourth alphabet,Sis four letters to the right ofE; placing it in the same position with respect toEin the second and sixth, we haveSunderI. We have already noted thatSprobably represents a vowel in these two alphabets. In this way, we may addDandUto the third alphabet from their position in the fifth with respect toLand we may addIandOto the fifth from their position in the third with respect toL. In every case we check results from the frequency tables and find nothing unlikely in the results.Now in the second and sixth, let us tryQ,DandUasD,NandRrespectively. We may add these letters to the third, fourth and fifth alphabets by the method of observing the number of letters to the right or left of some letter already fixed. We now addLto the second, third, fourth and sixth from its position with reference toDandUin the fifth.Mis probablyDin the fourth and we may add it to each of the alphabets, except the first, in the same way. The table is now complete as shown.Let us try these letters on the first line of the message and see if some other letters will be self-evident.Alphabet123456123456123456123456123456MessageDDLRMERGLMUJTLLCHERSLSOEESMEJUDeciphered_NA_UE__ADE_ABAL_E_IAENE_IGA_RReferring to our frequency tables as a check on suppositions, we find everything agrees well enough if we assume the first line to read:UNAFUERZA DECABALLERIA ENEMIGAWe will now put the newly found letters in the table. The letters previously found are in capitals and the new letters in small letters. The addition ofD(=U) to the first alphabet permits us to add all the letters of the other alphabets to the first by the methods already discussed. Each of the other letters may then be added to every alphabet by these methods:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stT xhgoljqei msr d c u2dt xhgOLjQEI MSr D C U3dt xhgOLjQEI MSr D C U4tht xhgOLjQEI MSr D C U5tht xhgOLjQEI MSr D C U6tht xhgOLjQEI MSr D C UOne alphabet checks another in this way and we find everything to fit so far. We will decipher a few words more of the cipher message by the above alphabets and see if we can determine some new letters.Alphabet5612345612345612345612345612345612345612345612345612345612MessageJUZJIMUDAEESDUTDBGUGPNRCHOBEQEIEOOACDEIOOGCOLJLPDUVMIGIYXQDecipheredPR_CEDEN_EDEARAU__UEZ_ILLA_ECASEHA_LAENAZUCAICA_AR_HEUS_EDAgain referring to the frequency tables the first word is evidentlyPROCEDENTE. We have alsoHALLAandMARCHEUSTED. The letterBmay be determined from another cipher group,JFBSQDLD(56123456) =POSICION. The letterNmay be determined fromBETNDQXUC(123456123) =SERRADERO. The lettersFandYmay be determined fromJCPJOISLYDUASIUPF(23456123456123456)=COMPANIA PARTIENDO. The completed alphabets, arranged as before, are:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stTYVNXHGOLJQEIZMSRBADFCPU2dTYVNXHGOLJQEIZMSRBADFCPU3dTYVNXHGOLJQEIZMSRBADFCPU4thTYVNXHGOLJQEIZMSRBADFCPU5thTYVNXHGOLJQEIZMSRBADFCPU6thTYVNXHGOLJQEIZMSRBADFCPUThe key word isTOLEDOand the completely deciphered message is:“Una fuerza de caballeria enemiga procedente de Aranjuez y Villaseca se halla en Azucaica. 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 halla. (Q) Esta acantonada (Q) Se hallan otras tropas detras de ella (Q). El resultado del reconocimiento necesito saberlo dentro de tres horas y media cuando mas. Pongo a sus ordenes un ciclista (X) Fin.”
Frequency TablesFirst AlphabetSecond AlphabetLetterPrefix (6)Suffix (2)LetterPrefix (1)Suffix (3)A1113DUDESFA0B111111118OOOFEEOSEOESYSCYB1113TQQALLC0C11BCD11114TYTDJUDD1111116DTPDXTLBCNVEE11ESE11111111111 11ABNBNINRRYNEOATLATYQTFF0F1113QIAIQFG0G112RRLLH0H11ZOI111111118EOFFEOVSOSEFQYJI0J0J11114ZLDIILCRL11OJL11TLM11FOM11VIN11114FEDUEEEEN11PRO11EOO11111117OIBQRMRAOEYYYYP112GENDP11TYQ11114UEOEOFBBQ111115XXITXOIRCRR11111117EEEYYBBGSGOOEER0S11DVS111111118REIATBVBLMLIQQDVT111111118JUJMQYVFLDSBPQDTT11TNU0U1113XDZCLLV112UFMSV11SIX1111116YQTQQAQUQDYQX0Y11OEY11114BIXBLCTLZ1113UUMJHUZ0Third AlphabetFourth AlphabetLetterPrefix (2)Suffix (4)LetterPrefix (3)Suffix (5)A11114OEEBCEREA0B11DGB0C1111116JUDYQCPYNUMUC111115LRAQTHHDDLD11SDD112QDLUE1113EODSSTE111111118MQAYQALRJICHCQCCF112FESSF0G0G11114BOIYUCIHH0H11YEI1111116JMSFQVMGUXRXI0J0J0L1111111111111114DGLSJSUEGYBBUYRMCSPYXQXEUVXLL11LTM11SEM111115LIYYCUUUUUN112DTPXN1113TCVDZLO11OGO0P0P1113LCNDJUQ11111117EQSFHSEETESCDTQ11LMR11114NQQJCXEZR1113LAIMNMS0S1111111119LEETQYFTFODHCEVCIIT11114EEEYNSCST11114QQVEOOIGU0U11114ICLCPDLYV112SDTNV11LUX0X11111117LILRILNPZBUBLY1111116OPOOOEESHMMGY112LCDLJZ0Z11RHFifth AlphabetSixth AlphabetLetterPrefix (4)Suffix (6)LetterPrefix (5)Suffix (1)A0A11BXB112XXEAB112UURRC11111117GDDSDSDOOFFOEVC0D1111116SCPYNCUUEUUQTQD11114UNLUANSAE112SHTPE111111111111113MHOIDPZZMBQUCRREOIQPNRIBQBF0F11111117PCCJEOCNIIBMVTG11UTG11UPH1111116CCSDGZEOOYYSH0I111115EGTSSEYOMVI0J1113EPXUOPJ112UMTTL1111116YDUCNXUDYQQUL0M1113RQREJEM112UITZN11RDN0O1113STTETFO1111111119HCJCHCVIGBLIBBIQYBP112UXFEP0Q11EEQ11114DDLLXTXXR0R0S0S112HTBIT11LST1113OEDDDXU111111111110MMGPXMMVMDJDGUMYEBBDU11111117JDDDLULZTVAQZNV11SOV112CITIX0X10IY11UFY111115IHLUHXDRRTZ112XNEEZ0We will now set down some of the determinations which can be made at once from these frequency tables. Clearly several mixed alphabets have been used. As was to be expected from the analysis of the recurring groups, we note that the frequency tables for alphabets 2 and 6 are of so nearly the same general form that certainly these two alphabets are one and the same. If a Spanish word has been used as a key word, this means thatAis probably represented by a vowel in these two alphabets and probably equalsAorO, because these two letters are such common finals in Spanish.1st Alphabet. Probable vowelsT,X; probable common consonants,B,I,N,R. We conclude this because of the frequency of occurrence ofTandXand the variety of their prefixes and suffixes. On the other hand,B,I,N, andRhave for prefixes and suffixes, in a majority of cases,E,F,OandSwhich are the probable vowels in the 2d and 6th alphabets.2d and 6th Alphabets.—Probable vowelsE,F,O,S; probable common consonants,D,J,Q,U,Y.3d Alphabet.—Probable vowelsC,I,L; probable common consonantsA,Q,T,Y.4th Alphabet.—Probable vowels,E,G,S,T; probable common consonants,C,M,N,P,U,X.5th Alphabet.—Probable vowels,D,L,U; probable common consonants,C,H,I.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 equivalent, having the regular alphabet on the fixed disk and the mixed alphabet on the movable disk. An equivalent form of apparatus (not using the mixed alphabet in question) is one like this:Fixed Alphabet of TextABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZPCJVRQZBAODFSUTMXIYHLGENMovable Alphabet of CipherHereAof the plain text is enciphered bySand the other letters come as they will. If we move the cipher alphabet one space to the left,Awill be enciphered byUand the whole sequence of the alphabet will be changed.We will therefore use some such form as the above and see if we can insert our letters, as they are determined, in such a way as to have each of the cipher slips identical. We may start thus:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stAlphabett x2dol qei ms d c u3dol qei ms d c u4thol qei ms d c u5thd c u ol qei ms6thol qei ms d c uIn the 1st alphabet,TandXare placed asAandErespectively on the basis of frequency. In the 2d and 6th alphabets,OandEare placed asAandErespectively on the basis of frequency. In the 4thalphabet,EandSare placed asAandE, and in the 5th,D,UandLare placed asA,EandOfor the same reason. We now have an excess of E’s and a deficiency of A’s, which will be corrected if, in the 3d alphabet, we placeL,IandCasA,EandOrespectively. As a check, this gives usTOLEDOas the key word.In the second alphabet,Ois four letters to the left ofE; we may placeOfour letters to the left ofEin the fourth and it comes underV. Note that in the fourth frequency tableO(=V) does not occur. In the same way in the fourth alphabet,Sis four letters to the right ofE; placing it in the same position with respect toEin the second and sixth, we haveSunderI. We have already noted thatSprobably represents a vowel in these two alphabets. In this way, we may addDandUto the third alphabet from their position in the fifth with respect toLand we may addIandOto the fifth from their position in the third with respect toL. In every case we check results from the frequency tables and find nothing unlikely in the results.Now in the second and sixth, let us tryQ,DandUasD,NandRrespectively. We may add these letters to the third, fourth and fifth alphabets by the method of observing the number of letters to the right or left of some letter already fixed. We now addLto the second, third, fourth and sixth from its position with reference toDandUin the fifth.Mis probablyDin the fourth and we may add it to each of the alphabets, except the first, in the same way. The table is now complete as shown.Let us try these letters on the first line of the message and see if some other letters will be self-evident.Alphabet123456123456123456123456123456MessageDDLRMERGLMUJTLLCHERSLSOEESMEJUDeciphered_NA_UE__ADE_ABAL_E_IAENE_IGA_RReferring to our frequency tables as a check on suppositions, we find everything agrees well enough if we assume the first line to read:UNAFUERZA DECABALLERIA ENEMIGAWe will now put the newly found letters in the table. The letters previously found are in capitals and the new letters in small letters. The addition ofD(=U) to the first alphabet permits us to add all the letters of the other alphabets to the first by the methods already discussed. Each of the other letters may then be added to every alphabet by these methods:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stT xhgoljqei msr d c u2dt xhgOLjQEI MSr D C U3dt xhgOLjQEI MSr D C U4tht xhgOLjQEI MSr D C U5tht xhgOLjQEI MSr D C U6tht xhgOLjQEI MSr D C UOne alphabet checks another in this way and we find everything to fit so far. We will decipher a few words more of the cipher message by the above alphabets and see if we can determine some new letters.Alphabet5612345612345612345612345612345612345612345612345612345612MessageJUZJIMUDAEESDUTDBGUGPNRCHOBEQEIEOOACDEIOOGCOLJLPDUVMIGIYXQDecipheredPR_CEDEN_EDEARAU__UEZ_ILLA_ECASEHA_LAENAZUCAICA_AR_HEUS_EDAgain referring to the frequency tables the first word is evidentlyPROCEDENTE. We have alsoHALLAandMARCHEUSTED. The letterBmay be determined from another cipher group,JFBSQDLD(56123456) =POSICION. The letterNmay be determined fromBETNDQXUC(123456123) =SERRADERO. The lettersFandYmay be determined fromJCPJOISLYDUASIUPF(23456123456123456)=COMPANIA PARTIENDO. The completed alphabets, arranged as before, are:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stTYVNXHGOLJQEIZMSRBADFCPU2dTYVNXHGOLJQEIZMSRBADFCPU3dTYVNXHGOLJQEIZMSRBADFCPU4thTYVNXHGOLJQEIZMSRBADFCPU5thTYVNXHGOLJQEIZMSRBADFCPU6thTYVNXHGOLJQEIZMSRBADFCPUThe key word isTOLEDOand the completely deciphered message is:“Una fuerza de caballeria enemiga procedente de Aranjuez y Villaseca se halla en Azucaica. 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 halla. (Q) Esta acantonada (Q) Se hallan otras tropas detras de ella (Q). El resultado del reconocimiento necesito saberlo dentro de tres horas y media cuando mas. Pongo a sus ordenes un ciclista (X) Fin.”
Frequency TablesFirst AlphabetSecond AlphabetLetterPrefix (6)Suffix (2)LetterPrefix (1)Suffix (3)A1113DUDESFA0B111111118OOOFEEOSEOESYSCYB1113TQQALLC0C11BCD11114TYTDJUDD1111116DTPDXTLBCNVEE11ESE11111111111 11ABNBNINRRYNEOATLATYQTFF0F1113QIAIQFG0G112RRLLH0H11ZOI111111118EOFFEOVSOSEFQYJI0J0J11114ZLDIILCRL11OJL11TLM11FOM11VIN11114FEDUEEEEN11PRO11EOO11111117OIBQRMRAOEYYYYP112GENDP11TYQ11114UEOEOFBBQ111115XXITXOIRCRR11111117EEEYYBBGSGOOEER0S11DVS111111118REIATBVBLMLIQQDVT111111118JUJMQYVFLDSBPQDTT11TNU0U1113XDZCLLV112UFMSV11SIX1111116YQTQQAQUQDYQX0Y11OEY11114BIXBLCTLZ1113UUMJHUZ0Third AlphabetFourth AlphabetLetterPrefix (2)Suffix (4)LetterPrefix (3)Suffix (5)A11114OEEBCEREA0B11DGB0C1111116JUDYQCPYNUMUC111115LRAQTHHDDLD11SDD112QDLUE1113EODSSTE111111118MQAYQALRJICHCQCCF112FESSF0G0G11114BOIYUCIHH0H11YEI1111116JMSFQVMGUXRXI0J0J0L1111111111111114DGLSJSUEGYBBUYRMCSPYXQXEUVXLL11LTM11SEM111115LIYYCUUUUUN112DTPXN1113TCVDZLO11OGO0P0P1113LCNDJUQ11111117EQSFHSEETESCDTQ11LMR11114NQQJCXEZR1113LAIMNMS0S1111111119LEETQYFTFODHCEVCIIT11114EEEYNSCST11114QQVEOOIGU0U11114ICLCPDLYV112SDTNV11LUX0X11111117LILRILNPZBUBLY1111116OPOOOEESHMMGY112LCDLJZ0Z11RHFifth AlphabetSixth AlphabetLetterPrefix (4)Suffix (6)LetterPrefix (5)Suffix (1)A0A11BXB112XXEAB112UURRC11111117GDDSDSDOOFFOEVC0D1111116SCPYNCUUEUUQTQD11114UNLUANSAE112SHTPE111111111111113MHOIDPZZMBQUCRREOIQPNRIBQBF0F11111117PCCJEOCNIIBMVTG11UTG11UPH1111116CCSDGZEOOYYSH0I111115EGTSSEYOMVI0J1113EPXUOPJ112UMTTL1111116YDUCNXUDYQQUL0M1113RQREJEM112UITZN11RDN0O1113STTETFO1111111119HCJCHCVIGBLIBBIQYBP112UXFEP0Q11EEQ11114DDLLXTXXR0R0S0S112HTBIT11LST1113OEDDDXU111111111110MMGPXMMVMDJDGUMYEBBDU11111117JDDDLULZTVAQZNV11SOV112CITIX0X10IY11UFY111115IHLUHXDRRTZ112XNEEZ0We will now set down some of the determinations which can be made at once from these frequency tables. Clearly several mixed alphabets have been used. As was to be expected from the analysis of the recurring groups, we note that the frequency tables for alphabets 2 and 6 are of so nearly the same general form that certainly these two alphabets are one and the same. If a Spanish word has been used as a key word, this means thatAis probably represented by a vowel in these two alphabets and probably equalsAorO, because these two letters are such common finals in Spanish.1st Alphabet. Probable vowelsT,X; probable common consonants,B,I,N,R. We conclude this because of the frequency of occurrence ofTandXand the variety of their prefixes and suffixes. On the other hand,B,I,N, andRhave for prefixes and suffixes, in a majority of cases,E,F,OandSwhich are the probable vowels in the 2d and 6th alphabets.2d and 6th Alphabets.—Probable vowelsE,F,O,S; probable common consonants,D,J,Q,U,Y.3d Alphabet.—Probable vowelsC,I,L; probable common consonantsA,Q,T,Y.4th Alphabet.—Probable vowels,E,G,S,T; probable common consonants,C,M,N,P,U,X.5th Alphabet.—Probable vowels,D,L,U; probable common consonants,C,H,I.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 equivalent, having the regular alphabet on the fixed disk and the mixed alphabet on the movable disk. An equivalent form of apparatus (not using the mixed alphabet in question) is one like this:Fixed Alphabet of TextABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZPCJVRQZBAODFSUTMXIYHLGENMovable Alphabet of CipherHereAof the plain text is enciphered bySand the other letters come as they will. If we move the cipher alphabet one space to the left,Awill be enciphered byUand the whole sequence of the alphabet will be changed.We will therefore use some such form as the above and see if we can insert our letters, as they are determined, in such a way as to have each of the cipher slips identical. We may start thus:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stAlphabett x2dol qei ms d c u3dol qei ms d c u4thol qei ms d c u5thd c u ol qei ms6thol qei ms d c uIn the 1st alphabet,TandXare placed asAandErespectively on the basis of frequency. In the 2d and 6th alphabets,OandEare placed asAandErespectively on the basis of frequency. In the 4thalphabet,EandSare placed asAandE, and in the 5th,D,UandLare placed asA,EandOfor the same reason. We now have an excess of E’s and a deficiency of A’s, which will be corrected if, in the 3d alphabet, we placeL,IandCasA,EandOrespectively. As a check, this gives usTOLEDOas the key word.In the second alphabet,Ois four letters to the left ofE; we may placeOfour letters to the left ofEin the fourth and it comes underV. Note that in the fourth frequency tableO(=V) does not occur. In the same way in the fourth alphabet,Sis four letters to the right ofE; placing it in the same position with respect toEin the second and sixth, we haveSunderI. We have already noted thatSprobably represents a vowel in these two alphabets. In this way, we may addDandUto the third alphabet from their position in the fifth with respect toLand we may addIandOto the fifth from their position in the third with respect toL. In every case we check results from the frequency tables and find nothing unlikely in the results.Now in the second and sixth, let us tryQ,DandUasD,NandRrespectively. We may add these letters to the third, fourth and fifth alphabets by the method of observing the number of letters to the right or left of some letter already fixed. We now addLto the second, third, fourth and sixth from its position with reference toDandUin the fifth.Mis probablyDin the fourth and we may add it to each of the alphabets, except the first, in the same way. The table is now complete as shown.Let us try these letters on the first line of the message and see if some other letters will be self-evident.Alphabet123456123456123456123456123456MessageDDLRMERGLMUJTLLCHERSLSOEESMEJUDeciphered_NA_UE__ADE_ABAL_E_IAENE_IGA_RReferring to our frequency tables as a check on suppositions, we find everything agrees well enough if we assume the first line to read:UNAFUERZA DECABALLERIA ENEMIGAWe will now put the newly found letters in the table. The letters previously found are in capitals and the new letters in small letters. The addition ofD(=U) to the first alphabet permits us to add all the letters of the other alphabets to the first by the methods already discussed. Each of the other letters may then be added to every alphabet by these methods:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stT xhgoljqei msr d c u2dt xhgOLjQEI MSr D C U3dt xhgOLjQEI MSr D C U4tht xhgOLjQEI MSr D C U5tht xhgOLjQEI MSr D C U6tht xhgOLjQEI MSr D C UOne alphabet checks another in this way and we find everything to fit so far. We will decipher a few words more of the cipher message by the above alphabets and see if we can determine some new letters.Alphabet5612345612345612345612345612345612345612345612345612345612MessageJUZJIMUDAEESDUTDBGUGPNRCHOBEQEIEOOACDEIOOGCOLJLPDUVMIGIYXQDecipheredPR_CEDEN_EDEARAU__UEZ_ILLA_ECASEHA_LAENAZUCAICA_AR_HEUS_EDAgain referring to the frequency tables the first word is evidentlyPROCEDENTE. We have alsoHALLAandMARCHEUSTED. The letterBmay be determined from another cipher group,JFBSQDLD(56123456) =POSICION. The letterNmay be determined fromBETNDQXUC(123456123) =SERRADERO. The lettersFandYmay be determined fromJCPJOISLYDUASIUPF(23456123456123456)=COMPANIA PARTIENDO. The completed alphabets, arranged as before, are:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stTYVNXHGOLJQEIZMSRBADFCPU2dTYVNXHGOLJQEIZMSRBADFCPU3dTYVNXHGOLJQEIZMSRBADFCPU4thTYVNXHGOLJQEIZMSRBADFCPU5thTYVNXHGOLJQEIZMSRBADFCPU6thTYVNXHGOLJQEIZMSRBADFCPUThe key word isTOLEDOand the completely deciphered message is:“Una fuerza de caballeria enemiga procedente de Aranjuez y Villaseca se halla en Azucaica. 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 halla. (Q) Esta acantonada (Q) Se hallan otras tropas detras de ella (Q). El resultado del reconocimiento necesito saberlo dentro de tres horas y media cuando mas. Pongo a sus ordenes un ciclista (X) Fin.”
Frequency Tables
First AlphabetSecond AlphabetLetterPrefix (6)Suffix (2)LetterPrefix (1)Suffix (3)A1113DUDESFA0B111111118OOOFEEOSEOESYSCYB1113TQQALLC0C11BCD11114TYTDJUDD1111116DTPDXTLBCNVEE11ESE11111111111 11ABNBNINRRYNEOATLATYQTFF0F1113QIAIQFG0G112RRLLH0H11ZOI111111118EOFFEOVSOSEFQYJI0J0J11114ZLDIILCRL11OJL11TLM11FOM11VIN11114FEDUEEEEN11PRO11EOO11111117OIBQRMRAOEYYYYP112GENDP11TYQ11114UEOEOFBBQ111115XXITXOIRCRR11111117EEEYYBBGSGOOEER0S11DVS111111118REIATBVBLMLIQQDVT111111118JUJMQYVFLDSBPQDTT11TNU0U1113XDZCLLV112UFMSV11SIX1111116YQTQQAQUQDYQX0Y11OEY11114BIXBLCTLZ1113UUMJHUZ0Third AlphabetFourth AlphabetLetterPrefix (2)Suffix (4)LetterPrefix (3)Suffix (5)A11114OEEBCEREA0B11DGB0C1111116JUDYQCPYNUMUC111115LRAQTHHDDLD11SDD112QDLUE1113EODSSTE111111118MQAYQALRJICHCQCCF112FESSF0G0G11114BOIYUCIHH0H11YEI1111116JMSFQVMGUXRXI0J0J0L1111111111111114DGLSJSUEGYBBUYRMCSPYXQXEUVXLL11LTM11SEM111115LIYYCUUUUUN112DTPXN1113TCVDZLO11OGO0P0P1113LCNDJUQ11111117EQSFHSEETESCDTQ11LMR11114NQQJCXEZR1113LAIMNMS0S1111111119LEETQYFTFODHCEVCIIT11114EEEYNSCST11114QQVEOOIGU0U11114ICLCPDLYV112SDTNV11LUX0X11111117LILRILNPZBUBLY1111116OPOOOEESHMMGY112LCDLJZ0Z11RHFifth AlphabetSixth AlphabetLetterPrefix (4)Suffix (6)LetterPrefix (5)Suffix (1)A0A11BXB112XXEAB112UURRC11111117GDDSDSDOOFFOEVC0D1111116SCPYNCUUEUUQTQD11114UNLUANSAE112SHTPE111111111111113MHOIDPZZMBQUCRREOIQPNRIBQBF0F11111117PCCJEOCNIIBMVTG11UTG11UPH1111116CCSDGZEOOYYSH0I111115EGTSSEYOMVI0J1113EPXUOPJ112UMTTL1111116YDUCNXUDYQQUL0M1113RQREJEM112UITZN11RDN0O1113STTETFO1111111119HCJCHCVIGBLIBBIQYBP112UXFEP0Q11EEQ11114DDLLXTXXR0R0S0S112HTBIT11LST1113OEDDDXU111111111110MMGPXMMVMDJDGUMYEBBDU11111117JDDDLULZTVAQZNV11SOV112CITIX0X10IY11UFY111115IHLUHXDRRTZ112XNEEZ0We will now set down some of the determinations which can be made at once from these frequency tables. Clearly several mixed alphabets have been used. As was to be expected from the analysis of the recurring groups, we note that the frequency tables for alphabets 2 and 6 are of so nearly the same general form that certainly these two alphabets are one and the same. If a Spanish word has been used as a key word, this means thatAis probably represented by a vowel in these two alphabets and probably equalsAorO, because these two letters are such common finals in Spanish.1st Alphabet. Probable vowelsT,X; probable common consonants,B,I,N,R. We conclude this because of the frequency of occurrence ofTandXand the variety of their prefixes and suffixes. On the other hand,B,I,N, andRhave for prefixes and suffixes, in a majority of cases,E,F,OandSwhich are the probable vowels in the 2d and 6th alphabets.2d and 6th Alphabets.—Probable vowelsE,F,O,S; probable common consonants,D,J,Q,U,Y.3d Alphabet.—Probable vowelsC,I,L; probable common consonantsA,Q,T,Y.4th Alphabet.—Probable vowels,E,G,S,T; probable common consonants,C,M,N,P,U,X.5th Alphabet.—Probable vowels,D,L,U; probable common consonants,C,H,I.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 equivalent, having the regular alphabet on the fixed disk and the mixed alphabet on the movable disk. An equivalent form of apparatus (not using the mixed alphabet in question) is one like this:Fixed Alphabet of TextABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZPCJVRQZBAODFSUTMXIYHLGENMovable Alphabet of CipherHereAof the plain text is enciphered bySand the other letters come as they will. If we move the cipher alphabet one space to the left,Awill be enciphered byUand the whole sequence of the alphabet will be changed.We will therefore use some such form as the above and see if we can insert our letters, as they are determined, in such a way as to have each of the cipher slips identical. We may start thus:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stAlphabett x2dol qei ms d c u3dol qei ms d c u4thol qei ms d c u5thd c u ol qei ms6thol qei ms d c uIn the 1st alphabet,TandXare placed asAandErespectively on the basis of frequency. In the 2d and 6th alphabets,OandEare placed asAandErespectively on the basis of frequency. In the 4thalphabet,EandSare placed asAandE, and in the 5th,D,UandLare placed asA,EandOfor the same reason. We now have an excess of E’s and a deficiency of A’s, which will be corrected if, in the 3d alphabet, we placeL,IandCasA,EandOrespectively. As a check, this gives usTOLEDOas the key word.In the second alphabet,Ois four letters to the left ofE; we may placeOfour letters to the left ofEin the fourth and it comes underV. Note that in the fourth frequency tableO(=V) does not occur. In the same way in the fourth alphabet,Sis four letters to the right ofE; placing it in the same position with respect toEin the second and sixth, we haveSunderI. We have already noted thatSprobably represents a vowel in these two alphabets. In this way, we may addDandUto the third alphabet from their position in the fifth with respect toLand we may addIandOto the fifth from their position in the third with respect toL. In every case we check results from the frequency tables and find nothing unlikely in the results.Now in the second and sixth, let us tryQ,DandUasD,NandRrespectively. We may add these letters to the third, fourth and fifth alphabets by the method of observing the number of letters to the right or left of some letter already fixed. We now addLto the second, third, fourth and sixth from its position with reference toDandUin the fifth.Mis probablyDin the fourth and we may add it to each of the alphabets, except the first, in the same way. The table is now complete as shown.Let us try these letters on the first line of the message and see if some other letters will be self-evident.Alphabet123456123456123456123456123456MessageDDLRMERGLMUJTLLCHERSLSOEESMEJUDeciphered_NA_UE__ADE_ABAL_E_IAENE_IGA_RReferring to our frequency tables as a check on suppositions, we find everything agrees well enough if we assume the first line to read:UNAFUERZA DECABALLERIA ENEMIGAWe will now put the newly found letters in the table. The letters previously found are in capitals and the new letters in small letters. The addition ofD(=U) to the first alphabet permits us to add all the letters of the other alphabets to the first by the methods already discussed. Each of the other letters may then be added to every alphabet by these methods:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stT xhgoljqei msr d c u2dt xhgOLjQEI MSr D C U3dt xhgOLjQEI MSr D C U4tht xhgOLjQEI MSr D C U5tht xhgOLjQEI MSr D C U6tht xhgOLjQEI MSr D C UOne alphabet checks another in this way and we find everything to fit so far. We will decipher a few words more of the cipher message by the above alphabets and see if we can determine some new letters.Alphabet5612345612345612345612345612345612345612345612345612345612MessageJUZJIMUDAEESDUTDBGUGPNRCHOBEQEIEOOACDEIOOGCOLJLPDUVMIGIYXQDecipheredPR_CEDEN_EDEARAU__UEZ_ILLA_ECASEHA_LAENAZUCAICA_AR_HEUS_EDAgain referring to the frequency tables the first word is evidentlyPROCEDENTE. We have alsoHALLAandMARCHEUSTED. The letterBmay be determined from another cipher group,JFBSQDLD(56123456) =POSICION. The letterNmay be determined fromBETNDQXUC(123456123) =SERRADERO. The lettersFandYmay be determined fromJCPJOISLYDUASIUPF(23456123456123456)=COMPANIA PARTIENDO. The completed alphabets, arranged as before, are:ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stTYVNXHGOLJQEIZMSRBADFCPU2dTYVNXHGOLJQEIZMSRBADFCPU3dTYVNXHGOLJQEIZMSRBADFCPU4thTYVNXHGOLJQEIZMSRBADFCPU5thTYVNXHGOLJQEIZMSRBADFCPU6thTYVNXHGOLJQEIZMSRBADFCPUThe key word isTOLEDOand the completely deciphered message is:“Una fuerza de caballeria enemiga procedente de Aranjuez y Villaseca se halla en Azucaica. 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 halla. (Q) Esta acantonada (Q) Se hallan otras tropas detras de ella (Q). El resultado del reconocimiento necesito saberlo dentro de tres horas y media cuando mas. Pongo a sus ordenes un ciclista (X) Fin.”
First AlphabetSecond AlphabetLetterPrefix (6)Suffix (2)LetterPrefix (1)Suffix (3)A1113DUDESFA0B111111118OOOFEEOSEOESYSCYB1113TQQALLC0C11BCD11114TYTDJUDD1111116DTPDXTLBCNVEE11ESE11111111111 11ABNBNINRRYNEOATLATYQTFF0F1113QIAIQFG0G112RRLLH0H11ZOI111111118EOFFEOVSOSEFQYJI0J0J11114ZLDIILCRL11OJL11TLM11FOM11VIN11114FEDUEEEEN11PRO11EOO11111117OIBQRMRAOEYYYYP112GENDP11TYQ11114UEOEOFBBQ111115XXITXOIRCRR11111117EEEYYBBGSGOOEER0S11DVS111111118REIATBVBLMLIQQDVT111111118JUJMQYVFLDSBPQDTT11TNU0U1113XDZCLLV112UFMSV11SIX1111116YQTQQAQUQDYQX0Y11OEY11114BIXBLCTLZ1113UUMJHUZ0Third AlphabetFourth AlphabetLetterPrefix (2)Suffix (4)LetterPrefix (3)Suffix (5)A11114OEEBCEREA0B11DGB0C1111116JUDYQCPYNUMUC111115LRAQTHHDDLD11SDD112QDLUE1113EODSSTE111111118MQAYQALRJICHCQCCF112FESSF0G0G11114BOIYUCIHH0H11YEI1111116JMSFQVMGUXRXI0J0J0L1111111111111114DGLSJSUEGYBBUYRMCSPYXQXEUVXLL11LTM11SEM111115LIYYCUUUUUN112DTPXN1113TCVDZLO11OGO0P0P1113LCNDJUQ11111117EQSFHSEETESCDTQ11LMR11114NQQJCXEZR1113LAIMNMS0S1111111119LEETQYFTFODHCEVCIIT11114EEEYNSCST11114QQVEOOIGU0U11114ICLCPDLYV112SDTNV11LUX0X11111117LILRILNPZBUBLY1111116OPOOOEESHMMGY112LCDLJZ0Z11RHFifth AlphabetSixth AlphabetLetterPrefix (4)Suffix (6)LetterPrefix (5)Suffix (1)A0A11BXB112XXEAB112UURRC11111117GDDSDSDOOFFOEVC0D1111116SCPYNCUUEUUQTQD11114UNLUANSAE112SHTPE111111111111113MHOIDPZZMBQUCRREOIQPNRIBQBF0F11111117PCCJEOCNIIBMVTG11UTG11UPH1111116CCSDGZEOOYYSH0I111115EGTSSEYOMVI0J1113EPXUOPJ112UMTTL1111116YDUCNXUDYQQUL0M1113RQREJEM112UITZN11RDN0O1113STTETFO1111111119HCJCHCVIGBLIBBIQYBP112UXFEP0Q11EEQ11114DDLLXTXXR0R0S0S112HTBIT11LST1113OEDDDXU111111111110MMGPXMMVMDJDGUMYEBBDU11111117JDDDLULZTVAQZNV11SOV112CITIX0X10IY11UFY111115IHLUHXDRRTZ112XNEEZ0
We will now set down some of the determinations which can be made at once from these frequency tables. Clearly several mixed alphabets have been used. As was to be expected from the analysis of the recurring groups, we note that the frequency tables for alphabets 2 and 6 are of so nearly the same general form that certainly these two alphabets are one and the same. If a Spanish word has been used as a key word, this means thatAis probably represented by a vowel in these two alphabets and probably equalsAorO, because these two letters are such common finals in Spanish.
1st Alphabet. Probable vowelsT,X; probable common consonants,B,I,N,R. We conclude this because of the frequency of occurrence ofTandXand the variety of their prefixes and suffixes. On the other hand,B,I,N, andRhave for prefixes and suffixes, in a majority of cases,E,F,OandSwhich are the probable vowels in the 2d and 6th alphabets.
2d and 6th Alphabets.—Probable vowelsE,F,O,S; probable common consonants,D,J,Q,U,Y.
3d Alphabet.—Probable vowelsC,I,L; probable common consonantsA,Q,T,Y.
4th Alphabet.—Probable vowels,E,G,S,T; probable common consonants,C,M,N,P,U,X.
5th Alphabet.—Probable vowels,D,L,U; probable common consonants,C,H,I.
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 equivalent, having the regular alphabet on the fixed disk and the mixed alphabet on the movable disk. An equivalent form of apparatus (not using the mixed alphabet in question) is one like this:
Fixed Alphabet of TextABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZPCJVRQZBAODFSUTMXIYHLGENMovable Alphabet of Cipher
HereAof the plain text is enciphered bySand the other letters come as they will. If we move the cipher alphabet one space to the left,Awill be enciphered byUand the whole sequence of the alphabet will be changed.
We will therefore use some such form as the above and see if we can insert our letters, as they are determined, in such a way as to have each of the cipher slips identical. We may start thus:
ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stAlphabett x2dol qei ms d c u3dol qei ms d c u4thol qei ms d c u5thd c u ol qei ms6thol qei ms d c u
In the 1st alphabet,TandXare placed asAandErespectively on the basis of frequency. In the 2d and 6th alphabets,OandEare placed asAandErespectively on the basis of frequency. In the 4thalphabet,EandSare placed asAandE, and in the 5th,D,UandLare placed asA,EandOfor the same reason. We now have an excess of E’s and a deficiency of A’s, which will be corrected if, in the 3d alphabet, we placeL,IandCasA,EandOrespectively. As a check, this gives usTOLEDOas the key word.
In the second alphabet,Ois four letters to the left ofE; we may placeOfour letters to the left ofEin the fourth and it comes underV. Note that in the fourth frequency tableO(=V) does not occur. In the same way in the fourth alphabet,Sis four letters to the right ofE; placing it in the same position with respect toEin the second and sixth, we haveSunderI. We have already noted thatSprobably represents a vowel in these two alphabets. In this way, we may addDandUto the third alphabet from their position in the fifth with respect toLand we may addIandOto the fifth from their position in the third with respect toL. In every case we check results from the frequency tables and find nothing unlikely in the results.
Now in the second and sixth, let us tryQ,DandUasD,NandRrespectively. We may add these letters to the third, fourth and fifth alphabets by the method of observing the number of letters to the right or left of some letter already fixed. We now addLto the second, third, fourth and sixth from its position with reference toDandUin the fifth.Mis probablyDin the fourth and we may add it to each of the alphabets, except the first, in the same way. The table is now complete as shown.
Let us try these letters on the first line of the message and see if some other letters will be self-evident.
Alphabet123456123456123456123456123456MessageDDLRMERGLMUJTLLCHERSLSOEESMEJUDeciphered_NA_UE__ADE_ABAL_E_IAENE_IGA_R
Referring to our frequency tables as a check on suppositions, we find everything agrees well enough if we assume the first line to read:
UNAFUERZA DECABALLERIA ENEMIGA
UNAFUERZA DECABALLERIA ENEMIGA
We will now put the newly found letters in the table. The letters previously found are in capitals and the new letters in small letters. The addition ofD(=U) to the first alphabet permits us to add all the letters of the other alphabets to the first by the methods already discussed. Each of the other letters may then be added to every alphabet by these methods:
ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stT xhgoljqei msr d c u2dt xhgOLjQEI MSr D C U3dt xhgOLjQEI MSr D C U4tht xhgOLjQEI MSr D C U5tht xhgOLjQEI MSr D C U6tht xhgOLjQEI MSr D C U
One alphabet checks another in this way and we find everything to fit so far. We will decipher a few words more of the cipher message by the above alphabets and see if we can determine some new letters.
Alphabet5612345612345612345612345612345612345612345612345612345612MessageJUZJIMUDAEESDUTDBGUGPNRCHOBEQEIEOOACDEIOOGCOLJLPDUVMIGIYXQDecipheredPR_CEDEN_EDEARAU__UEZ_ILLA_ECASEHA_LAENAZUCAICA_AR_HEUS_ED
Again referring to the frequency tables the first word is evidentlyPROCEDENTE. We have alsoHALLAandMARCHEUSTED. The letterBmay be determined from another cipher group,JFBSQDLD(56123456) =POSICION. The letterNmay be determined fromBETNDQXUC(123456123) =SERRADERO. The lettersFandYmay be determined fromJCPJOISLYDUASIUPF(23456123456123456)=COMPANIA PARTIENDO. The completed alphabets, arranged as before, are:
ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ1stTYVNXHGOLJQEIZMSRBADFCPU2dTYVNXHGOLJQEIZMSRBADFCPU3dTYVNXHGOLJQEIZMSRBADFCPU4thTYVNXHGOLJQEIZMSRBADFCPU5thTYVNXHGOLJQEIZMSRBADFCPU6thTYVNXHGOLJQEIZMSRBADFCPU
The key word isTOLEDOand the completely deciphered message is:
“Una fuerza de caballeria enemiga procedente de Aranjuez y Villaseca se halla en Azucaica. 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 halla. (Q) Esta acantonada (Q) Se hallan otras tropas detras de ella (Q). El resultado del reconocimiento necesito saberlo dentro de tres horas y media cuando mas. Pongo a sus ordenes un ciclista (X) Fin.”
“Una fuerza de caballeria enemiga procedente de Aranjuez y Villaseca se halla en Azucaica. 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 halla. (Q) Esta acantonada (Q) Se hallan otras tropas detras de ella (Q). El resultado del reconocimiento necesito saberlo dentro de tres horas y media cuando mas. Pongo a sus ordenes un ciclista (X) Fin.”