Case 7-b.

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 determination, we have the following count of letters out of a total of 385:

A 8 L 23 J 9
E 38 N 11 Q 22
I 19 R 14 V 9
O 21 S 20 X 13
U 24 T 21 Z 6
Total 110 Total 89 Total 59
28% 23% 15%

Every letter except K and W occurs at least six times. We may say then that it is a substitution cipher, Spanish text, and certainly not Case 4, 5 or 6. We will now analyze it for recurring pairs or groups to determine, if it be Case 7, how many alphabets were used. The following is a complete list of such recurring groups and pairs with the number of letters intervening and the factors thereof. In work of this kind, the groups of three or more letters are always much more valuable than single pairs. For example, the groups, HOBE, OYMU, RMERGL and UBRE show, without question, that six alphabets were used. It is not necessary, as a rule, to make a complete list like the following:

AE 74=2×37 IE 110=2×5×11 RE 50=2×5×5
AE 120=2×2×2×3×5 IM 302=2×151 RMERGL 198=2×3×3×11
BE 88=2×2×2×11 IO 250=2×5×5×5 SC 132=2×2×3×11
CD 132=2×2×3×11 IX 78=2×3×13 SD 262=2×131
CFI 12=2×2×3 LY 158=2×79 SI 230=2×5×23
CH 36=2×2×3×3 JT 150=2×3×5×5 SI 34=2×17
CO 42=2×3×7 LL 367 No factors SI 264=2×2×2×3×11
CO 126=2×3×3×7 LQ 164=2×2×41 SI 12=2×2×3
CU 114=2×3×19 LQX 6=2×3 SL 78=2×3×13
DD 186=2×3×31 LU 124=2×2×31 SQ 54=2×3×3×3
DD 116=2×2×29 LU 110=2×5×11 SV 27=3×3×3
DE 285=5×57 LU 234=2×3×3×13 SV 63=3×3×7
DL 218=2×109 LX 66=2×3×11 SV 90=2×3×3×5
DN 14=2×7 LXB 132=2×2×3×11 TD 47 No factors
DQ 120=2×2×2×3×5 LY 158=2×79 TD 165=3×5×11
DU 36=2×2×3×3 ME 22=2×11 TD 96=2×2×2×2×2×3
DU 24=2×2×2×3 MU 24=2×2×2×3 TN 239 No factors
DU 38=2×19 MU 240=2×2×2×2×3×5 TS 14=2×7
DU 165=3×5×11 MU 18=2×3×3 TS 156=2×2×3×13
EA 30=2×3×5 ND 47 No factors TSI 50=2×5×5
EB 78=2×3×13 NE 48=2×2×2×2×3 UBRE 12=2×2×3
EC 180=2×2×3×3×5 NE 18=2×3×3 UD 60=2×2×3×5
ECO 126=2×3×3×7 NE 192=2×2×2×2×2×2×3 UDA 270=2×3×3×3×5
EES 14=2×7 OB 6=2×3 UL 114=2×3×19
EF 105=3×5×7 OB 234=2×3×3×13 ULX 198=2×3×3×11
EI 8=2×2×2 OE 93=3×31 UY 89 No factors
EI 152=2×2×2×19 OI 144=2×2×2×2×3×3 UZ 162=2×3×3×3×3
EQ 88=2×2×2×11 OO 7 No factors VI 148=2×2×37
EQ 264=2×2×2×3×11 OY 6=2×3 VT 33=3×11
EQ 44=2×2×11 OY 46=2×23 XQ 114=2×3×19
EQE 176=2×2×2×2×11 OYMU 6=2×3 XQ 144=2×2×2×2×3×3
ER 12=2×2×3 PD 75=3×5×5 XU 99=3×3×11
ES 78=2×3×13 QBL 24=2×2×2×3 YE 184=2×2×2×23
ET 135=3×3×5 QC 95=5×19 YL 106=2×53
ET 9=3×3 QE 108=2×2×3×3×3 YL 144=2×2×2×2×3×3
ET 54=2×3×3×3 QE 68=2×2×17 YM 6=2×3
ET 31 No factors QR 132=2×2×3×11 YRO 12=2×2×3
HE 245=5×7×7 QTO 210=2×3×5×7 ZE 6=2×3
HOBE 66=2×3×11 QX 198=2×3×3×11 ZH 183=3×61

Out of one hundred and one recurring pairs we have fifty with the factors 2×3=6; out of twelve recurring triplets, nine have these factors; and the four recurring groups of four or more letters all have these factors. The percentages are respectively 49.5%, 75% and 100% and we may be certain from this that six alphabets were used. But, before the six frequency tables are made up, there is one more point to be considered; why are there so many recurring groups which do not have six as a factor? The answer is that one or more of the alphabets is repeated in each cycle; that is, a key word of the form HAVANA has been used. If this were the key word, the second, fourth and sixth alphabets would be the same. 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 6.

We will now proceed to make a frequency table for each alphabet. As the message is written in thirty columns, we take the first, seventh, thirteenth, etc., as constituting the first alphabet; the second, eighth, fourteenth, etc., as constituting the second alphabet and so on. The prefix and suffix letter is noted for each occurrence of each letter. The importance of this will be appreciated when the form of the frequency tables is examined. None bears any resemblance to the normal frequency table except that each is evidently a mixed up alphabet. The numbers after “Prefix” and “Suffix” refer to the alphabet to which these belong, for convenience in future reference.