Polygram substitution contemplates the encipherment of several letters collectively: Digrams are to be replaced with other digrams, or with three-digit numbers; trigrams are to be replaced with other trigrams, or with four-digit numbers; and so on, the substitute for an individual letter being entirely dependent upon the combination in which it happens to occur. Many devices have been contrived for accomplishing this. For pair-encipherment, tableaux of the general kind shown in Fig. 164 are fairly common.
| Figure 164 A M E R I C N B D F G H J K L O P Q S T U V W X Y Z E AA BA CA DA EA FA GA HA IA JA KA LA MA NA OA PA QA RA SA TA UA VA WA XA YA ZA Q AB BB CB DB EB FB GB HB IB JB KB LB MB NB OB PB QB RB SB TB UB VB WB XB YB ZB U AC BC CC DC EC FC GC HC IC JC KC LC MC NC OC PC QC RC SC TC UC VC WC XC YC ZC A AD BD CD DD ED FD GD HD ID JD KD LD MD ND OD PD QD RD SD TD UD VD WD XD YD ZD L AE BE CE DE EE FE GE HE IE JE KE LE ME NE OE PE QE RE SE TE UE VE WE XE YE ZE I AF BF CF DF EF FF GF HF IF JF KF LF MF NF OF PF QF RF SF TF UF VF WF XF YF ZF T AG BG CG DG EG FG GG HG IG JG KG LG MG NG OG PG QG RG SG TG UG VG WG XG YG ZG Y AH BH CH DH EH FH GH HH IH JH KH LH MH NH OH PH QH RH SH TH UH VH WH XH YH ZH B AI BI CI DI EI FI GI HI II JI KI LI MI NI OI PI QI RI SI TI UI VI WI XI YI ZI C AJ BJ CJ DJ EJ FJ GJ HJ IJ JJ KJ LJ MJ NJ OJ PJ QJ RJ SJ TJ UJ VJ WJ XJ YJ ZJ D AK BK CK DK EK FK GK HK IK JK KK LK MK NK OK PK QK RK SK TK UK VK WK XK YK ZK F AL BL CL DL EL FL GL HL IL JL KL LL ML NL OL PL QL RL SL TL UL VL WL XL YL ZL G AM BM CM DM EM FM GM HM IM JM KM LM MM NM OM PM QM RM SM TM UM VM WM XM YM ZM H AN BN CN DN EN FN GN HN IN JN KN LN MN NN ON PN QN RN SN TN UN VN WN XN YN ZN J AO BO CO DO EO FO GO HO IO JO KO LO MO NO OO PO QO RO SO TO UO VO WO XO YO ZO K AP BP CP DP EP FP GP HP IP JP KP LP MP NP OP PP QP RP SP TP UP VP WP XP YP ZP M AQ BQ CQ DQ EQ FQ GQ HQ IQ JQ KQ LQ MQ NQ OQ PQ QQ RQ SQ TQ UQ VQ WQ XQ YQ ZQ N AR BR CR DR ER FR GR HR IR JR KR LR MR NR OR PR QR RR SR TR UR VR WR XR YR ZR O AS BS CS DS ES FS GS HS IS JS KS LS MS NS OS PS QS RS SS TS US VS WS XS YS ZS P AT BT CT DT ET FT GT HT IT JT KT LT MT NT OT PT QT RT ST TT UT VT WT XT YT ZT R AU BU CU DU EU FU GU HU IU JU KU LU MU NU OU PU QU RU SU TU UU VU WU XU YU ZU S AV BV CV DV EV FV GV HV IV JV KV LV MV NV OV PV QV RV SV TV UV VV WV XV YV ZV V AW BW CW DW EW FW GW HW IW JW KW LW MW NW OW PW QW RW SW TW UW VW WW XW YW ZW W AX BX CX DX EX FX GX HX IX JX KX LX MX NX OX PX QX RX SX TX UX VX WX XX YX ZX X AY BY CY DY EY FY GY HY IY JY KY LY MY NY OY PY QY RY SY TY UY VY WY XY YY ZY Z AZ BZ CZ DZ EZ FZ GZ HZ IZ JZ KZ LZ MZ NZ OZ PZ QZ RZ SZ TZ UZ VZ WZ XZ YZ ZZ |
The tableau proper includes a full list of the 676 possible two-letter combinations, while two external alphabets will furnish another possible 676 two-letter combinations. With the plaintext marked off into pairs, the encipherment of a pair is usually accomplished by finding its two letters in the two external alphabets, where they act as co-ordinates, and replacing this pair with the one which is found at the cell of intersection. Thus, using the tableau of the figure, and the order row-column, the substitute for th would be LG; or, using the order column-row, TN. With a tableau like that of the figure (notice the straight unshifted alphabets), it is also possible to encipher by what is ordinarily considered the decipherment process, finding the plaintext pair inside the tableau and replacing it with the two co-ordinates. But many of these tableaux are filled in a thoroughly haphazard manner, and when this is the case, only the ordinary encipherment plan is really feasible; in fact, the decipherer has trouble in finding his cryptogram pairs, and it is usually necessary that a second tableau be prepared especially for decipherment purposes. On the other hand, it is very easy to construct a mixed tableau in such a way that all of its encipherment is reciprocal, and in this case there is no need for a second tableau, since encipherment and decipherment are the same process. In most forms of tableau, one or both of the external alphabets may be made to slide and for the most part external alphabets are readily changeable. But the tableaux themselves will have to be of more or less fixed nature. Those which are safest are least readily reconstructed from memory, and even those most easily remembered are not set up very rapidly.
Another common method for pair encipherment can be understood from the following description: Picture a chart of 100 cells which is divided sharply into four quarters; that is, having much the appearance of a 100-cell Fleissner grille. Each of the four quarters is a 5 x 5 square and contains a 25-letter alphabet. At
| Figure 165 The "SLIDEFAIR" Cipher -(H. F. GAINES) Key: H E R C U L E S Plaintext: SE ND DI AM ON DS TO AM CIPHER:..... XZ ZR RU KC TI HO KX US ST ER DA MM ON DA YW EE ..... MZ NI JU KO TI PO SC MW KW IT HO UT FA IL ..... PR PM XY RW GZ AT Cryptogram taken off: X Z Z R R U K C T I H O K X U , etc. |
least two of these alphabets are mixed, usually with different keys. To encipher a pair, find its two letters in two different squares, and substitute two others which occupy certain relative positions in the other two squares.
The writer’s own contribution, accomplished with a slide, may be examined in Fig. 165; the slide used in the example was the Saint-Cyr, and details are self-explanatory, except for the method of enciphering pairs, which was as follows: To encipher those of the H-column, bring the H-alphabet into position on the slide; then, for each pair, find its first letter in the upper alphabet and its second letter in the lower one; imagine these to be standing at the two ends of a diagonal, and substitute the two letters from the two ends of the corresponding cross-diagonal, taking the upper one first. Where the two plaintext letters happen to coincide (as would be the case with a pair EL using the H-alphabet of the Saint-Cyr slide) use the two letters which have also coincided immediately to their right (as FM for EL in the given case).
Occasionally, such a tableau as that of Fig. 164 is made to serve (not very successfully) for trigram encipherment. A third external alphabet is added beside one of the others, so that the two which are parallel will make provision for the encipherment of a third letter simultaneously with the encipherment of each pair. But for trigram encipherment, another type of tableau is commoner: The tableau proper is not a list of pairs, but an alphabet square such as could be prepared for one of the mixed-alphabet slides of [Chapter XVIII], and is accompanied by four external alphabets, two on the left and two across the top. The exact details of construction are not always the same, and the methods prescribed for using such a tableau are sometimes quite devious, but results are fairly uniform: We obtain cryptograms in which enciphered pairs have alternated with enciphered (sometimes not enciphered!) single letters.
In all of the foregoing, no system has been mentioned which the student will not be able to analyze for himself. At worst, he has a case very much like simple substitution, except that he would require a great deal more material, and would use a digram chart instead of a frequency list. Otherwise, he usually finds that he has merely a variation of pure periodic encipherment. There are, of course, more effective methods. Trigrams, tetragrams, and other polygrams, found in alphabet squares, can always be considered as geometrical figures, and replaced with other series of letters in related geometrical figures; and Lester S. Hill, in the American Mathematical Monthly, has described an “algebraic” method which appears practical, provided a machine is used. These methods, however, even