Route Transposition and Phenomenon

[Jarlve]

Great stuff smokie, excellent work so far.

What is your conclusion on period 1 and more general thoughts?

[smokie treats]

Great stuff smokie, excellent work so far.

What is your conclusion on period 1 and more general thoughts?

Glad you asked. I think that it is a pretty slim chance that the 340 is a digraph cipher. A person CAN make one that looks like the 340 as far as repeats go, but the odd even stats show that it is not. At least not with one transposition error. I think we can safely cross digraph off of the list, at least with a dotted line.

What do you think? Did you want to do some more detection work on it, just for educational purposes?

EDIT: I have been wondering about a periodical bias for the repeats, not just odds evens, but thirds, fourths, etc. Not related to digraph, but I think that I will explore this. I probably should have done this a long time ago. Maybe not just for 15 / 19, but 29 / 39 also.

[Jarlve]

I think we can safely cross digraph off of the list, at least with a dotted line.

I agree.

A few questions though,

1. What happens when interchanging the order of the transposition and digraph substitution steps?
2. Period 2 bigrams are diminished or even non-existent with digraph substitution?
3. Are the weaknesses of digraph substitution related to the quality of the digraph table?

EDIT: I have been wondering about a periodical bias for the repeats, not just odds evens, but thirds, fourths, etc. Not related to digraph, but I think that I will explore this.

I have been wondering about that too. But there may not be enough information to work with.

[smokie treats]

A few questions though,

1. What happens when interchanging the order of the transposition and digraph substitution steps?
2. Period 2 bigrams are diminished or even non-existent with digraph substitution?
3. Are the weaknesses of digraph substitution related to the quality of the digraph table?

I'll start with question 3. Here is a digraph chart from FIELD MANUAL NO 34-40-2. The rightmost ciphertext in each cell is the same when looking at any one column. The EDIT: leftmost ciphertext in each cell is different when looking at any one column. It looks like someone made this with some keywords, because the ciphertext is somewhat in alphabetical order, but not exactly.

digraph.18.png

Here is a digraph chart made by one of my spreadsheets, but it is completely randomized. There are no duplicates, and I used random charts for the experiments. It seems like this one would be more secure.

digraph.19.png

I made a spreadsheet that creates digraph charts from a four square cipher. Keywords are DINOSAUR and FLAMINGO for this one. And you can see by looking at the chart, look at column A. If the second plaintext in a plaintext bigram is A, then there are five situations where the first ciphertext in the ciphertext digraph is D { A B C D E }. So there is a pattern to it, but not as much as in the one from FIELD MANUAL NO 34-40-2.

I am not sure if patterns in the digraph chart would affect the odd even bias of a message. It wouldn't I am pretty sure.

digraph.20.png

[smokie treats]

Maybe we should not discard digraph so quickly. I was thinking about what you said about period 2 and the digraph chart not being carefully constructed and the FIELD MANUAL NO 34-40-2 digraph chart. It is not carefully constructed. I put a red line here. The second digraph ciphertext is the same for every second plaintext bigram. TH would become WQ, CH would become AQ, SH would become ZQ, etc. The first ciphertext is polyalphabetic, but the second ciphertext is a 1:1 substitute.

With the FIELD MANUAL NO 34-40-2 digraph chart, would not half of the period 2 repeats be made up of 1:1 substitutes?

Could a digraph chart, made from a certain type of digraph cipher, combined with poly literal transposition ( transposing two ciphertext at a time ), create a lot of period 19 and period 39 repeats ? Or period 15 and period 29 repeats, and therefore pivots? Or something similar?

digraph.18.png

[Jarlve]

I don't know smokie.

How was the field manual digraph table created?

The first letter appears to be following the key (WINCHESTR ABDFGJKLMOPQUVXYZ) horizontally and vertically and the second letter follows the key (ZYXWVURQPONMLKJIHFDCB TGAES) but only horizontally.

[smokie treats]

Maybe it is SEAGATE, "a navigable channel giving access to the sea," or maybe that was a military acronym in the navy at the time.

[Jarlve]

I have added a digraph encoder to AZdecrypt and below is the 408 plaintext encoded with the field manual table.

Odd/even bigrams: 49/28. Period 1 bigram peak. But stacking (period 2 untransposition + period 171 untransposition) OR (period 172 transposition + period 173 untransposition) peaks quite a bit higher. I think that may be due to every second letter being the same in the digraph table as smokie already indicated. This period stacking peak persists after homophonic substitution with about 45 bigrams and about 37 period 1 bigrams normally. There also seem to be allot of unigram repeats after encoding.

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PPOPJVPPPMPKPICJK
MEYNXFBFVICBDWJVB
FQTBIPWPWLUFZUSKT
QXKPPPMPKHGJMSRLL
UPWCAVEJUFDDEYNXF
BLVGZWPWCLVSJVCGZ
BREFFBGZQPDZPJDZH
MYJPPCMWJXVKQPKJR
ZTHDXVDQWLDDWCZFV
MUPBRFAUVMVSXIPWP
ZVMVEYFCUVWCGZBRF
CUPHRRJRFLJNNPJIU
IPTQJRNFWCEVVVRCM
ZTCGUICDDTQKCDQUK
DWFVHGVMEYUFKYHFU
PKIMFDWSXGZCWVMWC
FVTQZTONVMTVHGVME
YLXLLBLCDUZVVHPPP
YMTJJRZTFESBDEFZE
VSVQZVDFELBPPHMKF


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a   WZ IY NX CW HV EU SR TQ RP AO BN DM FL GK JJ KI LH MF OD PC QB UT VG XA YE ZS
b   IZ NY CX HW EV SU TR RQ AP BO DN FM GL JK KJ LI MH OF PD QC UB VT XG YA ZE WS
c   NZ CY HX EW SV TU RR AQ BP DO FN GM JL KK LJ MI OH PF QD UC VB XT YG ZA WE IS
d   CZ HY EX SW TV RU AR BQ DP FO GN JM KL LK MJ OI PH QF UD VC XB YT ZG WA IE NS
e   HZ EY SX TW RV AU BR DQ FP GO JN KM LL MK OJ PI QH UF VD XC YB ZT WG IA NE CS
f   EZ SY TX RW AV BU DR FQ GP JO KN LM ML OK PJ QI UH VF XD YC ZB WT IG NA CE HS
g   SZ TY RX AW BV DU FR GQ JP KO LN MM OL PK QJ UI VH XF YD ZC WB IT NG CA HE ES
h   TZ RY AX BW DV FU GR JQ KP LO MN OM PL QK UJ VI XH YF ZD WC IB NT CG HA EE SS
i   RZ AY BX DW FV GU JR KQ LP MO ON PM QL UK VJ XI YH ZF WD IC NB CT HG EA SE TS
j   AZ BY DX FW GV JU KR LQ MP OO PN QM UL VK XJ YI ZH WF ID NC CB HT EG SA TE RS
k   BZ DY FX GW JV KU LR MQ OP PO QN UM VL XK YJ ZI WH IF ND CC HB ET SG TA RE AS
l   DZ FY GX JW KV LU MR OQ PP QO UN VM XL YK ZJ WI IH NF CD HC EB ST TG RA AE BS
m   FZ GY JX KW LV MU OR PQ QP UO VN XM YL ZK WJ II NH CF HD EC SB TT RG AA BE DS
n   GZ JY KX LW MV OU PR QQ UP VO XN YM ZL WK IJ NI CH HF ED SC TB RT AG BA DE FS
o   JZ KY LX MW OV PU QR UQ VP XO YN ZM WL IK NJ CI HH EF SD TC RB AT BG DA FE GS
p   KZ LY MX OW PV QU UR VQ XP YO ZN WM IL NK CJ HI EH SF TD RC AB BT DG FA GE JS
q   LZ MY OX PW QV UU VR XQ YP ZO WN IM NL CK HJ EI SH TF RD AC BB DT FG GA JE KS
r   MZ OY PX QW UV VU XR YQ ZP WO IN NM CL HK EJ SI TH RF AD BC DB FT GG JA KE LS
s   OZ PY QX UW VV XU YR ZQ WP IO NN CM HL EK SJ TI RH AF BD DC FB GT JG KA LE MS
t   PZ QY UX VW XV YU ZR WQ IP NO CN HM EL SK TJ RI AH BF DD FC GB JT KG LA ME OS
u   QZ UY VX XW YV ZU WR IQ NP CO HN EM SL TK RJ AI BH DF FD GC JB KT LG MA OE PS
v   UZ VY XX YW ZV WU IR NQ CP HO EN SM TL RK AJ BI DH FF GD JC KB LT MG OA PE QS
w   VZ XY YX ZW WV IU NR CQ HP EO SN TM RL AK BJ DI FH GF JD KC LB MT OG PA QE US
x   XZ YY ZX WW IV NU CR HQ EP SO TN RM AL BK DJ FI GH JF KD LC MB OT PG QA UE VS
y   YZ ZY WX IW NV CU HR EQ SP TO RN AM BL DK FJ GI JH KF LD MC OB PT QG UA VE XS
z   ZZ WY IX NW CV HU ER SQ TP RO AN BM DL FK GJ JI KH LF MD OC PB QT UG VA XE YS


[Jarlve]

1. What happens when interchanging the order of the transposition and digraph substitution steps?

408 plaintext INTO period 19 transposition INTO digraph encoding with the table below using keywords "zodiac" and "killer" INTO homophonic substitution.

Odd/even bigrams: 9/9. So, most of the odd/even bias seems to get lost while switching the order? No bigram peak at untransposed period 19 at all. Bigram peak of 38 at untransposed period 44 (random?). Keyword length spikes at multiples of 2.

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GCDTKEMKPHISJEHPK
IKIQEPGCQZHTJHQQE
JBQJHCSCEMKCTQMKB
SKCPLKLSKYCSBKSQE
TRUCVCSSXEUCUPEKO
SJAIKVNRHATHQHAWH
NCWSLVFCAKZCKCFHB
QOMYPOSWSKPEHNEVC
OCWQMAJQESFCDEDEA
GDPTIBKNGNCORLLPQ
VMKCELMLSCFUFKPCS
CFMCJJRDLBGKCKAAS
LLTKDVKQZKBJQEJJP
CNGBGTHINYJZTBMEA
CMSQAKDENGCHVEMEP
HXEAGQEULXJFMNBUE
KCPWHPXBYLFCFSDLY
JYMFSHSEBAEACIHRG
BJTKRGFERMTSVGKCD
XNRTBHQUESPWIYMVG


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1  2  3  4  5  6  7  8  9  10 11 12 13 6  14 15 5
16 8  11 17 18 9  19 20 17 21 10 22 23 14 24 17 6
25 26 24 27 10 28 29 2  6  7  5  20 30 17 7  8  31
32 5  28 9  33 8  34 12 5  35 20 29 36 8  32 17 18
4  37 38 28 39 2  12 29 40 6  41 20 42 15 18 5  43
32 13 44 16 8  45 46 47 14 48 4  10 17 14 44 49 10
50 28 51 12 52 53 54 2  48 5  21 28 8  2  55 14 26
24 56 7  57 9  43 32 49 29 5  15 6  10 46 18 45 20
56 28 58 17 7  44 23 17 6  32 54 2  3  18 3  6  48
59 3  9  22 11 31 8  50 19 46 20 43 60 33 33 15 24
53 7  5  28 18 34 7  52 12 2  55 42 54 8  15 20 29
28 54 7  2  25 27 61 3  34 36 1  5  20 8  44 48 32
33 34 30 8  3  39 5  17 21 8  26 13 24 6  23 25 9
28 50 59 31 19 4  14 16 46 57 27 21 22 36 7  18 44
28 7  12 24 48 8  3  6  50 1  2  10 45 18 7  6  9
14 62 18 44 59 17 6  41 52 40 13 55 7  50 26 42 18
5  20 15 51 14 9  62 31 35 33 54 28 55 29 3  34 57
23 35 7  54 32 10 12 6  36 48 18 44 2  11 14 37 19
26 25 22 8  47 1  55 6  60 7  22 29 53 59 5  2  3
40 46 61 30 31 10 24 63 18 32 15 49 16 57 7  39 19


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a   ZK OI DL IL AE CR BA EB FC GD HF JG KH LJ MM NN PO QP RQ SS TT UU VV WW XX YY
b   OK DI IL AL CE BR EA FB GC HD JF KG LH MJ NM PN QO RP SQ TS UT VU WV XW YX ZY
c   DK II AL CL BE ER FA GB HC JD KF LG MH NJ PM QN RO SP TQ US VT WU XV YW ZX OY
d   IK AI CL BL EE FR GA HB JC KD LF MG NH PJ QM RN SO TP UQ VS WT XU YV ZW OX DY
e   AK CI BL EL FE GR HA JB KC LD MF NG PH QJ RM SN TO UP VQ WS XT YU ZV OW DX IY
f   CK BI EL FL GE HR JA KB LC MD NF PG QH RJ SM TN UO VP WQ XS YT ZU OV DW IX AY
g   BK EI FL GL HE JR KA LB MC ND PF QG RH SJ TM UN VO WP XQ YS ZT OU DV IW AX CY
h   EK FI GL HL JE KR LA MB NC PD QF RG SH TJ UM VN WO XP YQ ZS OT DU IV AW CX BY
i   FK GI HL JL KE LR MA NB PC QD RF SG TH UJ VM WN XO YP ZQ OS DT IU AV CW BX EY
j   GK HI JL KL LE MR NA PB QC RD SF TG UH VJ WM XN YO ZP OQ DS IT AU CV BW EX FY
k   HK JI KL LL ME NR PA QB RC SD TF UG VH WJ XM YN ZO OP DQ IS AT CU BV EW FX GY
l   JK KI LL ML NE PR QA RB SC TD UF VG WH XJ YM ZN OO DP IQ AS CT BU EV FW GX HY
m   KK LI ML NL PE QR RA SB TC UD VF WG XH YJ ZM ON DO IP AQ CS BT EU FV GW HX JY
n   LK MI NL PL QE RR SA TB UC VD WF XG YH ZJ OM DN IO AP CQ BS ET FU GV HW JX KY
o   MK NI PL QL RE SR TA UB VC WD XF YG ZH OJ DM IN AO CP BQ ES FT GU HV JW KX LY
p   NK PI QL RL SE TR UA VB WC XD YF ZG OH DJ IM AN CO BP EQ FS GT HU JV KW LX MY
q   PK QI RL SL TE UR VA WB XC YD ZF OG DH IJ AM CN BO EP FQ GS HT JU KV LW MX NY
r   QK RI SL TL UE VR WA XB YC ZD OF DG IH AJ CM BN EO FP GQ HS JT KU LV MW NX PY
s   RK SI TL UL VE WR XA YB ZC OD DF IG AH CJ BM EN FO GP HQ JS KT LU MV NW PX QY
t   SK TI UL VL WE XR YA ZB OC DD IF AG CH BJ EM FN GO HP JQ KS LT MU NV PW QX RY
u   TK UI VL WL XE YR ZA OB DC ID AF CG BH EJ FM GN HO JP KQ LS MT NU PV QW RX SY
v   UK VI WL XL YE ZR OA DB IC AD CF BG EH FJ GM HN JO KP LQ MS NT PU QV RW SX TY
w   VK WI XL YL ZE OR DA IB AC CD BF EG FH GJ HM JN KO LP MQ NS PT QU RV SW TX UY
x   WK XI YL ZL OE DR IA AB CC BD EF FG GH HJ JM KN LO MP NQ PS QT RU SV TW UX VY
y   XK YI ZL OL DE IR AA CB BC ED FF GG HH JJ KM LN MO NP PQ QS RT SU TV UW VX WY
z   YK ZI OL DL IE AR CA BB EC FD GF HG JH KJ LM MN NO PP QQ RS ST TU UV VW WX XY


[Jarlve]

Maybe it is SEAGATE, "a navigable channel giving access to the sea," or maybe that was a military acronym in the navy at the time.

You are right, WINCHESTER and SEAGATE since repeated letters are usually discarded with keyword schemes in these books.