I don’t have a graph for this one. I just made 100 digraph and 100 digraph + transposition messages, same settings as prior experiment. I counted the period 1 repeats that start only on odd positions, and the period 1 repeats that start only on even positions.

Digraph

110 Average count of bigram repeats when only looking at odd positions ( "true" ) repeats
53 Average count of bigram repeats when only looking at even positions ( "false" ) repeats

That makes sense. I don’t think that I have seen this detection technique in any cryptography book and wonder why because it is so simple.

Digraph + Transposition ( another step of diffusion )

33 Average count of bigram repeats when only looking at odd positions ( "true" ) repeats
10 Average count of bigram repeats when only looking at even positions ( "false" ) repeats

22 Average difference between true and false repeat counts

Zodiac 340 Period 19

22 bigram repeats when only looking at odd positions
17 bigram repeats when only looking at even positions

Although more on odd, there is not that big of a difference. Of the 100 messages, two had similar stats, small count when only looking at odd / even, and small difference. I guess that is why they call it practical cryptography.

That makes sense. I don’t think that I have seen this detection technique in any cryptography book and wonder why because it is so simple.

I love your detection technique. Very good thinking! Simple things are the best and often overlooked.

Jarlve, I have been thinking about a remark that I made yesterday or the day before. That maybe a 26 x 26 digraph chart could be hill climbed. I do not think so maybe with such a short message.

I have a spreadsheet that adds up all of the period x bigrams for your 100 messages. A good enough sample of the English language I think. I can change the period and the totals change. For instance, at period 1, bigram TH appears 1043 times. There are much fewer cells in this chart to work with because a lot of bigrams do not exist at all, or do not exist in a high count.

Anyway, I am not so sure that even a smaller chart, deleting some of the darker rows and columns could be hill climbed, because a message of 340 is too short. I do not know for sure, but to solve a digraph cipher of length 340, it may be necessary to know if it is Playfair, four square, two square or whatever.

Just thoughts.

For the 340, there is not a big difference between the repeats that occur only on odds and the repeats that occur only on evens. I am going to be thorough though. I am going to make a spreadsheet that will detect a skip, to see what happens if a null is inserted to replace the skip. See if any position creates a lot more odds than it destroys, and makes the odd / even stats more like a true digraph cipher. Then make some test messages, both with and without skips, and compare. Find a detection method and see if it is reliable. See if we can eliminate digraph with the spreadsheets.

Personally, I like digraph + scytale + homophonic. Not saying that I like it for the 340 at this point, but I like it as an idea in general. It is very simple, yet clever, and applies three very classical / historical ciphers.

I made a really cool skip detector. It detects the position of a skipped symbol. Let’s say I make a message, digraph encode, the homophonic encode. But I skip a symbol when homophonic encoding, or, if it is a scytale, skip a symbol when changing the count of columns in the message ( transposition ). There will not be as much of an odd even bias for the period x bigram repeats. There would be without the skip. The spreadsheet generates digraph + homophonic, finds the odd even bias, then skips a symbol and finds the odd even statistics. Then adds a null at all positions 1 – 340 to find out which position causes the greatest odd even bias, thus detecting the position of the skip.

Below I generated a message and the odd even bias difference was 26 repeats. After the skip it was only 7 repeats ( similar to 340 stats ). X axis is position of inserted null, and y position is odd even bias difference. The goal was to find the position where the difference was 26. It works really well. Not perfectly all the time, but I really like it.

Okay smokie,

Your digraph message 34 cipher is only 306 characters long. Anyway, I encoded your digraph plaintext with my encoder matching the raw ioc of the 340 to get a feel for it without assuming any further complications. With your odd/even bigram system, the cipher is easily identified with a very large difference. There are 38 period 1 bigram repeats.

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

When comparing your digraph plaintext to other normal english language plaintext I noted some differences besides the odd/even bigram bias.

– It has a lower raw ioc which lowers the repeats. Could this be due to a not so careful digraph substitution table?
– Large difference between unigram repeats grouped by 2 and 3 characters. May this be another detection method?
– Very high deep bigram score (measurement system of mine) for its ioc.
– No increased period 2 bigram repeats.

Unigram repeats:
--------------------------------------------------
Grouped per 2 characters: 3
Grouped per 3 characters: 22
Grouped per 4 characters: 16

Here are three more if you want to compare stats. Most of the time there is a big difference between odd and even bigram repeats, but not all of the time.

A

P R I E S T L Y T E R R O R I S M
G O D O R D A I N E D M U R D E R
F O R U N B E L I E F T H E J E W
I S H F O R G E R S O F T H E N E
A R S A C R E D B O O K S O F E N
O C H E S D R A S E T C H A D P I
L F E R E D F R O M T H E S A C R
E D B O O K S A N D S Y S T E M O
F Z O R O A S T E R O F P E R S I
A T H E I R S U P E R S T I T I O
N S O F A N G E L S A N D D E V I
L S A N D H E L L F I R E A N D H
A D I N V E N T E D T H E I N F E
R N A L D O C T R I N E S O F O R
I G I N A L S I N A N D E T E R N
A L D A M N A T I O N T H E R E F
O R A L L W H I C H C O U N T E R
F E I T P A S S E D T O A N D B E
C A M E C U R R E N T A M O N G T
H E R E L I G I O U S Z E A L O T

YU YO WO IL IB LU PK KB FN EU EW ZS CS ZM VD AZ HE ZN TC KO PR PR SE YG GQ MY
EJ PH SA ZI YV YA BB MP CP KG UB EH JY FJ KO VH WK KI MD KA UR TZ IK TY DH GR
CK LO JC LT ND HB SK AR NP RX LB CB ZC RV JE ET AW ND PE HZ ZO SM CX RN NB GW
LX GB GF UJ WL GA BN EW GR NJ YL KU FU FS AI TY JM FB RO NV QY HF TK XR JI LN
DL ZA WI ZV IT BK UG LB GL EV IT AD OU YU YV KQ JI JV NL DL DN PL IL QX TB SC
FP SJ CO VY ED OW WX ZO FG UC FH LQ YQ VG JU AB FK UC EZ XC CB WA PC GA QW CH
UL GF RP GM LA FO RD YI HH MX EF NS DJ QD MO HH NV HA YJ NL HU TZ SF UK KI RA
MX PA WI SA XH NW PC CL IY KA GT WI HC VY DX AJ ZF AX RH RO JP WI BI PU VN XD
AW IE CL UB LV SQ SU OR AS BT NG TO DJ IH RZ CO BZ EE YV QD VX IL NW WL UQ VM
BD DV LQ BV JM KO VZ DM NK QA HM HX OB YM WX SC VZ LQ EQ CA KV LV BC CQ XL BL
WT QB CV AT KZ LW JF CN RJ BH WA OW VY YS UQ ZX LY NG QC UP VI BR FZ BM ZO HH
XL VO KO DN FJ JR DT HI OV CA YE AY GR XD BI BN CO IE IT GX QU JQ MI NF MD JV
ZY RU CP EG YW EX SH LW FY MR FK XQ WY SV UH MK PC KQ PC KR KI NZ RB UF UL XE
IK SS SS ES OP EF DD WC IK YS HH UL UY IF KX GG EZ WD OS IW CN RG EA PH ZM PR
QR RW IG OS AB IE NF QU NE OI XH BH DI GY HK MP JN SS YW UA AW TB GP ZF EE KB
RI HF TW XT TF HU TR KB PA NW WK RR ET ZN VB AM UK ST XO AI NG NL ZQ FC JF ZM
QF AX YM XF HH IE BN CV BN QF JZ QQ AP WR HF CA OT GT YG NY SU SS OW OW KQ HT
YN AP TL DU TM ZO FT YJ ZY MC JG PE RZ MM WD LM VM SU BE VG XW RE SM ZI DK CK
DM UW IC EV IQ AT JE AU XN ZE QN DN KD TO MS BR LG JS VC QR OZ JG JU MQ KT EB
EJ LS GM UO XD RA DG DQ MQ FE LX TY JY OX DS GJ LD QD KM FD CG HO NN XH KJ KU
MZ VX CE DN PM FX ZH TD PZ FU QK GJ BR IP WJ PG QN GS XR TS LV OT CP BJ UM PA
RX FG FZ XL PP MI MY YG VZ GT PS HJ UV HE DP QV SO DP XF TP WV OH XZ YT TO LG
XX IJ TC LU WP MK NN BW OH FV RI VH ZQ MZ QD GZ UG OU GP OF AX MD MJ PA LJ XD
EP ST TP QL TC JN OY AZ XP WQ XC MY TT PI VE AQ TS QJ NY JL ES DR SJ QT FQ AB
YJ HZ UU TA WK BS WK RF PH VR MF HR VP EF OY WG IL BN JC PS VC QX RD OS CC QZ
XM IE ZV LK DE SF OU GR OE IK MI FT HN UM DW VE RG AY RK SX FP OQ BJ VB ZA YW

S T L V Q R M D X D S U S S Y V S
H O S S S L X I H Z V K I D U J V
J U X W S S A D L V X C X H J M O
H A U J U F T J V M S X C X H O P
Z N D M N D Z V K O X H M S E D K
X A R N L F B T C D L A R I L P A
J R J V Z V U C D I D Q N L W O T
M G B H K Q C Z M R O J C X D U H
C H S S Q R Q R J V I E T F B E A
W D Q G L B E P G J V Q R Q D R Z
O S I E Z M L A I T Z M U J P L T
O D M E S X H A Y F G T M Z M E W
I L I H P P I W Z V D Q G L E F J
V I K D N I G Q D I H N L I E S S
S U I H Z S X N I K E S D L J V I
K D N C S I K M Q G Y D Q J V B K
S S Z S M I I Y A R J E I P X D Z
O G L G J T C I Q N V Q R E S Y V
C K Y W Z O S U Y U E J U H D D D
Q J V A D S U R Z X R D E Z S U A

43 47 29 51 39 41 31 7 57 8 44 49 45 46 59 52 43
17 35 44 45 46 30 58 19 18 61 53 27 20 9 50 23 54
24 49 57 55 43 44 1 10 29 51 58 5 57 17 25 32 36
18 2 50 26 49 13 48 23 52 31 45 58 6 57 17 35 37
62 33 43 32 34 7 63 53 28 36 58 18 31 46 11 8 27
57 1 42 33 30 14 3 47 5 9 29 2 41 21 30 38 1
24 42 25 54 64 51 50 6 10 22 43 40 34 29 56 35 48
32 15 4 17 28 39 5 61 31 41 36 26 6 58 7 49 18
5 17 43 44 40 42 39 41 23 52 43 12 47 13 3 11 2
55 8 40 16 30 4 12 37 15 24 53 39 42 40 9 41 62
35 45 19 11 63 32 29 1 20 48 64 31 50 25 38 30 47
36 10 32 12 46 57 18 2 60 14 16 48 31 61 32 11 56
21 29 22 17 37 38 43 55 62 54 43 39 15 30 12 13 26
51 19 27 7 33 20 16 40 8 21 18 34 29 22 11 43 44
45 49 43 17 63 46 58 33 19 28 12 43 9 30 23 52 20
27 10 34 6 44 21 28 31 39 15 59 43 40 24 53 3 27
45 46 64 43 32 22 43 60 1 42 25 11 19 37 57 7 61
35 16 29 15 26 47 5 20 39 33 54 40 41 12 44 59 51
6 28 60 56 62 36 45 50 59 49 11 23 50 18 8 9 10
39 24 52 2 43 46 49 42 63 58 41 7 12 64 43 50 1

B

M O S T O F T H E S C E N E S B A
C K G R O U N D S A N D V I S U A
L E F F E C T S I N T H E F I L M
W E R E C R E A T E D U S I N G M
O R E T R A D I T I O N A L T E C
H N I Q U E S A N D A U N I Q U E
P R O C E S S K N O W N A S B A C
K L I T A N I M A T I O N I N T H
I S P R O C E S S L I V E A C T I
O N S C E N E S I N S I D E T H E
C O M P U T E R W O R L D W E R E
F I L M E D I N B L A C K A N D W
H I T E O N A N E N T I R E L Y B
L A C K S E T P R I N T E D O N L
A R G E F O R M A T K O D A L I T
H H I G H C O N T R A S T F I L M
T H E N C O L O R E D W I T H P H
O T O G R A P H I C A N D R O T O
S C O P I C T E C H N I Q U E S T
O G I V E T H E M A T E C H N O L

GW UC IJ LX FF QP VM EW KD CV OM HJ OB KN MS WO BX KG IC VT FU SM RH QP RH LN
EQ HI PZ VG BI RP SB GJ MA SI CC CE SX JI EM VL DN ER EB TU LR VT NF NC FQ SW
WF KD RB NK TZ WH BM CJ EE ZB MS WK OL WP DP PH PV YL OO AI QU AN LK YH RL BH
SN XB HK OG KV HW YX SA WC OG WP XM JF PU GD MT DX QO GP JL KW KS MY YB PR FB
VU VE GB XT MN QO OX UR HI LE TZ QF JS JJ RK BZ TT ZL ML CG GH QJ HJ GS IH VL
WY XQ LW RQ HT IJ EA BA WU VH PV ZJ XM SU DT ZP XG WP ZX PF SD DE TJ IB GI JI
DI PR YM XZ CB UM ZQ TW TS FP EY RZ BG SE WK CU KD AL KK ZP TE FX WQ CZ VE BK
HU NI OY HM UK FU XY YE DL LP ZM NM NT FO NE EN PU TF YW LA JW MY ZC NV LS TS
VX CE PV FC PQ XW NP CX UK RP IM AN PD GZ JY EF BD MJ MY VG SB EV EF UU AA HD
KD TL FY IK RG SA MH GK AX HJ BG XR OT WR JF JV UK EI EH SG ZR JX OZ AN AH AS
LZ BN YV IG IO DG HX UN VC CI NO KW CY HS NT FL EQ TA IH LN FK QC BD AN JJ JV
QD BG ZI LC CI AN BD SO RN DM DV LS DC JT UG DG RM UG TE QX XH ED YM SI XC YR
JZ DS VO ZK CS VI UD XR IR AJ TA OO TI KA CP GY FT HB SQ AO LE QA AV MX VP WW
RH FW UL QE ZY XB HC ZT HK EW ZZ EI RD NO UD QE IQ VL UV GS AM SW VT LI IB PQ
YY DF KF RT AR HU XT XR GU ND IW VO DD DK DN SN VX FE CP MI VX ZJ BG EX RH WC
YZ MF IU DS KB QS NG ZQ CF MC TC YQ FP DN VK GI JO YT AC ZJ TA VG LA KJ PY ZU
BR EY UQ PI NU UF JH ZM KN ER AC RD MS AY HV SM QB YZ OQ UT XN UB GP JB MC OZ
PL DW IL DF IV IF AI SO LO UH CD JE CA LY EO ZB YQ NN DT GR RO PJ LZ OY ER UT
JZ GL KO YP YE QA FL SQ IL PT AH WJ MX XV GQ EZ VB JS IV BR YL FV OR QV AU PG
FF OE QC PU LR UA KW LX RD ML AW ND MF RU YA XO HH SK WK DH RG JP TC HN NY OA
UH SQ KZ CU OA NF KL FM JS XY YA PW BB NT IE ST WB BR BF FP AS SB ZQ WS DL GC
ZP ON MX QU QL JD IO WL CX RK LD YU CE TX UK QV OJ UF BE JR KZ FV GA BU FA GR
XV KM PZ AK UP LG PF CI NM TS IY HD GI XY HU NC RZ BC LF HY QJ EM CE OV TZ DQ
CZ NH FL TM GQ IR SA MM XX KQ KW IC WO WP XR AG QQ FV PV HQ BD LZ WK CE ZY NJ
NN UT MJ YC GS TY RO KF NH WM YO RP TH KH MN OJ OA OX BV GN LY WX FW VW HJ VR
HA PO GB TW OG TU XS RK JA QS EG ZZ MF PW IO ZJ XE DW WT QI YE BB QS YQ MT OK

C P B R H U L X M L T Z Z Y G L I
J H X E O N T G P K N K S M Y U H
C I I J G B W K G Z L X Q O A N A
V Z L G B I V V T X T B F G Z B G
F E C G P L W C R D D K H J L R C
J H K X N M L K N S N N T B D O A
Y T K F M L A H U D X Y I C E Q M
S R N F F H K J Z R D D K G Z L X
M Y Y T K F M L W J E V V U A I J
Y U V T Z Z Y I L U V F C C G U K
D P G Y F P Z L H U J E M Y Z L Q
O A N C S W C F W Q D M S K N M Y
D L L R D K K N J J R D I V X C C
E I J I H C G Y T G Z L R G D E I
K G C B D T C A V T N T S N R N L
X D L T W D P G S P L B R W U D C
L X J J D P U G I V M Y V G E N N
E Y A A L W O D L W F Q E E O Y A
K O S N P V L R C J H K X N M L Y
A T S Q L L X J S V T G B F O V O

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

C

L I K E M I L L I O N S O F M Y R
A C E M Y M O T H E R A N D F A T
H E R W E R E B O R N S L A V E S
B U T W E R E N O T C O N T E N T
E D T O L I V E A N D D I E S O M
Y F A T H E R P U R C H A S E D H
I M S E L F I N E A R L Y M A N H
O O D B Y H A R D T O I L M O T H
E R S A W N O W A Y F O R H E R S
E L F A N D C H I L D R E N T O E
S C A P E T H E H O R R O R S O F
B O N D A G E B U T B Y F L I G H
T B R A V E L Y W I T H H E R F O
U R L I T T L E O N E S W I T H F
I R M F A I T H I N G O D A N D A
N A R D E N T D E S I R E T O B E
F R E E S H E F O R S O O K T H E
P R I S O N H O U S E A N D S U C
C E E D E D T H R O U G H T H E A
I D O F M Y F A T H E R T O R E A

UL MA PB XX HG DK KA TK NX TX UT RC MY HQ TU MQ VU KL YP EM PU LY VI ZM TB RD
BU GP IZ BV WJ LV AN DU WT WG NX QW MM NP TF AA CR VW DX OY WU OO TS PD FK IE
QE CO OM SJ NH XB UI FC UI CR XI UR XN OP MB TV FH ER PK SU DF BT DP GM FS GJ
BY CB QO XL PU IZ KH BF TF EN JH JJ CO EU AE WT NC LV BT KX MK AX HX NV FE JU
YU YZ QY JN OM LY DO AW AP DZ DL YQ KD NW PZ OE IW FB CS CS NA XC ZZ RH MX FK
MR SV BM MA RZ PK JS MW ZF EO GN HT QF HQ ZI LL MB EJ ET NJ IF PC RB EE TR II
XN VR YJ HJ DH LD TE NT XA WH EK OX RR KY PR WC KH JQ UY FJ VR FC SA OV RQ VC
CB FW CD NZ UC RL LV WV PP ZZ HN CD HA FW BQ ZM AF VK JN ZD JM WF GK JS CS KK
BE XP LN PR TT WL VS YB SG JN EP NR SS LM EV JG XU AF UL BM DM DF XH HB PL NF
ZS PU HK AZ CX KS WC LR DY MN CS ZC FQ OI YX CI VR PY VE RA UA SK LR VL IX EP
SR SG QV WO XS PI JP VU AG XJ KS ZN XK JX IE QM DH ZJ HU IO HC YU VO KC NW KP
QP JT MQ VU HD JP VQ YI CA SG EO SI MN SH OG RD AC YG TT KV QB AA WI FN CS WU
ZJ WM GR QV RJ LG SB XP DO VF TZ QI BA GG TA FY UK RO YU HQ WF VD NC KW SU DM
RC QS SH QN DP ZR HR OD QG QS LT FT AD DS IQ WZ LL TU VQ QG FA GF GT HD WY MF
HB DE SO TW EY NL VX OY GH SD HY QK TD TP FE GO RV FS YB UJ EG KN HZ IE XG TM
AQ UW SJ XP HD ZD SV JM NL WQ PN RK LI JO KT UT XN VT AF PB BF OT NQ EY UZ EL
OL OO JZ LS AP RM YB WQ NT TF MX PU GL WU WO IH RB NB XV OZ FE VW PK HB BF UA
DS QH OI XG TW KK RH OA DG JE BV LQ KG EW LA ZP UZ GC ZV BU EC QY EA RW PW CH
FZ LF KW GO DH OC CD WF CV UB EY GV RP DJ NZ BC NI QT RQ IM SA OJ FW KN SG YN
YC RE YE ZO IX HL AN AL VW KX SX RJ OJ ON HT ID ID NA GJ CX BN UQ YM UY PG PL
BZ CT MO GK JW XI KE YJ RU XT AZ ID MT WR UX AI MG UJ MB UM VE JH UT KZ GI RG
XV JE XY ZQ IW ER WH FQ IQ DR YA MG HH ZR HK KH ZF YE MH QO IS EO YI IS AZ VD
FV JT GD BK NK LR GX VL BJ MI UW II MV TY DL PE GD CD LH OM GG TQ AL MI US EZ
OM KI NM WA BV KA CH JY IN FP QJ YL LK CX PO PG YX GQ BO BW NO XC GZ YU BA TD
DE AB SP RN OY LB TY GS SS JI SY IB XC FQ FC ZF EL YL ZR OE ZL BF AE HX ZG DB
LO PP QJ JK CR MI EV VF LA IN QM YP SZ IW GE ZK BY QP CM AC TX ZW AJ QC UH LV

C A X S D O S I E V V Q N L S U D
S N H S U T A A L F B H Q I Z E M
U C E A F B Y Z F S V Q Q P I W L
F U M N K T W I Q Y E T P I X Q G
J N H T C A I W H Q X L T T N Z S
U M R A L F B B F O I C B D H B F
S S D H J P L M Y U L Q X C H Q B
Q T W F K C B X G H T N R T A A L
F B F Z T Y H Z T B Z I O A F B D
H J P H Q Q O P P V U T W Q G E Y
K W M Q C S U C B Q G C F S N Z S
V T P B Y D H W U R E L B C A N T
R E D S I W C S B J A L U C K K E
G L Q B M R J P Z D P F W B M R L
A F L G N X A L L M P R B Y Q N H
Q K L P U Q G P U C V T W H T W J
E J O M W F L Y F S N Z H Y A L O
E D G N Z O D E G D H H Q B T M O
N H J N J N A L L A K E Z D U C N
X A E Q F L B E M U C B U F S Y U

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

Zodiac 340 period x repeats ODD / EVEN statistics

22 100 test messages average difference between odd / even
8 100 test messages standard deviation between odd / even
14 – 30 100 test messages average difference + / – standard deviation

Zodiac 340 redrafted into 19 columns, transposed 90 degrees; the same flipped and mirrored
19 Odd
21 Even

Maximum difference = 10 search for one skip or one null ( note choppy shape of graph )

Zodiac 340 redrafted into 19 columns, transposed 90 degrees, mirrored; the same flipped
21 Odd
26 Even

Maximum difference = 9 search for one skip or one null ( note choppy shape of graph )

Conclusion: For period 19, not in the range of the test messages. Not much of a difference between odds and evens, and even replacing a skip or deleting a symbol sliding through the message from position 1 to 340 results in a difference that is not in range.

Zodiac 340 mirrored, redrafted into 15 columns, transposed 90 degrees; the same flipped and mirrored
20 Odd
18 Even

Maximum difference = 9 search for one skip or null

Zodiac 340 mirrored, redrafted into 15 columns, transposed 90 degrees, mirrored; the same flipped
21 Odd
18 Even

Maximum difference = 9 search for one skip or null

Note the choppy shape of the graphs. Here is a graph of a true digraph + homophonic cipher. There are 39 odd and 6 even, with a difference of 33. Then a null is introduced at position 169, shifting all symbols to the right of position 169 over one. After the null, there are 21 odd and 16 even. The detector was only semi accurate because it could maximize the difference at about position 200. But it is not choppy like the graphs above it is more smooth.

Here is a homophonic message. 14 odd, 21 even.

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

The skip detector was able to maximize to a difference of 15 at about position 277, which is barely in the digraph range. There is no digraph encoding and no skip. But it is also choppy. I made some homophonic only messages and they are generally choppy with a lot of flat spots like the Zodiac 340.

Great stuff smokie, excellent work so far.

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

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.

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.

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.

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.

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.

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?