Bigrams

K4: Bigrams & Visual Observations

Ciphertext In Groups Of 14:
?OBKRUOXOGHULB
SOLIFBBWFLRVQQ
PRNGKSSOTWTQSJ
QSSEKZZWATJKLU
DIAWINFBNYPVTT
MZFPKWGDKZXTJC
DIGKUHUAUEKCAR

FULL CIPHERTEXT IN 14×7 Split Matrix:
+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+
|  1|  2|  3|  4|  5|  6|  7|    |  8|  9 | 10 | 11 | 12 | 13 | 14 |
+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+
| ? | O | B | K | R | U | O |    | X | O  | G  | H  | U  | L  | B  |
| S | O | L | I | F | B | B |    | W | F  | L  | R  | V  | Q  | Q  |
| P | R | N | G | K | S | S |    | O | T  | W  | T  | Q  | S  | J  |
| Q | S | S | E | K | Z | Z |    | W | A  | T  | J  | K  | L  | U  |
| D | I | A | W | I | N | F |    | B | N  | Y  | P  | V  | T  | T  |
| M | Z | F | P | K | W | G |    | D | K  | Z  | X  | T  | J  | C  |
| D | I | G | K | U | H | U |    | A | U  | E  | K  | C  | A  | R  |
+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+


I Moved The "?" To The End Because It Isn't Part Of The K4 Ciphertext & Only There To Line Up Evenly In The Grid To Show The Bigram Doublets.

Since I Can't Upload Images, This Will Be More Difficult To Present These Findings, But I Will Fo My Best.

In This Matrix Grid, We Can Find Matching Bigram Doublet Pairs Of Identical Letters (Eg; BB, SS, QQ, TT...) Looking In All Directions (Horizontal, Vertical & Diagonal) That Are Directly Touching Within 1 Cell.

We Can Further See Bigrams Doublets That Are Not Identical, Such As "SO" & "DI" Which Appears As Repeating Bigrams.

I Have Identified All Bigrams In K4, Matched The Values Of Each Line To The Distance Of The Nearest Identical Letters & Have Found Some Patterns Which May Reveal How The Ciphertext Was Transposed.

The 97 Characters Of K4 Do Not Move, They Are Shifted With A Transposition/Substitution Method Using A Specific Route.

More Observations:
•There Are 2 Letters "Y" & "M" And The "?" Padding, That Are Only Seen Once Inside The Ciphertext.

•If We Leave The "?" At The Beginning, The Letters "O" (First Letter In Each Group) & "D" (Last Letter Of Each Group)Line Up In Right Angles Opposite To Each Other (Essentially Creating A Box).

+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+
|  1|  2|  3|  4|  5|  6|  7|    |  8|  9 | 10 | 11 | 12 | 13 | 14 |
+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+
|[O]| B | K | R | U | O | X |    |[O]| G  | H  | U  | L  | B  | S  |
|[O]| L | I | F | B | B | W |    | F | L  | R  | V  | Q  | Q  | P  |
| R | N | G | K | S | S | O |    | T | W  | T  | Q  | S  | J  | Q  |
| S | S | E | K | Z | Z | W |    | A | T  | J  | K  | L  | U  |[D] |
| I | A | W | I | N | F | B |    | N | Y  | P  | V  | T  | T  | M  |
| Z | F | P | K | W | G |[D]|    | K | Z  | X  | T  | J  | C  |[D] |
| I | G | K | U | H | U | A |    | U | E  | K  | C  | A  | R  | ?  |
+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+
Note:
This Is With Padding "?" At The End, Not The Beginning Of The Grid.

Now I Will Try To Give The Data Of My Grids & Handwritten Matrixes In A Human Readable Way.

• Assume The Grid Is 14 Columns Wide, By 7 Rows Deep.

+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+
|  1|  2|  3|  4|  5|  6|  7|    |  8|  9 | 10 | 11 | 12 | 13 | 14 |
+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+
| ? | O | B | K | R | U | O |    | X | O  | G  | H  | U  | L  | B  |
| S | O | L | I | F | B | B |    | W | F  | L  | R  | V  | Q  | Q  |
| P | R | N | G | K | S | S |    | O | T  | W  | T  | Q  | S  | J  |
| Q | S | S | E | K | Z | Z |    | W | A  | T  | J  | K  | L  | U  |
| D | I | A | W | I | N | F |    | B | N  | Y  | P  | V  | T  | T  |
| M | Z | F | P | K | W | G |    | D | K  | Z  | X  | T  | J  | C  |
| D | I | G | K | U | H | U |    | A | U  | E  | K  | C  | A  | R  |
+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+

Note:
We Will Read The Bigram Locations As Follows:
Bigram (Row:Column)


Vertical:
OO (1:2, 2:2)
KK (3:5, 4:5)

+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+
|  1|  2|  3|  4|  5|  6|  7|    |  8|  9 | 10 | 11 | 12 | 13 | 14 |
+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+
| ? |[O]| B | K | R | U | O |    | X | O  | G  | H  | U  | L  | B  |
| S |[O]| L | I | F | B | B |    | W | F  | L  | R  | V  | Q  | Q  |
| P | R | N | G |[K]| S | S |    | O | T  | W  | T  | Q  | S  | J  |
| Q | S | S | E |[K]| Z | Z |    | W | A  | T  | J  | K  | L  | U  |
| D | I | A | W | I | N | F |    | B | N  | Y  | P  | V  | T  | T  |
| M | Z | F | P | K | W | G |    | D | K  | Z  | X  | T  | J  | C  |
| D | I | G | K | U | H | U |    | A | U  | E  | K  | C  | A  | R  |
+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+

Horizontal:
BB (2:6, 2:7)
QQ (2:13, 2:14)
SS (3:6, 3:7)
SS (4:2, 4:3)
ZZ (4:6, 4:7)
TT (5:13, 5:14)

+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+
|  1|  2|  3|  4|  5|  6|  7|    |  8|  9 | 10 | 11 | 12 | 13 | 14 |
+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+
| ? | O | B | K | R | U | O |    | X | O  | G  | H  | U  | L  | B  |
| S | O | L | I | F |[B]|[B]|    | W | F  | L  | R  | V  |[Q] |[Q] |
| P | R | N | G | K |[S]|[S]|    | O | T  | W  | T  | Q  | S  | J  |
| Q |[S]|[S]| E | K |[Z]|[Z]|    | W | A  | T  | J  | K  | L  | U  |
| D | I | A | W | I | N | F |    | B | N  | Y  | P  | V  |[T] |[T] |
| M | Z | F | P | K | W | G |    | D | K  | Z  | X  | T  | J  | C  |
| D | I | G | K | U | H | U |    | A | U  | E  | K  | C  | A  | R  |
+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+

Diagonal:
QQ (2:13, 3:12)
TT (3:9, 4:10)
TT (3:11, 4:10)
TT (5:13, 6:12)
KK (6:5, 7:4)

+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+
|  1|  2|  3|  4|  5|  6|  7|    |  8|  9 | 10 | 11 | 12 | 13 | 14 |
+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+
| ? | O | B | K | R | U | O |    | X | O  | G  | H  | U  | L  | B  |
| S | O | L | I | F | B | B |    | W | F  | L  | R  | V  |[Q] | Q  |
| P | R | N | G | K | S | S |    | O |[T] | W  |[T] |[Q] | S  | J  |
| Q | S | S | E | K | Z | Z |    | W | A  |[T] | J  | K  | L  | U  |
| D | I | A | W | I | N | F |    | B | N  | Y  | P  | V  |[T] | T  |
| M | Z | F | P |[K]| W | G |    | D | K  | Z  | X  |[T] | J  | C  |
| D | I | G |[K]| U | H | U |    | A | U  | E  | K  | C  | A  | R  |
+---+---+---+---+---+---+---+----+---+----+----+----+----+----+----+

Non-Identical Repeating Bigram Pairs: (Need To Order List)

AT (4:9, 3:9)
AT (4:9, 4:10)
AT (7:13, 6:12)

BS (2:6, 3:6)
BS (2:7, 3:7)

CA (6:14, 7:13)
CA (7:12, 7:13)

DI (5:1, 5:2)
DI (7:1, 7:2)
DZ (5:1, 6:2)
DZ (7:1, 6:2)
DM (5:1, 6:1)
DM (7:1, 6:1)

EK (4:4, 4:5)
EK (4:4, 3:5)
EK (7:10, 6:9)
EK (7:10, 7:11)

FB (2:5, 2:6)
FB (5:7, 5:8)
FK (2:5, 3:5)
FK (6:3, 7:4)
FW (2:9, 2:8)
FW (2:9, 3:10)
FW (6:3, 5:4)
FW (5:7, 4:8)
FW (5:7, 6:6)
FZ (5:7, 4:6)
FZ (5:7, 4:7)
FZ (6:3, 6:2)

HU (1:11, 1:12)
HU (7:6, 7:5)
HU (7:6, 7:7)

IK (2:4, 1:4)
IK (2:4, 3:5)
IK (5:5, 4:5)
IK (5:5, 6:5)
IM (5:2, 6:1)
IM (7:2, 6:1)
IW (5:5, 5:4)
IW (5:5, 6:6)
IF (2:4, 2:5)
IF (5:2, 6:3)
IF (7:2, 6:3)
IN (2:4, 3:3)
IN (5:5, 5:6)
IZ (7:2, 6:2)
IZ (5:5, 4:6)
IZ (5:2, 6:2)

JT (4:11, 4:10)
JT (4:11, 3:11)
JT (6:13, 6:12)
JT (6:13, 5:13)
JT (6:13, 5:14)
JQ (3:14, 2:13)
JQ (3:14, 2:14)
JQ (4:11, 3:12)

KB (3:5, 2:6)
KB (6:9, 5:8)
KL (1:4, 2:3)
KL (4:12, 4:13)
KS (3:5, 3:6)
KS (4:5, 3:6)
KS (4:12, 3:13)
KZ (3:5, 4:6)
KZ (4:5, 4:6)
KZ (6:9, 6:10)
KZ (7:11, 6:10)

NG (3:3, 3:4)
NG (5:6, 6:7)
NW (5:9, 4:8)
NW (5:6, 6:6)

OB (1:2, 1:3)
OB (2:2, 1:3)
OB (1:7, 2:6)
OB (1:7, 2:7)
OB (3:8, 2:7)
OF (1:9, 2:9)
OF (3:8, 2:9)
OL (1:2, 2:3)
OL (2:2, 2:3)
OL (1:9, 2:10)
OW (1:7, 2:8)
OW (1:9, 2:8)
OW (3:9, 2:8)
OW (3:8, 4:8)
OX (1:7, 1:8)
OX (1:9, 1:8)

PK (6:4, 6:5)
PK (6:4, 7:4)
PK (5:11, 4:12)

SK (3:6, 3:5)
SK (3:6, 4:5)
SK (3:13, 4:12)
SO (2:1, 1:2)
SO (2:1, 2:2)
SO (3:6, 3:7)
SP (2:1, 3:1)
SP (4:2, 3:1)
SW (3:7, 2:8)
SW (3:7, 4:8)
SW (4:3, 5:4)
SZ (3:6, 4:6)
SZ (3:7, 4:7)

UD (7:7, 6:8)
UD 7:9, 6:8)

WA (4:8, 4:9)
WA (5:4, 5:3)
WA (3:10, 4:9)
WT (2:8, 3:9)
WT (4:8, 3:9)
WT (3:10, 3:9)
WT (3:10, 3:11)
WT (3:10, 4:10)

ZN (4:6, 5:6)
ZN (4:7, 5:6)
ZN (6:10, 5:9)


Distance To Nearest Matching Letter:

Rules:
• Count By Spaces Between The Matching Letters.
• No Word Wrapping. It Must Be Counted Inside The 14×7 Matrix Grid.
(Otherwise We Also See Bigrams Such As QQ (2:13, 3:14) + Change Q In 4:1 To "1" Instead Of "11" Which Is Not Used)
• You Can Move In Any Direction, Vertical, Horizontal & Diagonal.
• You Can Move Multiple Directions To Reach The Matching Letters.
• You Must Find The Shortest Path.

Here Is The Full Distance List Along With A Vertical And Horizontal Count For Every Row & Column:

Note:
The Higher The Value, The More Mixed Up It Is.

By Rows:

Row 1: 0,1,3,2,3,6,2,5,2,5,6,3,3,6
Sum: 47

Row 2: 2,1,7,3,4,1,1,2,4,3,5,3,1,1
Sum: 38

Row 3: 3,3,3,3,1,1,1,2,1,2,1,1,6,3
Sum: 31

Row 4: 11,1,1,6,1,1,1,2,3,1,3,3,3,3
Sum: 40

Row 5: 2,2,5,2,3,3,3,3,3,0,7,3,1,1
Sum: 38

Row 6: 0,4,4,3,1,2,4,7,2,3,5,1,2,2
Sum: 40

Row 7: 2,2,4,1,2,6,2,3,2,6,2,2,5,5
Sum: 44

By Columns:

Column 1: 0,2,3,11,2,0,2
Sum: 20

Column 2: 1,1,3,1,2,4,2
Sum: 14

Column 3: 3,7,3,1,5,4,4
Sum: 27

Column 4: 2,3,3,6,2,3,1
Sum: 20

Column 5: 3,4,1,1,3,1,2
Sum: 15

Column 6: 6,1,1,1,3,1,2
Sum: 20

Column 7: 2,1,1,1,3,4,2
Sum: 14

Column 8: 5,2,2,2,3,7,3
Sum: 24

Column 9: 2,4,1,3,3,2,2
Sum: 17

Column 10: 5,3,2,1,0,3,6
Sum: 20

Column 11: 6,5,1,3,7,5,2
Sum: 29

Column 12: 3,3,1,3,3,1,2
Sum: 16

Column 13: 3,1,6,3,1,2,5
Sum: 21

Column 14: 6,1,3,3,1,2,5
Sum: 21

Row Average: 40 (39.714285714285)
Column Average: 20 (19.857142857142)

Note:
If The Values Of The Row Or Column Average Is Greater Than The Row Or Column Sum,
It Is More Mixed Up & Has A Higher Probability For Additional Steps In The Transposition Route.
Lower Sum Values Mean It Is Closer To Plaintext & May Require Only 1 Step, Or It Remains The Same Value.