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Classical Cryptography Course by Lanaki |
Lecture 24Special Topics |
Lecture 24 will be devoted to special topics and will present additional cryptograms for solution. I will update and restructure my Volume II references and resources file. Lecture 24 will constitute my final efforts. Updated Volume II references will replace Lecture 25.
Those students interested in course participation certificates please advise me by e-mail, so I have an idea how many to order.
Volume II of our textbook is available through RAGYR and Aegean Park Press. You are encouraged to buy a copy. All of the corrections presented to me by our capable class are included in the book. Those interested in signed copies please advise by private E-mail, and I will maintain a small inventory for that purpose.
I want to clean up some loose ends in the Transposition area and then shift to a review of some of the more popular ciphers presented in Lectures 1-20. I will present more problems, not so much for a "final exam" as for a chance to improve/enjoy our cryptographic skills. I also want to present some additional legal information regarding Defamation on the Net (an expansion on my Privacy Lecture).
The Übchi (the U is umlauted) is a double columnar transposition cipher used by the Germans during WWI. It was broken by the French thanks to in part to a radio message sent in unprotected cleartext early in the conflict.
The Übchi had a keyphrase that was represented by numerals according to the position of its letters. Two identical letters were labeled consecutively if they appeared in the same keyphrase. For example,
| 5 | 3 | 7 | 8 | 9 | 2 | 6 | 1 | 4 | 10 | |
| Keyword: | h | e | r | r | s | c | h | a | f | t |
For the plaintext: First army X Plan five activated X Cross Marne at set hour.
Ciphertext key block 1:
| 5 | 3 | 7 | 8 | 9 | 2 | 6 | 1 | 4 | 10 |
| h | e | r | r | s | c | h | a | f | t |
| F | I | R | S | T | A | R | M | Y | X |
| P | L | A | N | F | I | V | E | A | C |
| T | I | V | A | T | E | D | X | C | R |
| O | S | S | M | A | R | N | E | A | T |
| S | E | T | H | O | U | R |
The ciphertext was taken off by columns in numerical order of the keyword columns:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Ciphertext: | MEXE | AIERU | ILISE | YACA | FPTOS | RVDNR | RAVST | SNAMH | TFTAO | XCRT. |
(Note the 5 letters groups not observed.)
These groups were then transcribed horizontally into another block beneath the same number sequence:
| 5 | 3 | 7 | 8 | 9 | 2 | 6 | 1 | 4 | 10 |
| h | e | r | r | s | c | h | a | f | t |
| M | E | X | E | A | I | E | R | U | I |
| L | I | S | E | Y | A | C | A | F | P |
| T | O | S | R | V | D | N | R | R | A |
| V | S | T | S | N | A | M | H | T | F |
| T | A | O | X | C | R | T | (Z) |
The next step was to add as many Null letters as there are words in the Keyphrase or Keyword. One null Z was added after the last letter in the last row, T.
The German encipherer once more took these letters from the block by columns in the same numerical sequence and separated into standard groups of five letters each:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| RARHZ | IADAR | EIOSA | UFRTM | LTVTE | CNMTX | SSTOE | ERSXA | YVNCI | PAF. |
To decipher the message, the recipient first had to discern the size of the transposition rectangle in order to learn how long the columns were. This was accomp- lished by dividing the total number of key numbers into the total number of letters into the message (48 / 10). The quotient was the number of complete rows. The remainder 8 was the number of letters in the incomplete columns. The succeeding steps reversed the corre- sponding steps in the enciphering process.
Note the similarity with the U.S. Army Double Trans- position Cipher System. Barker gives a detailed breakdown of this type of cipher in his book. [BARK] It is not coincidental that the two countries at war had very similar cipher systems in play.
One of the more interesting transposition ciphers is the double transposition cipher. One of the guru's in this area is Colonel Wayne Barker. His "Cryptanalysis of the Double Transposition Cipher" is enjoyable reading. I thank him for his liberal permission to excerpt from his reference. [BARK2]
In its most effective form the double transposition cipher is based upon two incompletely filled rectangles with two different length keywords. Nulls must be added before encipherment, not to the end after encipherment. In the deciphering process, we must determine the exact dimensions of the enciphering rectangles R-1 and R-2 by keywords K-1 and K-2, respectively.
The process of encipherment is relatively straight forward. The plain text is read into R-1 by rows, taken out by columns in the order of K-1, transcribed into R-2 in rows and removed from R-2 by columns as dictated by K-2. The ciphertext is then separated into the standard groups of 5 letters for transmission.
The difficulty in decipherment occurs when we must determine the exact dimensions of R-1 and R-2 as well as the sequence and width of K-1 and K-2. Recall that we can use the division of the message length by the key length to give us the number of long columns and length of the short columns. For example, for message length 99 with keylength of 13, we have:
7 - length of short column
------
keylength =13 | 99 - message length
91
--
8 - number of long columns
The length of the long columns is 1 more than short or 8. The number of short columns is 13 - 8 = 5.
This is Step 1.
To decipher the double transposition cipher, the ciphertext letters are inscribed within R-2, whose dimensions have been determined in Step 1, following the column order of K-2. Thereafter, the horizontal letters within R-2 are inscribed within R-1 following the column order of K-1. The resulting plaintext is read horizont- ally within R-1. So there we have Steps 2 and 3.
Regardless of how complex a transposition system may be, the resulting ciphertext messages may be put in depth, superimposed one above the other, the resulting columns may potentially be matched against one another to produce plaintext. Messages must be the same length. This is not a difficult requirement, especially when nulls are added to get an even number letters in groups of 5.
In essence we construct a giant single columnar transposition cipher of message length L. The problem is reduced to juxtaposing (matching the columns) so that the plaintext is readable.
Given the following six messages at L = 115 letters:
1 1 1 1 1 1 1 1 1 1 2
1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0
Message 1: T L R N T A H I I O D F Y N P T R I E A
Message 2: P E U L N R B Q T L C R L E W E X B O I
Message 3: T H N N I N U A T O T E E I S S X I O E
Message 4: T E N G I R A E E O R E E I L I X E E A
Message 5: O I E O L T I L W U V U R T O E O C R P
Message 6: T A F H E R N A D O S I I I T E H Y F W
2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4
1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0
Message 1: O E E B T Y E I P O S V I V A E X R F T
Message 2: T E A Y A X J T N P W E I R W D X S E E
Message 3: V P O T H X G G I D O S R N E P X T I P
Message 4: V T D R E X P G R D S S R U E S X E I H
Message 5: R C R O A P E S U I I A W E N N X R O R
Message 6: G S W P I X C G R D E R U E G V X K I P
4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6
1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0
Message 1: I S R T W M B U F F O D R E E A E U S H
Message 2: S V E E O T O Y U A E A C P O R X W I E
Message 3: T S P N S N B N N N R I W T G U S S D T
Message 4: T G P E S U L T R N O I P T I T S V D E
Message 5: V I I U R T E S E N S H R Y Y R T N Y L
Message 6: D E P O S Y E I L N O H S T S C T E R Y
6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8
1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0
Message 1: E T E S R C C I R R T R Y E S N I S F S
Message 2: E O S E T Y W X N U R I N D T E L S R E
Message 3: E R R C T G S I O O R A F O O M K L O S
Message 4: E P H C S G T I N T L W O A A M N L T S
Message 5: S L A R E A P A L T A Y O N Y S M E U I
Message 6: H E Y C U O T E E A N E V E O M T R W M
1
8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 0
1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0
Message 1: L S R F I A I O O C T Q O G D R U P E O
Message 2: C A S O A C M W S Y T R E S O E E T P L
Message 3: E O G L O O R R O D M O A M O A S N I R
Message 4: Y C C V O O R S O E A N E M N A S N Q S
Message 5: N P D W P S N T L A H E A O O D Q E C S
Message 6: E E R U O A C C N D R M E M L E H T A O
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 0 0 0 0 0 0 0 0 1 1 1 1 1 1
1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
Message 1: E O A O I N A N R S R L S T U
Message 2: U P R O G E W K E E N E N S E
Message 3: T S A T R A O I A I L N W F F
Message 4: M E A E R U O R U E S N L F O
Message 5: I E I E E Y F O T N C T A R E
Message 6: L R A Y I D O T T S W N R T A
We look for letters of low frequency such as Q or QU combinations. We may assume that the messages end in X(s) for nulls. We start with this fact.
| 17 | 26 | 37 | 57 | 68 |
| R | Y | X | E | I |
| X | X | X | X | X |
| X | X | X | S | I |
| X | X | X | S | I |
| O | P | X | T | A |
| H | X | X | T | E |
Column 37 is the last, 26 is before it, and 17 with three X's is the antepenultimate column.
17 26 37 - - - R Y X X X X X X X X X X O P X H X XPutting column 57 in the group gives us (QU)ERY and (S)TOP. We might work back from this point with maybe GENERAL SMITH for the last message. We can hook up the QU's for breaks in the middle of the messages.
92 48 57 17 26 37 - - - - - - Q U E R Y X R Y X X X X O N S X X X N T S X X X E S T O P X (S) M I T H X XSolve the rest.
The next step in the process is to recover the keys.
Given 4 messages of L = 85 letters, and their anagramed equivalent:
7 7 7 2 6 2 6 6 6 5 5 4 5 3 4 4 1 3 1 3
9 6 2 5 3 2 0 9 6 1 7 2 4 9 8 5 9 6 0 3
Message 1: M E S S A G E S I X O N E S T O P O U R
Message 2: W E A R E R U N N I N G I N T O H E A V
Message 3: T O C O M M A N D I N G O F F I C E R T
Message 4: O P E R A T I O N S O R D E R S I X T E
0 1 1 3 0 8 0 8 2 2 6 7 7 7 7 5 5 4 6 5
7 6 3 0 4 4 1 1 7 4 2 8 4 5 1 9 6 1 8 3
Message 1: A D V A N C E H A S B E E N S L O W E D
Message 2: Y M I N E F I E L D S S T O P W E U R G
Message 3: H I R D B A T T A L I O N S T O P H A V
Message 4: E N I S B E I N G S E N T Y O U B Y C O
6 5 3 3 0 4 2 4 1 0 0 8 1 3 1 2 8 7 7 2
5 0 8 5 9 7 1 4 8 6 3 3 5 2 2 9 0 7 3 6
Message 1: B Y H E A V Y M O R T A R F I R E S T O
Message 2: E N T L Y N E E D E N G I N E E R P E R
Message 3: E R E P R E S E N T A T I V E Y O U R U
Message 4: U R I E R S T O P A D V I S E B Y R A D
6 2 6 7 6 5 5 4 5 4 4 4 2 3 1 3 0 1 1 3
4 3 1 0 7 2 8 3 5 0 9 6 0 7 1 4 8 7 4 1
Message 1: P W E N E E D C O U N T E R F I R E S T
Message 2: S O N N E L T O R E M O V E M I N E S S
Message 3: N I T H E R E T O M O R R O W F O R M E
Message 4: I O W H E N Y O U H A V E R E C E I V E
0 8 0 8 2
5 5 2 2 8
Message 1: O P X X X
Message 2: T O P X X
Message 3: E T I N G
Message 4: D I T X X
The C � P sequence is also known as the anagram key. Given the anagram keys we can recover the keys K-1 and K-2.
The anagram key of the above ciphertext example is:
79 76 72 25 63 22 60 69 66 51 57 42 54 39 48 45 19 36 10 33 07 16 13 30 04 84 01 81 27 24 62 78 74 75 71 59 56 41 68 53 65 50 38 35 09 47 21 44 18 06 03 83 15 32 12 29 80 77 73 26 64 23 61 70 67 52 58 43 55 40 49 46 20 37 11 34 08 17 14 31 05 85 02 82 28
We can index the anagram key as follows:
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 79 76 72 25 63 22 60 69 66 51 57 42 54 39 48 45 19 36 10 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 33 07 16 13 30 04 84 01 81 27 24 62 78 74 75 71 59 56 41 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 68 53 65 50 38 35 09 47 21 44 18 06 03 83 15 32 12 29 80 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 73 26 64 23 61 70 67 52 58 43 55 40 49 46 20 37 11 34 77 78 79 80 81 82 83 84 85 08 17 14 31 05 85 02 82 28
The indexed version is known as the P -> C sequence. It is also called the encipher key. Inverting the encipher key index gives us the encipher key derived from the recovered anagram key:
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 27 83 51 25 81 50 21 77 45 19 75 55 23 79 53 22 78 49 17 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 73 47 06 62 30 04 60 29 85 56 24 80 54 20 76 44 18 74 43 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 14 70 38 12 68 48 16 72 46 15 71 42 10 66 40 13 69 37 11 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 67 36 07 63 31 05 61 41 09 65 39 08 64 35 03 59 33 34 02 77 78 79 80 81 82 83 84 85 58 32 01 57 28 84 52 26 82
The anagram key is the order of the ciphertext letters to produce plaintext, and the encipher key is the order of the plaintext letters to produce ciphertext.
From the encipher key we derive the Interval Key. The interval key provides the intervals both positive and negative, between successive terms of the encipher key.:
+56 -32 -26 +56 -31 -29 +56 -32 -26 +56 -20 -32 +56 -26 -31 +56 -29 -32 +56 -26 -41 +56 -32 -26 +566 -31 +56 -29 -32 +56 -26 -34 +56 -32 -26 +56 -31 -29 +566 -32 -26 +56 -20 -32 +56 -26 -31 +56 -29 -32 +56 -26 -277 +56 -32 -26 +56 -31 -29 +56 -32 -26 +56 -20 -32 +56 -26 -31 +56 -29 -32 +56 -26 +01 -32 +56 -26 -31 +56 -29 +566 -32 -26 +56
We start at identifying K-1 length. There are three lengthy repetitions in the interval key starting with +56 and ending with -26. We look at the terms that give rise to these repetitions.
27 83 51 25 81 50 21 77 45 19 75 55 23 79 53 22 78 49 17 20 76 44 18 74 43 14 70 38 12 68 48 16 72 46 15 71 42 10 -------------------------------------------------------- 07 07 07 07 07 07 07 07 07 07 07 07 07 07 07 07 07 07 07 20 76 44 18 74 43 14 70 38 12 68 48 16 72 46 15 71 42 10 13 69 37 11 67 36 07 63 31 05 61 41 09 65 39 08 64 35 03 -------------------------------------------------------- 07 07 07 07 07 07 07 07 07 07 07 07 07 07 07 07 07 07 07
The common difference is the length of K-1.
Setting up R-1:
------------------- 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
Using the derived encipher key, the first column is
27 83 51 25 81 50 21 77 45 19 75
We start by reconstructing R-2. We know that its horizontal rows come from the vertical columns of R-1 and its vertical columns come from the terms of the encipher key.
1
6 13 20 27 34 41 48 55
62 69 76 83 02 09 16 23
30 37 44 51
25
81
50
21
Knowing the width of R-2 gives the dimensions of R-2.
85 = 3 - 10's
5 - 11's
The reconstruction of R-2 continues as we discover the order of columns in R-1 entering R-2. This is done by knowing the vertical terms in R-2, which are successive terms of the encipher key.
The reconstruction of R-1 and R-2 with keys identified are:
04 02 06 03 07 01 05 K-1 =7
-------------------
01 02 03 04 05 06 07
08 09 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31 32 33 34 35
36 37 38 39 40 41 42
43 44 45 46 47 48 49
50 51 52 53 54 55 56
57 58 59 60 61 62 63
64 65 66 67 68 69 70
71 72 73 74 75 76 77
78 79 80 81 82 83 84
85 3 6 4 1 8 7 5 2
----------------------
6 13 20 27 34 41 48 55
62 69 76 83 02 09 16 23
30 37 44 51 58 65 72 79
04 11 18 25 32 39 46 53
60 67 74 81 01 08 15 22
29 36 43 50 57 64 71 78
85 07 14 21 28 35 42 49
56 63 70 77 84 03 10 17
24 31 38 45 52 59 66 73
80 05 12 19 26 33 40 47
54 61 68 75 82
Solution where known plaintext occurs at any point within the message.
Barker describes solution of several special "crib" situations. He uses stereotyped beginnings, endings and shows the process of overlaying the crib into R-1 and converting it into R-2. Of more interest is the solution when the plaintext crib is anywhere in the message.
Consider the following problem:
DTHIS ERTRS OUEST RRTER NMNCT ODANO TOCFO ARTPN OEXOS VWMUW ODPOD ECNEQ APTIT AMIIF CAENA SWMCC AILAO OIMOT DAJLG NRFOZ SPUOO RTTEO EBRRO INNE. (119)
Known plaintext: ROAD JUNCTION QUEBEC FOXTROT TWO FIVE EIGHT ZERO
K-1 = 9
Analysis:
The first step is to number the positions of the letters in the ciphertext and make a bilateral frequency distribution.
D-1 T-2 H-3 I-4 S-5 E-6 R-7 T-8 R-9 S-10 O-11 U-12 E-13 S-14 T-15 R-16 R-17 T-18 E-19 R-20 N-21 M-22 N-23 C-24 T-25 O-26 D-27 A-28 N-29 O-30 T-31 O-32 C-33 F-34 O-35 A-36 R-37 T-38 P-39 N-40 O-41 E-42 X-43 O-44 S-45 V-46 W-47 M-48 U-49 W-50 O-51 D-52 P-53 O-54 D-55 E-56 C-57 N-58 E-59 Q-60 A-61 P-62 T-63 I-64 T-65 A-66 M-67 I-68 I-69 F-70 C-71 A-72 E-73 N-74 A-75 S-76 W-77 M-78 C-79 C-80 A-81 I-82 L-83 A-84 O-85 O-86 I-87 M-88 O-89 T-90 D-91 A-92 J-93 L-94 G-95 N-96 R-97 F-98 O-99 Z-100 S-01 P-02 U-03 O-04 O-05 R-06 T-07 T-08 E-09 O-110 E-11 B-12 R-13 R-14 O-15 I-16 N-17 N-18 E- 119 (119)
A 28 36 61 66 72 75 81 84 92 B 112 C 24 33 57 71 79 80 D 01 27 52 55 91 E 06 13 19 42 56 59 73 109 111 119 F 34 70 98 G 95 H 03 I 04 64 68 69 82 87 116 J 93 K L 83 94 M 22 48 67 78 88 N 21 23 29 40 58 74 96 117 118 O 11 26 30 32 35 41 44 51 54 85 86 89 99 104 105 110 115 P 39 53 62 102 Q 60 R 07 09 16 17 20 37 97 106 113 114 S 05 10 14 45 76 101 T 02 08 15 18 25 31 38 63 65 90 107 108 U 12 49 103 V 46 W 47 50 77 X 43 Y Z 100
Now on to K-1 at length 9, we write in the known plaintext:
1 2 3 4 5 6 7 8 9 ----------------- R O A D J U N C T I O N Q U E B E C F O X T R O T T W O F I V E E I G H T Z E R O
Focus on column 4 with the infrequent letters of Q and V. We can establish this as a row in R-2. We locate two columns that fit the pattern.
P P
O N
D O
E E
C X
N O
E S
D Q T V R
A W
P M
T U
I W
T O
A D
M P
The column added to R-2 come directly from the ciphertext. Lets analyze the positional information to reconstruct R-2.
Q and V occur in positions 46 and 60. We can expect the length of of K-2 will be a multiple of 14 because the difference is 14. Letters occurring in the same column of R-1 which occupy the same row of R-2 will be separated in the ciphertext by a multiple of R-2 column lengths. This is a multiple of the key. We might expect that R-2 is 14 for a column length. Two rectangle widths give rise to a column length of 14 for L = 119.
K-2 = 8
1] 119 = 7 - 15's
1 - 14
K-2 = 9
2] 119 = 2 - 14's
7 - 13's
Look at letters H and W:
H= 03
W = 47 50 77 � distances of 44 47 74 which is consistent with column length of 15 and 14 for K-2 =8.
So the width of R-2 is 8. We construct a analytical matrix of width 8:
1 2 3 4 5 6 7 8
T O S Q A T
D R T V A S D O
T R O W P W A R
H T C M T M J T
I E F U I C L T
S R O W T C G E
E N A O A A N O
R M R D M I R E
T N T P I L F B
R C P O I A O R
S T N D F O Z R
O O O E C O S O
U D E C A I P I
E A X N E M U N
S N O E N O O N
T O S Q A T O E
Using the DQTVR as the starting column, we locate columns 5 and 4 of R-1:
8 3 6 1 5 7 4 2
O T A D Q T V R
R O S T A D W T
T C W H P A M E
T F M I T J U R
E O C S I L W N
O A C E T G O M
E R A R A N D N
B T I T M R P C
R P L R I F O T
R N A S I O D O
O O O O F Z E D
I E O U C S C A
N X I E A P N N
N O M S E U E O
E S O T N O Q
We mark off the known plaintext and work up and down from the starting row to get the solution with K-1 =9:
1 2 3 4 5 6 7 8 9
-----------------
- O U R F O R W A
R D C O M M A N D
P O S T I S N O W
L O C A T E D A T
R O A D J U N C T
I O N Q U E B E C
F O X T R O T T W
0 F I V E E I G H
T Z E R O S T O P
R E A R C O M M A
N D P O S T R E M
A I N S I N P R E
S E N T L O C A T
I O N - - - - - -
Colonel Barker found that any double transposition cipher can be expressed as an equivalent single transposition cipher.
Consider the following double transposition encipherment:
3 2 1 5 4 K-1 = 5
--------------
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
R-1 21 22 23 24 25
26 27 28 29 30
31 32 33 34 35 13 X 5 matrix
36 37 38 39 40
41 42 43 44 45
46 47 48 49 50
51 52 53 54 55
56 57 58 59 60
61 62 63 - - 63 = 3 @ 13 long
2 @ 12 short
and
3 2 4 1 K-2 =4
-----------
03 08 13 18
23 28 33 38
43 48 53 58
63 02 07 12
17 22 27 32
37 42 47 52 16 X 4 matrix
57 62 01 06
R-2 11 16 21 26
31 36 41 46 63 = 3 @ 16 long
51 56 61 05 1 @ 15 short
10 15 20 25
30 35 40 45
50 55 60 04
09 14 19 24
29 34 39 44
49 54 59 -
Ciphertext:
18 38 58 12 32 52 06 26 46 05 25 45 04 24 44 08 28 48 02 22 42 62 16 36 56 15 35 55 14 34 54 03 23 43 63 17 37 57 11 31 51 10 30 50 09 29 49 13 33 53 07 27 47 01 21 41 61 20 40 60 19 39 59 (63)
Note that where the plaintext is a straight numerical sequence, the resulting ciphertext is the encipher key. Exactly the same ciphertext or encipher key will result from the following single columnar transposition cipher:
18 07 11 05 04 03 17 06 15 14 13 02 16 10 09 08 12 01 20 19 ------------------------------------------------------------ 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63
Ciphertext:
18 38 58 12 32 52 06 26 46 05 25 45 04 24 44 08 28 48 02 22 42 62 16 36 56 15 35 55 14 34 54 03 23 43 63 17 37 57 11 31 51 10 30 50 09 29 49 13 33 53 07 27 47 01 21 41 61 20 40 60 19 39 59 (63)
matrix = 4 X 20
63 = 3 long @ 4
17 short @ 3
Very simply, the results of using the two double transposition keys 3-2-1-5-4 and 3-2-4-1 to encipher message L = 63 can be duplicated by using the single transposition key: 18-7-11-5-4-3-17-6-15-14-13-2-16-10-9-8-12-1-20-19. This result does not surprise the pure mathematicians in the group. The equivalent key, Keqv, reflects K-1, K-2 and the message length.
K-1 (length) X K-2 (length) = Keqv (length of single transposition key)To successfully attack the Keqv problem, the length of the message, L must be longer than the key.
Plaintext:
01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63
Ciphertext:
18 38 58 12 32 52 06 26 46 05 25 45 04 24 44 08 28 48 02 22 42 62 16 36 56 15 35 55 14 34 54 03 23 43 63 17 37 57 11 31 51 10 30 50 09 29 49 13 33 53 07 27 47 01 21 41 61 20 40 60 19 39 59 (63)
K-1: 3-2-1-5-4
K-2: 3-2-4-1
Equivalent Single
Transposition Key:
Col 1 | Col 2 | Col 3 | Col 4
18-7-11-5-4-3-17-6-15-14-13-2-16-10-9-8-12-1-20-19
Two points: 1) Given two double transposition keys, there are multiplicity of single columnar transposition keys, each depending upon the length of the plaintext being enciphered, and 2) Given a particular single transposition key, there are only two specific double transposition keys which will give rise to the single transposition key; and both keys K-1 and K-2 may be recovered regardless of the message length L. Keqv can be considered a rotating matrix.
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K-1 | ||||||||||||||||||||||||||||||
| K-2 |
The rotating matrix will be in the form of a complete rectangle and the correct rectangle can be recognized by each of its rows containing a single, different term of K-1. There are several symmetrical relations with respect to this rotating matrix:
|
|
for the entire matrix, we have:
| +15 | -10 | +05 | -10 |
| -10 | +15 | -10 | +05 |
| +05 | -10 | +15 | -10 |
| -10 | +05 | -10 | +15 |
| -10 | +05 | -10 | +15 |
The differences are the same, only rotated. If we renumber the values in each row as 'indicators' we have the following row identifications:
| 4 | 1 | 3 | 2 |
| 2 | 4 | 1 | 3 |
| 3 | 2 | 4 | 1 |
| 1 | 3 | 2 | 4 |
| 1 | 3 | 2 | 4 |
The row of the matrix containing 1 will not rotate. It will always reflect the value of K-2. The remaining rows will rotate with the rotation depending on the length of the message L. Each row in effect identifies one term of the key K-1. If 2 occurs in a particular row, we know that the position of that row will indicate the position of 2 in K-1. If we can identify a particular letter of the ciphertext as part of a column, we can identify one of the terms in the rotating matrix. The value of that term (mod n), will provide one of the terms of K-1. It is related to all the terms in its row mod n.
The solution of ciphertext problems follows the same lines as discussed previously on a single transposition rectangle. Barker gives three interesting examples. [BARK2] GUNG HO has also addressed the solution of double transposition ciphers. [GUNG]
The Augustus Cipher is closely related to the Viggy, and is attributed (possibly erroneously) to Emperor Augustus. The rumor is that he used a passage from Homer as the key to encrypt his messages. The key is equal to the length of the plaintext. He used as much keytext as required to meet the message size.
To encrypt the Mth letter of the plaintext, select the Mth letter of the keytext; the position of this letter in the alphabet determines the shift for the plaintext letter. If the Mth plaintext letter is O and the Mth key text letter is C, the shift is three, because C is the 3rd letter in the alphabet, and thus O is replaced by the R, which is 3 places further along in the alphabet. The process is Mod 26. So, the plaintext letter W encrypted by the key letter F (shift = 6) would result in the ciphertext letter C.
Example:
Plain: London calling Moscow with urgent message.
Key Phrase: To be or not to be that is the question whether
Plain: L O N D O N C A L L I N G M Key Text: T O B E O R N O T T O B E T Shift: 20 15 2 5 15 18 14 15 20 20 15 2 5 20 Cipher: F D P I D F Q P F F X P L G Plain: O S C O W W I T H U R G E N T Key Text: H A T I S T H E Q U E S T I O Shift: 8 1 20 9 19 20 8 5 17 21 5 19 20 9 15 Cipher: W T W X P Q Q Y Y P W Z Y W I Plain: M E S S A G E Key Text: N W H E T H E Shift: 14 23 8 5 20 8 5 Cipher: A B A X U O J
The Vigenere Tableau can be used to assign letters similar to the standard Viggy. The main difference is the Key text can be long and no repeating. The Augustus cipher can be attacked by dictionary type attacks or by high frequency letters is groups to identify small parts of the text.
This challenge was issued by Howard Liu of U. C. Davis:
FWNGF XSMCK JSVGK WOGWZ FSJJP QIMJR ESIIM GFMIM GOGIU DSDRX VFVTG GRDRR NOWCI KBOLZ EVVWV ACPLZ FSOVR PGAMX WFVXZ QBNXY QINEE FGJJK JSHQF XSHIE VCACF WFZCV DFJAJ OOFIJ GOMXY SIVOV.
ACA 's AAHJU (Larry Mayhew) solved this Viggy right away. Try it.
RIDDLER throws this Headliner from the Wall Street Journal out for us to play with:
1.
VJZ UXYMP LJQMG EKJR WMJVIMC'S JXYM XZ WIM VKJGGCPPQ?
2.
PNRO UN SWIODLSWJO OAYDBZUWNA OHZNDUM WM CASWGOSB UN MOUUSO VWQTUM NROD ZDWRLYB.
3.
FKOFMKS FKSZ THGUMKS ULDGU SLR NKQQKFMTSZ KX YODEKXF OHFKHT JKHU.
4.
QPKSYKE=CHKRZE FYHKG BKEKSPQ HEKSPQ ZU XYZJUEKJ
KJB YPBQFZJP.
5.
EUAHBZTLB EU ZPEB NJUS IEDPZ JBH DCEUB ZT QJG
ZPH QLTTRYGU.
Solve the headlines; recover hat, setting and key.
With the help of FLORDELIS, here are a few Risties to wet the appetite:
1. Naughty Words. K2
NF CH FXUS XE TDSSRHU HT EASSQW UHDS
ADSQXHGE FWNC JWSC N UNC WXFE WXE FWGUP
JXFW N WNUUSD. *UNDEWNOO *OGUERSC.
2. Be Flexible. K1
INPG NV: QCE FNSW, UYWNM, VECM SWNQ GNTSW,
SWNHWF CMWP GC FWNG WOXYG MWCMSW, YOPXW YCSVF
GYWB QOEBSK OP MSNUW.
3. Crackerjack. K?
DXYUV HLOCT LNBFAR MOBQC, ABDUT XBQC TXBS,
QBPUT MLQC HXUA RLNC, SYQCT OBQC, EFYQCOJ
SLQCT TDBQC YA CALSTLQC.
4. How's that again? K?
PTUKAKDKNA NU "QBNALT": RA TGBRAQKJYT
RJQNOBDKNA ZNPEYT QTAQKDKFT DN PKUUTOTADKRY
ZNYTSEYRO DTAQKNAQ.
5. Gone with the wind. K?
KZDFLVYEAT DZBPVJSKX OXSKD FSKDLVYQGW.
KZDBLIYQGF LSGTQF. OZYF GXZBPVL GWSDBLV
OEATVPSYDL. DZBPVYGYQ JXZBPV QDFL.
Here are a few "change-ups" to consider:
1. The way to get to nowhere.
SRE NR OCYNA MOOTG NI TTUCYLB AB ORP SISE LCRIC NI DNU ORA GNIOGFLESM IH SDN IFOH WYDO BYNA.
2.
NKWO HWRY PIAV WNNI LKWE SABA ELOT LSEE FPRO WTNE YTEY RANS NOOE HFSI ENGI BHRO HSDA SAET ERPO ALEY R.
3. Value System.
FIUOY ACPSN NEPAD RECEF LTSUY LESSE FARET ONINO ANREP EFLTC UYLES SEAMS NNYRE UOVAH LERAE ENOHD TWILO EV.
Solve.
Here are three fun Patristocrats for solution and key recovery:
1. Sir Galahad to the Rescue.IYAIS FWZBU BJLAX WVJAX OBLYB VNSJN DJSNY ISJZP UUBVQ WVYBT IYVAA ISQAM BMQPL YFAJA IVBIS JNFWR AVBMB QWTAV JSYNY FWRAV ATXPU UAI.
2. Orderly Words.
PHKWR HWMIA FDAYH JADUJ PUGXG HRXQI UJDQL FDTXA UYDQH WMXWD WXDTI AXSUH KIDTI AXJAU HKIDW IXJUH KIDJM PDYXA UHKI.
3. Oratory.
RFKRW UCQVK SYRFA UEKHC QVYDA HKIOK WAYAR FIRRF KWKYA RUUEC DFVKJ TRFRU RFKYW AHKKD FKAIJ XJURK JUCTF XKHRF.
I don't recall discussing the Key Phrase cipher in much detail. It is a regular cryptogram with a few new twists: 1) a letter may represent itself; 2) a cipher letter may represent more than one plaintext letter; 3) The key word is a 26 letter key phrase rather than a disarranged alphabet.
Edgar Allen Poe like this particular cipher. Example:
| Plain | ABCDEFGHIJKLMNOPQRSTUVWXYZ |
| Cipher | FORTITERINRESUAVITERINMODO |
The Latin Key phrase fortiter in re, suaviter in modo - "strongly in deed, gently in manner."
In Poe's example, the word GAMES would be enciphered EFSIE.
Note that letters may be missing from the cipher key. To solve a key phrase we start with a crib, and work back and forward between the key sentence and the the cryptogram. Remember that one cipher letter may stand for several plaintext, but each plaintext letter has but one substitute.
Try these two Key Phrase ciphers and recover their phrases:
1. Evelyn Wood for drivers?
VET EETTA SERSEVSRT SA DOTTE ATSETER TD VESV TV TESWUTD TSE VS ATREAT SEV VET EUSRTAUTSA DTRED TE VTST.
2. Handsome salary.
ABE BAAV AEV VPEH EETE ABE VPEH EBEL EANT BTEPAEHA PRREAEAL EPH AA EPTL ABE HPEPTE EAN OPLLAA EENE AL LAE.
Corinne Bure sent me a fun little challenge from France (to her from her boyfriend).
Ciphertext:
11 10 02 08 21 23 30 04 06 09 01 07 12 16 21 23 30 21 24 10 02 03 05 21
Give it a try then see the answer.
The only way to attack Null ciphers is to try everything. Here are four. The last in this group is a Doosey.
1. Business advice.
We are soon to enlarge night operations. Temporary
workers all now transferred. Notify our trainees.
2. Daddy was a crypee. He rearranged his son's French lesson:
aigle conversation printemps dehors entendre tuyau parler premier ouvert pied voyager ferme vite casuel vert oreille acheter apporter chien secret quelque savant sale profond liste violon citron
3. It's also Golden.
dashing brainy also Aesop giant fact maestro haggle jail avenue aerie case menace aorta implant bashful aegis brand swat.
4. The Key To Escape.
Sir John Trevanion was imprisoned in Colchester Castle in England during the days of Cromwell. He received this message and deciphered it rather quickly. Sir John was in prison for only a short period before making his dash for freedom. How long would it have taken you?
Worthie Sir John:
-Hope, that is ye best comport of ye afflictyd, cannot much, I fear me, help you now. That I wolde saye to you, is this only: if ever I may be able to requite that I do owe you, stand not upon asking of me. 'Tis not much I can do; but what I can do, bee verie sure I wille. I knowe that, if dethe comes, if ordinary men fear it, it frights not you, accounting it for a high honour, to have such a rewarde of your loyalty. Pray yet that you may be spared this soe bitter, cup. I fear not that you will grudge any sufferings; only if it bie submission you can turn them away, 'Tis the part of a wise man. Tell me, an if you can, to do for you any things that you would have done. The general goes back on Wednesday. Restinge your servant to command.
R. T.
Recall the 5 part substitute for each letter of the Baconian Cipher:
| A | aaaaa | I/J | abaaa | R | baaaa |
| B | aaaab | K | abaab | S | baaab |
| C | aaaba | L | ababa | T | baaba |
| D | aaabb | M | ababb | U/V | baabb |
| E | aabaa | N | abbaa | W | babaa |
| F | aabab | O | abbab | X | babab |
| G | aabba | P | abbba | Y | babba |
| H | aabbb | Q | abbbb | Z | babbb |
Any two dissimilar groups can be used to make a Baconian cipher.
Try these two.
1. Carpenters Rule.IXAPR IOBEE AEIOU POOOX BAYFG MAYOE EAGOA TOAZI YAFQP LOAIO OLEOA IOACY EESAA AOIEZ OEFAA EILOG AHWOK POOIE OABEO AEIRA VOEZB DEOPA FYYSO OHEOE EKQEA OOBME ATREQ ENNAO AEOCY OAMEA.
2. Tried and true.
1 2 1 1 1 1 1 1 4 2 2 1 1 2 5 1 5 1 3 2 5 3 3 1 5 1 6 1 6 1 2 1 2 1 3 2 2 1 1
The ADFGX cipher was invented by a skilled German cryptographer during World War I. In the original ADFGX cipher, there were three stages of encipherment, which added to the difficulty. The alphabet square permitted the enciphering alphabet to be inscribed in various ways: vertically, horizontally, circular, etc. Anyway that a Tramp could be defined, the cipher alphabet could be used. A crib was usually necessary to expedite the solution.
Here are three forms of the same cipher:
|
|
|
Try these on for size:
1. Cashless. [WALLET]
EO EE PN PO EE NY PM PN SO EE PM EM DE EN PO NN DM
SM DY PN PM DN NN NY DM PO SO DM EM EM DY PO PN NO
NY SO DY PE DY EO EE SM DY DE EE PM PE DN PE DY DE
NO PO DN DM PE DE PN.
2. Four-Legged Creatures. [CALLED]
EE IE TO TS EH GS TE GE ES IH TE GR GR TO IO EE IE
TO TH TO TR TS TE TE IE EH TS ES TO EE GH IS TO TS
TR TO IH TE RH ES TO EH IR GH EE ES ES EE TS GH EO
TO ES.
3. About this cipher.
aa ff gf gg fd xa dg ff aa df xa ad gf dg gg fd gd
fg fa gd xf fd xa dg gd fg gg fd xa fa fd xa fa xd
xa dg da gf aa dg ga.
These complete columnar transpositions should be easy:
1. Political Logic?
WSCCC SRTTE TIWTR EACFK HHTHH YDROT OPAAU USGOR CEILO RYORW MONIN IOELE ELSMT NHTOC OOIOE ITDNH
2. They spit in your face too.
LEARM ENOAC AWMSG STYUH OESHL RVIUA UUMAR IAYEO SNSGE METSY ETXHL FDSAO AYAYA IATET LHAHR IETAO RLMNV HUDNU HSSYR PETCN IGTEA EEMRE TAMNL HRHLU.
I have always enjoyed the Nihilist ciphers. Basically it is a square columnar which is written in by rows, and removed by columns. We rearrange the rows and columns by the same numerical (keyworded) sequence. For example:
1. Imported.
ISRSE EULCL SGRVT TESIU AOAEN HITHR YHEHN FINOE DHANE TAUCS NYTPS NPRET MEHSI OEUER AINIF CTCYI R.
2. Open 10 to 5.
IOINS YSKIL FSTAT DEIEO UATIF OAEOE OTSRT AFSMS RTHSI NLCFH GNOTL WOEER NEMOU ORMHU FTDIA ASCDN IIETC NPOTO CBFPK SIDCY.
Law on the net is way behind the technology. There is a particular danger and risk in the area of Defamation and Privacy. Assume that every thing you write on the net can be read and disseminated to millions of readers, without delay. This is particularly true if the material is "juicy." This week the Supreme Court must take up the questions of indecency and pornography on the net. Do they hold that their jurisdiction is world wide? Do they permit anyone to say anything - no matter how bad - no matter how true - in favor of the First Amendment Freedom of Speech provisions?
The cards are stacked the wrong way. A person defames another when he or she makes a false statement about that person that injures his or her reputation. This includes both libel and slander.
It is possible for a person to go to a national provider, like AOL, Free, upload 1,000,000 bytes of pure trash about you or your family, their medical, sexual, financial behavior - all being fiction! - to a common bulletin board, and then drop the service, leaving behind material that is perused by 1000's of people a day using "search engines". In the real world, reputation can be injured in public discussion, loss of job opportunity, or professional contact. This is especially true if one's circle of business and friends is well connected to the cyber world. Defamation suits involve big money - about $100,000 up front and $150/hour against time spent.
Why? A statement only defames if it is untrue. If a reasonable jury would say "so what if he called you.. how were you hurt?," then your case is not strong. Even when your case is strong, system operators have strong protection from liability. A major defense is the public figure exception. Online services qualify for this exception as both publishers and distributors of information. The private figure is given more protection. For practical purposes, a plaintiff can look forward to many depositions to harass before he will get his case before the jury. Amicus curiae briefs from all sorts of groups will surface to stop any restriction on the ability to defame your neighbor.
Even accusations detailing instances of dishonesty, disloyalty, distasteful sexual practices, and other reputation - staining events that never happened give rise to defamation claims. Even if an online service prints a retraction, how do you know that EVERY person who saw the lies will get the retraction? in Europe? In Africa? etc. The real problem created by defamations is the set of unpleasant associations created by the false accusations. Even when retracted, the negative image is carried in the mind for years. "Mere opinion" is protected speech as well as satirical and political commentary. Look at the attacks on the President.
A violation of Privacy may arise from publishing messages on an online service about a person's private affairs that a "reasonable person" would find highly offensive, and that are not part of the publics legitimate concern. As a practical matter the disclosure must be major and cause great pain and embarrassment to lead to legal justification for substantial money damages.
Privacy claims don't apply to events that occur in public, are a matter of public record, or can be claimed as newsworthy.
There is a variation on the standard right of privacy called "false light" privacy. A false light claim arises when someone reports something about someone else in a misleading context that injures that person. The false light claim needs to be offensive to the average reader or viewer.
Another privacy-related right is that of publicity. It prevents people from exploiting your name or image for profit without consent through licensing arrangements with the owner of the right.
The Daniel v Dow Jones, (520NYS2d 334) case relieved the online provider from giving out erroneous information that may injure another. The court stated, " The First Amendment precludes the imposition of liability for nondefamatory, negligently untruthful news." The only exception to this is when a "special relationship" existed with the systems operator.
Lance Rose has written an authoritative book on your online rights called: "Netlaw," The Guidebook to the Changing Legal Frontier, Osborne Mcgraw-Hill, NY, 1995. [ROSL]
I feel that cryptography is our way of limiting the damage - At least our E-mail can be safe from prying eyes. We may not be able to stop the loose cannons, but most of us have integrity and can protect our privacy with the appropriate use of cryptographic tools.
Key = COVER.
Discovery: The actual side of your face never revealed being trapped in a Labyrinth. I chase you. Hide transfigurations - thousands of them. Movement of your eyebrows make earthquake.
| Key | MEGAZORD |
| Setting | MORPH |
| Hat | RANGERS |
| 5 | 1 | 4 | 3 | 2 | 6 | 7 |
| R | A | N | G | E | R | S |
| M | E | G | A | Z | O | R |
| D | B | C | F | H | I | J |
| K | L | N | P | Q | S | T |
| U | V | W | X | Y | Z | � |
| E | B | L | Y | Z | H | Q | Y | A | F | P | X | G | C | N | W | M | D | K | U | O | I | S | R | J | T | |
| M | M | D | K | U | O | I | S | R | J | T | E | B | L | Y | Z | H | Q | Y | A | F | P | X | G | C | N | W |
| O | O | I | S | R | J | T | E | B | L | Y | Z | H | Q | Y | A | F | P | X | G | C | N | W | M | D | K | U |
| R | R | J | T | E | B | L | Y | Z | H | Q | Y | A | F | P | X | G | C | N | W | M | D | K | U | O | I | S |
| P | P | X | G | C | N | W | M | D | K | U | O | I | S | R | J | T | E | B | L | Y | Z | H | Q | Y | A | F |
| H | H | Q | Y | A | F | P | X | G | C | N | W | M | D | K | U | O | I | S | R | J | T | E | B | L | Y | Z |
Use the French Phrase " L'essentiel est invisible pour les yeux."
Invert the order and number sequentially.
| L | E | S | S | E | N | T | I | E | L | E | S | T | I | N | V | I | S | I | B | L | E | P | O | U | R | L | E | S | Y | E | U | X |
| 33 | 32 | 31 | 30 | 29 | 28 | 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 | 19 | 18 | 17 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 09 | 08 | 07 | 06 | 05 | 04 | 03 | 02 | 01 |
The Plaintext converts to:
"POUR TES YEUX L'EST EST L'OUEST" = For your eyes the East is the West.
Our course is complete. Together, we have made a special contribution to the science of cryptography. We have brought a new group of interested souls to the ACA. We have revitalized the very outlook of the ACA. As we move into the Millennium, we have accomplished our professional goals and improved our skills.
It has meant a lot to me to be your class facilitator. Please remember me when you write my VALE. Explain to Y-ME that the two years that we have been in cipher- space together was worth her patience.
Lastly, Classical Cryptography Course Volumes I and II represent our best efforts to leave a lasting reference in the study of the science of cryptography. Please buy them, put them in your cryptographic library and help us preserve a great legacy. Send me your comments, solutions and questions, as you complete the various lectures. So that I can order the correct amount, I need to know how many of you want me to send you a class participation certificate. It is not necessary to have completed all the problems to be eligible. If you enjoyed the effort and learned something along the way, then I am happy to include your NOM.
If you have enjoyed my course in classical cryptography, then Tell the EB, or write MICROPOD, FIZZY, QUIPOGAM, SCRYER or PHOENIX. They will appreciate your comments. I also would like to have your comments and evaluations so that I can improve the material should I attempt a rerun of this course at a later date.
My best to you and your families. Again, I am deeply honored to have been your teacher / facilitator for this course.LANAKI 20 March 1997
© 2004 Qsr Nrwn