By
Randy Nichols (LANAKI)
President of the American
Cryptogram Association from 1994-1996.
Executive Vice
President from 1992-1994
CLASSICAL CRYPTOGRAPHY COURSE
BY LANAKI
November 13, 1995
LECTURE 3
SUBSTITUTION WITH VARIANTS
Part II
MULTILITERAL SUBSTITUTION
SUMMARY
In Lecture 3, we continue our look into substitution
ciphers, and move into the multiliteral substitution case, we
field more tools for cryptanalysis, look at some fascinating
historical variations, we review "the unbreakable
cipher" and solve homework problems.
MULTILITERAL SUBSTITUTION WITH
SINGLE-EQUIVALENT CIPHER ALPHABETS
Monoalphabetic substitution methods are classified as
uniliteral and multiliteral systems. Uniliteral systems
maintain a strict one-to-one correspondence between the length
of the units of the plain and those of the cipher text. Each
letter of plain text is replaced by a single character in the
cipher text. In multiliteral monoalphabetic substitution
systems, this correspondence is no longer one plain to one
cipher but may be one plain to two cipher, where each letter of
the plain text is replaced by two characters in the cipher
text; or one plain to three cipher, where a three-character
combination in the cipher text represents a single letter of
the plain text. We refer to these systems as uniliteral,
biliteral, and triliteral, respectively. Ciphers in which one
plain text letter is represented by cipher characters of two or
more elements are classed as multiliteral. [FR1], [FR2], [FR5]
BILITERAL CIPHERS
Friedman gives some interesting examples of biliteral
monoalphabetic substitution. [FR1] Many cipher systems start
with a geometric shape. Using the square in Figure 3-1:
W H I T E
**********************
W * A B C D E
*
H * F G H IJ K
*
I * L M N O P
*
T * Q R S T U
*
E * V W X Y Z
Figure 3-1
| Plain |
a
|
b
|
c
|
d
|
e
|
f
|
g
|
h
|
i
|
j
|
k
|
l
|
m
|
n
|
o
|
p
|
q
|
r
|
s
|
t
|
u
|
v
|
w
|
x
|
y
|
z
|
| Cipher
|
WW
|
WH
|
WI
|
WT
|
WE
|
HW
|
HH
|
HI
|
HT
|
HE
|
HE
|
IW
|
IH
|
II
|
IT
|
IE
|
TW
|
TH
|
TI
|
TT
|
TE
|
EW
|
EH
|
EI
|
ET
|
EE
|
The alphabet derived from the cipher square or matrix is
referenced by row and column coordinates, respectively.
The key to this system is that when a message is
enciphered by this biliteral alphabet, the cryptogram is still
monoalphabetic in character. A frequency distribution based upon
pairs of letters will have all the characteristics of a simple
uniliteral distribution for a monoalphabetic substitution
cipher.
Numbers can be used as effectively as letters in the
biliteral cipher. The simplest form is A=01, B=02, C=03,...Z=26.
So, the plain text letters have as their equivalents two-digit
numbers indicating their position in the normal alphabet.
Other dinome (two digit) cipher matrices are previewed:
1 2 3 4 5 6 7 8 9 0
................................. Figure 3-2
1 . A B C D E F G H I J
2 . K L M N O P Q R S T
3 . U V W X Y Z . , : ;
Note that frequently-used punctuation marks can be enciphered in the
above matrix.
Another four examples are:
Figure 3-3 Figure 3-4
5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
.................... ............................
1 . A B C D E F 1 . A B C D E F G H I
2 . G H IJ K L M 2 . J K L M N O P Q R
3 . N O P Q R S 3 . S T U V W X Y Z *
4 . T UV W X Y Z
Figure 3-5 Figure 3-6
M U N I C H A B C D E F G H I
.................... .............................
B .A 7 E 5 R M A . A D G J M P S V Y
E .G 1 N Y B 2 B . B E H K N Q T W Z
R .C 3 D 4 F 6 C . C F I L O R U X 1
L .H 8 I 9 J 0 D . 2 3 4 5 6 7 8 9 0
I .K L O P Q S
N .T U V W X Z
It is possible to generate false or pseudo-code or artificial code
language by using an enciphering matrix with vowels as row
indicators and consonants as column indicators.
Figure 3-7
B C D F G
..............
A . A B C D E
E . F G H IJ K
I . L M N O P
O . Q R S T U
U . V W X Y Z
Enciphering the word RAIDS would be OCABE FAFOD. [FR5]
Another subterfuge used to camouflage the biliteral cipher
matrix is to append a third character to the row or column
indicator. This third character may be produced through the use
of cipher matrix shown in Figure 3-8 (wherein A=611, B=612,
etc.) or the third character can be the "sum checking"
digit which is the non-carrying sum (modulo 10) of the preceding
two digits such as trinomes 257, 831, and 662. It may also
involve self summing groups such as 254, 830, 669 all which sum
to the constant 1, or finally the third digit can be random,
inserted solely for the pleasure of the cryptanalyst.
Figure 3-8
1 2 3 4 5
..................
61 . A B C D E
72 . F G H IJ K
83 . L M N O P
94 . Q R S T U
05 . V W X Y Z
A=611 , B=612 X=053
All the above matrices are bipartite. They can be divided into two
separate parts that can be clearly and cleanly defined by row and
column indicators. This is the primary weakness of this type of
cipher. [FR1]
Sinkov presents a good description of the modulo
arithmetic required to solve biliteral cipher challenges. [SINK]
A more involved look at the statistics involved can be found in
[CULL].
BILITERAL BUT NOT BIPARTITE
Consider the following cipher matrix:
Figure 3-9
1 2 3 4 5
..................
09 . H Y D R A
15 . U L IJ C B
21 . E F G K M
27 . N O P Q S
33 . T V W X Z
We can produce a biliteral cipher alphabet in which the equivalent for
any letter in the matrix is the sum of the two coordinates which
indicate its cell in the matrix:
Plain A B C D E F G H I J K L M
Cipher 14 20 19 12 22 23 24 10 18 18 25 17 26
Plain N O P Q R S T U V W X Y Z
Cipher 28 29 30 31 13 32 34 16 35 36 37 11 38
A = 9+5 =14, E = 21 + 1 =22
The cipher units are biliteral but they are not bipartite. Cipher text
equivalent of plain text letter "A" is 14 and digits 1
and 4 have no meaning per se. Plain text letters whose cipher
equivalents begin with 1 may be found in two different rows of
the matrix and those of whose equivalents end in 4 appear in
three different columns. [FR1]
Another possibility lends itself to certain multiliteral
ciphers in the use of a word spacer or word separator. The word
space might be represented by a value in the matrix; i.e., the
separator is enciphered as a value (dinome 39 in Figure 3-4).
The word space might be an unenciphered element.
Lets break from the theory and look at four interesting
multiliteral historical ciphers before discussing the general
cryptanalytic attack on the multiliteral cipher.
TRITHEMIAN
The abbot Trithemius, born Johann von Heydenberg
(1462-1516) invented one of the first multiliteral ciphers. It
was fashioned similar to the Baconian Cipher and was a means for
disguising secret text. His work "Steganographia"
published in 1499 describes several systems of 'covered
writing.' [TRIT] [WATS], [FR1] The science of steganography is
named after him. Several Internet discussion groups currently
discuss the use of steganography to hide messages in graphics
files. (.GIF files)
His alphabet, modified to include 26 letters of
present-day English, is shown in Figure 3-10, below; it consists
of all the permutations of three things taken three at a time or
3 ** 3 = 27 in all.
Figure 3-10
A - 111 G - 131 M - 221 S - 311 Y - 331
B - 112 H - 132 N - 222 T - 312 Z - 332
C - 113 I - 133 O - 223 U - 313 * - 333
D - 121 J - 211 P - 231 V - 321
E - 122 K - 212 Q - 232 W - 322
F - 123 L - 213 R - 233 X - 323
The cipher text does not have to be restricted to digits; any groupings
of three things taken three at a time will do.
BACON
Sir Francis Bacon (1561-1626) invented a cipher in which
the cipher equivalents are five-letter groups and the resulting
cipher is monoalphabetic in character. Bacon uses a 24 letter
cipher with I and J, U and W used interchangeably.
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
Bacon described the steganographic effect of message enfolding in an
innocent external message. Suppose we let capitals be the
"a" element and lower-case letters represent the
"b" elements. The message "All is well with me
today" can be made to convey the message "Help."
Thus:
A L l i s W E l L W I t H m E T o d a Y
a a b b b a a b a a a b a b a a b b b a
H E l P
Bacon describes many several variations on the theme. [FR1], [DEAU] Note
the regularity of construction of Bacon's biliteral alphabet, a
feature which permits its reconstruction from memory.
HAYES CIPHERS
Probably the most corrupt political election occurred on
November 7, 1876 with the election of President Rutherford B.
Hayes (Republican). He defeated Samuel Jones Tilden (Democrat).
Tilden had won the popular vote by 700,000 votes but because of
frauds surrounding the electoral college, he was deprived of the
high office of President. Actually, both candidates were
involved with bribery, election tampering, voter fraud,
conspiracy and a host of other goodies. Tilden ran on a law and
order ticket that credited him with convicting Boss Tweed and
the Tweed Ring in New York City, which controlled the city
through Tammany Hall. For two years into Hayes Presidency, the
scandals persisted.
With the help of New York Tribune, Republicans finished
the Tilden 'honesty' horse. They published the Tilden Ciphers
and keys. There were about 400 of them representing substitution
and transposition forms. We will revisit the transposition forms
at a later juncture. They represented secret and illegal
operations by Tilden's men in Florida, Louisiana, South Carolina
and Oregon. The decipherments were done by investigators of the
Tribune. Here are two examples and their solution. [TILD] ,
[FR1] , [TRIB]
GEO. F. RANEY, Tallahassee.
P P Y Y E M N S N Y Y Y P I M A S H N S Y Y S S I T E P A A E
N S H N S P E N N S S H N S M M P I Y Y S N P P Y E A A P I E
I S S Y E S H A I N S S S P E E I Y Y S H N Y N S S S Y E P I
A A N Y I T N S S H Y Y S P Y Y P I N S Y Y S S I T E M E I P
I M M E I S S E I Y Y E I S S I T E I E P Y Y P E E I A A S S
I M A A Y E S P N S Y Y I A N S S S E I S S M M P P N S P I N
S S N P I N S I M I M Y Y I T E M Y Y S S P E Y Y M M N S Y Y S
S I T S P Y Y P E E P P P M A A A Y Y P I I T
L' Engle goes up tomorrow. Daniel
Examination of the message discloses a bipartite alphabet cipher with
only ten different letters used. Dividing the messages by twos,
assigning arbitrary letters for pairs of letters and performing a
triliteral frequency distribution will yield a solution.
PP YY EM NS NY YY PI MA SH NS YY SS etc
A B C D E B F G H D B I etc
Message reads:
Have Marble and Coyle telegraph for influential
men from Delaware and Virginia. Indications of weakening here.
Press advantage and watch board.
Here is another Tilden cipher using numerical substitutes:
S. PASCO AND E. M. L'ENGLE
84 55 84 25 93 34 82 31 31 75 93 82 77 33 55 42
93 20 93 66 77 66 33 84 66 31 31 93 20 82 33 66
52 48 44 55 42 82 48 89 42 93 31 82 66 75 31 93
DANIEL
There were several messages of this type. They disclosed that only 26
different numbers were used. Message reads:
Cocke will be ignored, Eagan called in. Authority
reliable.
The Tribune experts gave the following alphabets:
AA = O EN = Y IT = D NS = E PP = H SS = N
AI = U EP = C MA = B NY = M SH = L YE = F
EI = I IA = K MM = G PE = T SN = P YI = X
EM = V IM = S NN = J PI = R SP = W YY = A
-------------------------------------------------------
20 = D 33 = N 44 = H 62 = X 77 = G 89 = Y
25 = K 34 = W 48 = T 66 = A 82 = I 93 = E
27 = S 39 = P 52 = U 68 = F 84 = C 96 = M
31 = L 42 = R 55 = O 75 = B 87 = V 99 = J
William F. Friedman correlated these alphabets with the results being
amusing:
H I S P A Y M E N T
1 2 3 4 5 6 7 8 9 0
-------------------------------
H 1 . .
I 2 . K S D .
S 3 . L N W P .
P 4 . R H T .
A 5 . U O .
Y 6 . X A F .
M 7 . B G .
E 8 . I C V Y .
N 9 . E M J .
T 0 . .
------------------------------
The blank squares may have contained proper names and money
designations. Key = HISPAYMENT for bribery seems to be
appropriate. [HIS1], [TRIB], [TILD], [FR1]
BLUE AND GREY
One of the most fascinating stories of the American Civil
War (1861-65) is about communications using flag telegraphy or
also known as the wigwag signal system.
Wigwag is a system of positioning a flag (or flags) at
various angles that indicate the corresponding twenty-six
letters of the alphabet. It was created in the mid-1800s by
three men working at separate locations: Navy Captain Phillip
Colomb and, Army Captain Francis Bolton, in England, and
Surgeon-inventor Albert J. Meyer in America. [WRIX] Meyer
observed the railroad electromagnetic telegraph, developed by
Alexander Bain, and invented a touch method of communication for
the deaf and later the wigwag system. He developed companion
methods with torches and disks. The name "wigwag"
derived from the flag movements.
Three main color combinations were used in flags measuring
two, four and six feet square. The white banners had red square
centers while the black or red flags had white centers. Myers
method required three motions (elements) to be used for each
letter. The first position always initiated a message sequence.
Motion one went from head to toe and back on right side. Motion
2 went from head to toe and back on left side. Motion three went
from head to toe and back in front of the man. Each motion made
quickly. Chart 3-1 indicates the multiliteral alphabet and
directional orders required to convey a message.
Chart 3-1
A - 112 H - 312 O - 223 V - 222
B - 121 I - 213 P - 313 W - 311
C - 211 J - 232 Q - 131 X - 321
D - 212 K - 323 R - 331 Y - 111
E - 221 L - 231 S - 332 Z - 113
F - 122 M - 132 T - 133
G - 123 N - 322 U - 233
Myers Signal Directions
3 - End of a word
33 - End of a sentence
333 - End of message
22.22.22.3 - Signal of assent. Message understood
22.22.22.333 - Cease signaling
121.121.121.3 - Repeat
212121.3 - Error
211.211.211.3 - Move a little to the right
221.221.221.3 - Move a little to the left
As the Civil War wore on, Myer increased the wigwag motions to
four. This enabled more specialized words and abbreviations to be
used. In 1864, Myer invented a similar daytime system with disks.
For night signals, Myer applied his system with torches on
the signal poles and lanterns. A foot torch was used as a
reference point. Thus the direction of the flying wave could
better be seen. Compare this to the semaphore system used by
ships at sea when radio silence is a must.
Myer continuously improved his invention through 1859 and
presented his findings gratis to the Union Army (which gave him
a luke warm yawn for his trouble). Alexander Porter, his chief
assistant joined the Confederate Army and used the wigwag system
in actual combat. Porter was able to warn Colonel Nathan Evans
at Manassas Junction - Stone Bridge that the Union Army had
reached Sudley Ford and was about to surprise General
Beauregard's best Division. Porter sent from his observation
tower, the following message to Colonel Evans at the Stone
Bridge defenses: "Look out for your left, you are
turned."
Colonel Evans turned his cannons and musket fire toward
the Federal troops before they could initiate their attack.
Porter was credited later (and decorated), for his vigilance led
to changes in the tactics of the entire struggle around Manassas
Junction. The application of the new signal system had directly
influenced the shocking Union defeat that eventful July day.
Myers signaling system was catapulted into use at the
Battle of Gettysburg. General Lee had invaded northern soil in
June 1863. His Potomac crossing was relayed by flag system to
the War Department. General Joseph Hooker resigned under fire on
June 28. General George Meade (of NSA grounds fame) took over
command of the Army of the Potomac. His headquarters were at
Taneytown, MD. Startling news came via signalmen on July 1. A
skirmish on the Maryland border indicated that General Buford
was facing a major force not in Maryland but in Pennsylvania.
Lee was himself in command at Gettysburg. Signalmen of each army
unit sent out calls for help. Reinforcements from dozens of
units several miles away were committed to the fray. By July 1,
73,000 gray and 88,000 blue met in one of history's most
decisive battles. Rarely, if at all, do textbooks even hint that
the secret message system of flags affected these history
changing events. Yet the crucial sightings by Union observers
directly tipped the scales against Lee's best tactics. The most
famous incident was when Captain Castle on Cemetery Ridge,
refused to submit to Confederate artillery barrage as General
George Pickett charged the "thin blue line", used a
wooden pole and a bedsheet to make a makeshift flag to alert
Union forces under General Meade who ordered counter- measures.
Pickett's charge was stopped short of breaching the Union lines.
General Lee's gamble failed. Previously disregarded flagmen
enabled George Meade to enter the shrine of heros. [BLUE],
[ANNA], [MYER], [NIBL], [TRAD], [WRIX], [KAHN]
FURTHER NOTES ON CRYPTANALYSIS OF
MULTILITERAL CIPHERS
LIMITED CHARACTERS
Multiliteral ciphers are often recognized by the fact that
the cryptographic text is usually composed of but a very limited
number of different characters. They are handled in the same way
as are uniliteral monoalphabetic substitution ciphers. So long
as the same character or number is used to represent the same
plain text letter, and so long as a given letter of plain text
is always represented by the same character or combination of
characters, then the substitution is strictly monoalphabetic and
can be handled by methods in my Lectures 1 and 2.
BILITERAL CIPHERS
In the case of biliteral ciphers where the row and column
indicators are not identical, the direction of reading the
cipher pairs is chosen at will for each succeeding cipher pair,
and analysis of contacts of the letters comprising the cipher
pairs will disclose that there are two distinct families of
letters, and the cipher pair will never consist of two letters
of the same family. We reduce by further substitution to
uniliteral terms and solve by known methods.
WORD SEPARATORS
If a multiliteral cipher includes a provision for the
encipherment of a word separator, the cipher equivalent of this
word separator may be readily identified because it will have
the highest frequency of any cipher unit.
Friedman presents data on word separators:
For English, the average word length is 5.2 letters. The word
separator will be close to 16% frequency. [FR1] The letters of
the alphabet take on new percentage frequencies as follows:
A - 6.2 J - 0.16 S - 5.1
B - 0.84 K - 0.25 T - 7.7
C - 2.6 L - 3.0 U - 2.2
D - 3.5 M - 2.1 V - 1.3
E - 11.0 N - 6.6 W - 1.3
F - 2.3 O - 6.3 X - 0.41
G - 1.3 P - 2.3 Y - 1.6
H - 2.9 Q - 0.25 Z - 0.08
I - 6.2 R - 6.4
On the other hand, if the word separator is a single character, this
character may be identified by its positional appearance spaced
'wordlength-wise' in the cipher text and by the fact that it
never contacts itself.
ANAGRAMING
One of the first steps to solving a multiliteral cipher with a
cipher matrix, is to anagram the letters comprising the row and
column indicators in an attempt to disclose the key words used.
When the anagraming process does disclose any key word(s), a
skeleton reconstruction matrix which is the duplicate of the
original enciphering matrix is made to show the order of the row
and column indicators. Partial recovery of plain text may be
possible at this point in the analysis. Looking at the frequency
analysis (and location of the crests and troughs) may tell us
something about the enciphering alphabet as normal or keyed.
NUMERICAL CIPHERS
Cipher alphabets whose cipher components consist of
numbers are practicable for telegraph or radio transmission.
They may take forms corresponding to those employing letters.
Standard numerical cipher alphabets are those in which the
cipher component is a normal sequence of numbers.
Plain - A B C D E F G H I J K L M
Cipher - 11 12 13 14 15 16 17 18 19 20 21 22 23
Plain - N O P Q R S T U V W X Y Z
Cipher - 24 25 26 27 28 29 30 31 32 33 34 35 36
We could easily have started the cipher alphabet with A= 01, B=02,...,
Z=26 with the same results.
Mixed numerical cipher alphabets are those that have been
keyed by a key word turned into numerical cipher equivalents or
have a random combination of two or more digits for each letter
of plain text.
Plain - A B C D E F G H I - J K L M
Cipher - 76 88 01 67 04 80 66 99 96 96 02 69 90
Plain - N O P Q R S T U V W X Y Z
Cipher - 77 05 87 60 39 79 03 78 68 98 86 70 97
The computer whizzes are now thinking that the example has all numbers
less than 100. Therefore, a brute force attack on all
combinations of two letter-equivalents of the above ciphertext
numerical values taken two at a time in combination with the
digram frequency data could be a good approach to the cipher
matrix construction problem. The ASOLVER
computer program at the CDB does this kind analysis and adds
threshold limitations on the search.
Figure 3-3 and 3-4 could be arranged for simple numerical
equivalents like this:
Figure 3-3a Figure 3-4a
1 2 3 4 5 1 2 3 4 5 6 7 8 9
................ ............................
1 . A B C D E 1 . A B C D E F G H I
2 . F G H IJ K 2 . J K L M N O P Q R
3 . L M N O P 3 . S T U V W X Y Z *
4 . Q R S T U
5 . V W X Y Z
where: A = 11, R=42 Z=55
Numerical cipher values lend themselves to treatment by various
mathematical processes to further complicate the cipher system in
which they are used. These processes, mainly addition or
subtraction, may be applied to each cipher equivalent
individually, or to the complete numerical cipher message by
considering it as one number. [OP20]
Reference [NIC4] on Russian Cryptography describes the VIC
Cipher and the one-time pad. Both involve mathematical treatment
to numerical based ciphers. The Hill
Cipher is another good example of the use of mathematical
transformation processes on ciphers and is presented in David
Kahn's book. [KAHN]
In modern cryptographic systems, the DES family of ciphers
use simple S-Boxes [substitution boxes] that are reorganized by
ordered non-linear mathematical rules applied several times over
(know as rounds). [NIC4], [OP20], [RHEE], [HILL], [IBM1]
ONE-TIME PAD
The question of 'unbreakable' mathematical ciphers might
be poised at this juncture. Lets look at the famous one-time pad
and see what it offers. [NIC4]
The one-time pad is truly an unbreakable cipher system.
There are many descriptions of this cipher. One of the better
descriptions is by Bruce Schneier. [SCHN] It consists of a
nonrepetitive truly random key of letters or characters that is
used just once. The key is written on special sheets of paper
and glued together in a pad. The sender uses each key letter on
the pad to encrypt exactly one plain text letter or character.
The receiver has an identical pad and uses the key on the pad,
in turn, to decrypt each letter of the ciphertext. [SHAN]
Each key is used exactly once and for only one message.
The sender encrypts the message and destroys the pad's page. The
receiver does the same thing after decrypting the message. New
message - new page and new key letters/numbers - each time.
The one-time pad is unbreakable both in theory and in
practice. Interception of ciphertext does not help the
cryptographer break this cipher. No matter how much ciphertext
the analyst has available, or how much time he had to work on
it, he could never solve it. [KAHN]
The reason is that no pattern can be constructed for the
key. The perfect randomness of the one time system nullifies any
efforts to reconstruct the key or plain text via horizontal or
lengthwise analysis, via cohesion, via re-assembly (such as
Kasiski or Kerckhoff's columns) via repeats or via internal
framework erection. [KAHN] [KAH1], [WRIX], [NIC4], [SCHN]
Brute force (trial and error) might bring out the true
plaintext but it would also yield every other text of the same
length, and there is no way to tell which is the right one. The
worst of it is that the possible solutions increase as the
message lengthens.
Supposing the key were stolen, would this help to predict
future keys? No, because a random key has no underling system to
exploit. If it did, it would not be random. [KAHN]
A random key sequence XOR 'ed with a nonrandom plain text
message produces a completely random ciphertext message and no
amount of computing will change that. [SCHN] The one-time pad
can be extended to encryption of binary data. Instead of
letters, we use bits. [SCHN]
FRESH KEY DRAWBACK
The one-time pad has a drawback - the quantities of fresh
key required. For military messages in the field (a fluid
situation) a practical limit is reached. It is impossible to
produce and distribute sufficient fresh key to the units. During
WWII, the US Army's European theater HQ's transmitted, even
before the Normandy invasion, 2 million five (5) letter code
groups a day! It would have therefore, consumed 10 million
letters of key every 24 hours -the equivalent of a shelf of 20
average books. [KAH1] , [FRAA]
RANDOMNESS
The real issue for the one-time pad, is that the keys must
be truly random. Attacks against the one-time pad must be
against the method used to generate the key itself. [SCHN]
Pseudo- random number generators don't count; often they have
nonrandom properties. Reference [SCHN], Chapter 15, discusses in
detail random sequence generators and stream cipher. I take
exception to his remarks regarding keyboard latency measurement.
People's typing patterns are anything but random (especially us
two finger types). [SCHN] [MART]
ONE-TIME PAD SIMPLE EXAMPLE W/O
SUPERENCIPHERMENT OR XOR
Begin with a cipher (A=1, B=2 ...)
PT: T A X A T I O N I S T H E F T
CE: 20 1 24 1 20 9 15 14 9 19 20 8 5 6 20
From a table of truly random numbers:
10480 15011 01536 02011 81647 91646 69719 22368
45673 25595 85393 30995 89198 27982 24130 48360
22527 97265 76393 64809 15179 42167 ....
Add the cipher equivalent to the random key:
T A X A T I
20 1 24 1 20 9
10480 15011 01536 02011 81647 91646
----- ----- ----- ----- ----- ----- ...
10500 15012 01560 02012 81667 91655
Transmit new cipher text:
10500 15012 01560 02012 81667 91655 69734 .....
Receiver subtract key out of message and decodes equivalents.
Many variations exist. Note in the cipher text T1 .ne. T2
.ne. T(i) and A1 .ne. A2 .ne. A(i), etc. [MARO]
ONE-TIME PAD HISTORICAL
CONSIDERATIONS
The one-time pad originated from the work of Gilbert
Vernam in 1917. Vernam worked for ATT. He got his idea from the
French telegrapher Emile Baudot. Baudot code replaced letters
with electrical impulses, called units. Every character was
given 5 units that either signified a pulse of electrical
current ("marks") or its absence ("spaces")
during a given time period. [ 32 combinations in all]. In 1917,
paper tape was used and the marks and spaces were read by
metallic fingers. Vernam essentially automated the process and
devised a cipher on it.
In modern computer terms, key bits were added modulo 2 to
plaintext bits on a bit by bit basis. If X = x1, x2, x3..
denotes the plain text, and K = k1, k2, k3 .. the keystream,
Vernam's cipher produces a cipher text bit stream Y = Ek(X) =
y1, y2, y3. [VERN]
CONCURRENT DEVELOPMENTS
Other countries conducted similar research. Between
1918-1920, other one-time pad methods were developed. The German
Foreign Office employed the one-time pad in 1920. The Russians
first stole and then improved the German system. It was fully
deployed in 1925 for diplomatic use! OSS and SOE operatives in
WWII had special grid one-time pad's. By 1944, OSS technicians
had developed pages made of film that were read with a hand
magnifying glass. By 1960, Russian pads were the size of a
postage stamp or scrolls the size of a large eraser. The
Russians were first to conceal the one-time pad in microfilm.
One-time pads were made of cellulose nitrate for rapid
destruction. [RHEE] ,[VERN], [TERR], [KAHN]
RUSSIAN IMPLEMENTATION OF THE
ONE-TIME PAD
So why classify the one-time pad with Russian Ciphers?
Because they have been serious about using it since 1925! Before
1917, Russian diplomatic and military systems could be expressed
by the old axiom:
-
Cryptography + Loose Discipline =
Chaos
After her loss of trade information to the British in
1920, and defeats of her Army in WWI because of poor cipher
handling, she woke up. By 1916, Russia's intercept service at
Nicolaieff was in full service against the Germans. From 1920
through today, Russia has targeted stealing other countries
codes with "great vigor" as Kennedy once said. Code
stealing was done through the COMINT efforts of the former KGB
and GRU. The Spets-Odel (Special Department) was a primary
agency involved with Ciphers and Cryptanalysis. Section 6 grew
400% over a 10 year period prior to WWII.
The Soviet Union has employed the one-time pad to
protect ALL her diplomatic missions from 1930 on. Consequently
her crucial Foreign Office messages were not read by foes,
neutrals, nor allies. The GRU and the Soviet Spy rings -
"LUCY", "RED ORCHESTRA, and "Sorge's
Net" all used the one- time pad. They also used a
straddling checkerboard variant (not unbreakable).
The one-time pad is used in the old fashioned form in
the Soviet Mission - diplomatic , secret police, military,
commercial, political (Communist Party) - all have their own
keys. All cables coming into a legation look alike: simple
groups of five digits. Letters that are photographed,
codenames are applied and then enciphered in one-time pad
system. [COVT], [BLK], [BARR]
Agents in the field use the one-time pad. Radio links to
Moscow, are encrypted via one-time pads. The main Soviet spy
cipher today still employs the one-time pads.
The most dramatic spy stories (Klaus Fuchs, Iger
Gouzenko, Vladimir Petrov, Colonel Zabotin, Rudolf Abel,
Gregory Liolios, Eleftherious Voutsas, the Krogers, Guiseppe
Martelli, Ali Abbasi, Reino Hayhanen, Aldridge Ames ...) all
have used the one-time pads.
Such is cryptology in the Soviet Union - complex,
enigmatic, focused, state-of-the-art, applying the one-time
pad principles to other ciphers. Do you remember when the
diplomatic ciphers in use at the American embassy in Moscow
were solved? Russia has a profound understanding of
cryptography and cryptanalysis. [VOGE], [SUVO], [KAHN]
The U.S. history was different. Some would argue that
the U.S. became serious and superplayers in 1953. Some would
argue 1943. But not many will argue 1925 (we still had SIGTOT
then). [SISI]
LECTURE
4
In Lecture 4, we will complete
our look into English substitution ciphers, by describing
multiliteral substitution with difficult variants. The
Homophonic and GrandPre Ciphers will be covered. A synoptic
diagram of the substitution ciphers presented in Lectures 1-4
will be presented.
LECTURE
5 - 6
We will cover recognition and solution of XENOCRYPTS
(language substitution ciphers) in detail.
SOLUTION TO HOMEWORK PROBLEMS
FROM LECTURE 2
BOZOL gets the kudo for best solution on the homework.
Both problems were unkeyed.
Pd-1. Daniel
H Z K L X A L H X P N C I N Z X F L I X G N W Q X
P N Z K T L N K X O L X N I Z X G I N X P N E Z K
X W Q X P Z X L H X P N C I N Z X S N Q N T X W Q
X P N W V S N I K L K H B L X N W Q L X H F Z I L
N X A Z K S B W E N I.
Problem 1 breaks down as follows:
High frequency (top 7%), count = 8 : XNLZI
Medium frequency letters: : KPWHQS
Lo frequency (less than 3) : ABCEFGTOV
Zero (0) frequency : DJMRUY
By "N" Gram Count
6 gram Count CT Frequency
HXPNCI 2 5 19 6 17 2 8
LHXPNC 2 10 5 19 6 17 2
NCINZX 2 17 2 8 17 9 19
PNCINZ 2 6 17 2 8 17 9
XPNCIN 2 19 6 17 2 8 17
5 grams
CINZX 2 2 8 17 9 19
HXPNC 2 5 19 6 17 2
LHXPN 2 10 5 19 6 17
NCINZ 2 17 2 8 17 9
PNCIN 2 6 17 2 8 17
WQXPN 2 6 5 19 6 17
XPNCI 2 19 6 17 2 8
XWQXP (THATS)? 2 19 6 5 19 6
4 grams
CINX 2 2 8 17 9
HXPN 2 5 19 6 17
INZX 2 8 17 9 19
LHXP 2 10 5 19 6
NCIN 2 17 2 8 17
PNCI 2 6 17 2 8
QXPN 2 5 19 6 17
WQXP 2 6 5 19 6
YPNC 2 19 6 17 2
XWQX (THAT)? 2 19 6 5 19
3 grams
CIN 2 2 8 17
HXP 2 5 19 6
INZ 2 8 17 9
LHX 2 10 5 19
LXN 2 10 19 17
NCI 2 17 2 8
NWQ 2 17 6 5
NZX 2 17 9 19
PNC 2 6 17 2
QXP 3 5 19 6
WQX 3 6 5 19
XPN 5 19 6 17
XWQ 2 19 6 5
2 grams Count CT Frequency
CI 2 2 8
HX 2 5 19
IN 3 8 17
KL 2 7 10
KX 2 7 19
LH 2 10 5
LN 2 10 17
LX 4 10 19
NC 2 17 2
NI 2 17 8
NW 3 17 6
NX 2 17 19
NZ 3 17 9
PN 5 6 17
QX 3 5 19
SN 2 3 17
WQ 4 6 5
XA 2 19 2
XG 2 19 2
XN 2 19 17
XP 6 19 6
XW 2 19 6
ZK 4 9 7
ZX 4 9 19
Frequency * Variety = Contacts
A 2 3 6 XLZ
B 2 4 8 HLSW
C 2 2 4 NI
D 0 0 0
E 2 3 6 NZW
F 2 4 8 XLHZ
G 2 3 6 XNI
H 5 6 30 ZLXKBF
I 8 7 56 CNLXZGK
J 0 0 0
K 7 8 56 ZLTNXIHS
L 10 11 110 KXAHFITNOBQ
M 0 0 0
N 17 13 221 PCIZGWLKXESQT
O 1 2 2 XL
P 6 3 18 XNZ
Q 5 4 20 WXNL
R 0 0 0
S 3 5 15 XNVKB
T 2 4 8 KLNX
U 0 0 0
V 1 2 2 WS
W 6 6 36 NQXVBE
X 19 15 285 LAHPZFIGQKONWST
Y 0 0 0
Z 9 9 81 HKNXIEPFA
From above data we try X= t and N=e, P=h. Then E=y, L=i, W=o, S = D.
Message reads: Sanity is the great virtue of the ancient
literature; the want of that is the great defect of the
modern, in spite of its variety and power. Matthew Arnold
Pd-2. Join the army. Daniel
F L B B A O I A F Q E A O M Z U I L O N R Z O Q A
O P I L O M O L S F P F L I P F L B B A O E R I C
A O Q E F O P Q B L O W A V H Z O W E A P X Z Q Q
G A P Z I V V A Z Q E G A Q E F H T E L G L S A P
L R O W L R I Q O U F I E F P E A Z O Q Z I V I L
Q T F Q E E F P G F M P L I G U B L G G L T H A.
Problem 2 breaks down as follows:
High frequency (top 7%), count = 10 : LOAFQEI
Medium frequency letters: : PZGBRVHMTUW
Lo frequency (less than 3) : SCNX
Zero (0) frequency : DJKY
By "N" Gram Count
6 gram Count CT Frequency
FLBBAO 2 12 15 6 6 14 15
5 grams
FLBBA 2 12 15 6 6 14
LBBAO 2 15 6 6 14 15
4 grams
BBAO 2 6 6 14 15
FLBB 2 12 15 6 6
LBBA 2 12 6 6 14
3 grams
BAO 2 6 14 15
BBA 2 6 6 14
EFP 2 11 12 10
FLB 2 12 15 6
FQE 2 12 12 11
ILO 2 11 15 15
LBB 2 15 6 6
PFL 2 10 12 15
QEF 2 12 11 12
ZIV 2 8 11 4
ZOQ 2 8 15 12
2 grams Count CT. Frequency
AO 5 14 15
AP 3 14 10
AZ 2 14 8
BA 2 6 14
BB 2 6 6
BL 2 6 15
EA 3 11 14
EF 4 11 12
FL 3 12 15
FP 3 12 10
FQ 2 12 12
GA 2 7 14
GL 2 7 15
IL 3 11 15
IV 2 11 4
LB 2 15 6
LG 2 15 7
LI 2 15 11
LO 3 15 15
LR 2 15 4
LS 2 15 2
OM 2 15 3
OP 2 15 10
OQ 3 15 12
OW 3 15 3
PF 2 10 12
PL 2 10 15
QE 5 12 11
RI 2 4 11
ZI 2 8 11
ZO 3 8 15
ZQ 2 8 12
Frequency * Variety = Contacts
A 14 14 196 BOIFEQCWVPGZSH
B 6 5 30 LBAQU
C 1 2 2 IA
D 0 0 0
E 11 12 132 QAORFWGTLIPE
F 12 13 156 LAQSPEOHUITGM
G 7 9 63 QAELPFIUG
H 3 5 15 VZFTA
I 11 13 143 OAULPRCZVQFEG
J 0 0 0
K 0 0 0
L 15 12 180 FBIOSEGPRWQT
M 3 4 12 OZFP
N 1 2 2 OR
O 15 13 195 AIMLNZQPEFWRU
P 10 11 110 OIFQAXZLEGM
Q 12 12 144 FEOAPBZQGILT
R 4 6 24 NZEILO
S 2 3 6 LFA
T 3 5 15 HEQFL
U 3 6 18 ZIOFGB
V 4 4 16 AHIV
W 3 4 12 OAEL
X 1 2 2 PZ
Y 0 0 0
Z 8 10 80 MUROHQXPIA
BOZOL tried the crib word World from "Join the Army ..see the
world" The crib failed but did show him some
possibilities. LANAKI's caveat - Forget the tip, it is usually
a red hering.
Try the A=e, Q=t, e=h, O=r, and I=n. Look for words
offer, battles, death, country.
Message reads: "I offer neither pay nor quarters
nor provisions. I offer hunger, thirst, forced marches,
battles and death. Let him who loves our country in his heart
and not with his lips only, follow me." Made famous by
Girabaldi.
HOMEWORK LECTURE 3
Solve the following cipher problems.
Mv-1. From Martin Gardner.
8 5 1 8 5 1 9 1 1 9 9 1 3
1 6 1 2 5 1 1 2 1 6 8 1 2 5
2 0 9 3 3 1 5 4 5 2 0 8 1
2 0 9 2 2 5 1 4 5 2 2 5
1 8 1 9 5 5 1 4 2 5 6 1 5
1 8 5 1 3 1 2 5 2 5 2 5 1 5
2 1 3 1 1 4 2 1 1 9 5 9 2 0
9 1 4 2 5 1 5 2 1 1 8 3 1 5
1 2 2 1 1 3 1 4
1 3 1 1 8 2 0 9 1 4 7 1 1 8 4 1 4 5 1 8
8 5 1 4 4 5 1 8 1 9 1 5 1 4 2 2 9 1 2 1 2 5
1 4 1 5 1 8 2 0 8 3 1 1 8 1 5 1 2 9 1 4 1
Solve and reconstruct the cryptographic systems used.
Mv-2.
0 6 0 2 1 0 0 5 0 1 0 1 0 5 1 5 2 2 0 2 0 6 0 8 2
3 2 5 1 0 0 8 0 4 0 2 2 1 0 9 0 8 0 4 0 8 2 2 1 1
0 8 0 4 1 7 1 5 1 3 1 4 2 2 2 1 0 2 2 4 0 2 0 1 2
2 0 2 0 2 0 1 0 8 1 9 0 6 1 5 1 7 0 8 0 1 1 1 2 2
1 4 0 2 0 1 1 9 0 6 0 5 1 0 0 2 0 2 1 1 2 2 1 4 0
6 2 3 1 9 0 5 1 5 0 1 2 2 1 3 0 2 0 5 0 6 1 3 0 2
0 5 0 1 1 0 0 5 2 3 0 6 2 1 0 2 2 2 1 4 0 6 0 2 0
2 2 2 1 4 0 6 0 2 0 2 2 6 0 2 0 6 0 5 2 1 1 9 0 2
0 2 1 1 2 2 0 3 0 2 1 7 2 4 0 2 1 9 0 2 0 6 1 5 0
5 1 1 0 6 0 2 1 9 0 5 0 6 2 2 0 1 0 5 0 5 0 1 1 9
0 5 2 1 1 5 2 2 1 5 0 5 0 1 2 2 0 5 1 8 0 5 0 6 0
6 0 5 0 3
Mv-3.
5 3 2 4 1 5 4 5 3 2 2 4 4 3 2 5 1 2 4 3 2 4 2 3 1
5 4 4 4 5 4 5 3 2 5 1 4 3 4 4 1 4 1 5 2 1 4 1 1 5
4 3 4 5 3 5 2 1 2 3 3 5 1 2 5 1 1 4 2 1 5 3 3 3 4
5 3 2 4 4 2 3 1 5 4 5 4 5 2 4 4 3 2 4 1 4 4 4 3 2
1 2 5 3 2 4 4 3 4 4 2 4 1 5 4 4 4 5 2 4 4 3 3 5 2
1 5 3 3 3 1 3 1 4 4 4 1 5 4 5 4 4 5 1 4 3 2 5 1 5
2 3 2 4 1 5 5 2 2 4 4 3 1 5 3 1 3 3 1 3 3 1 4 5 5
3 2 4 1 3 4 5 2 1 2 5 3 3 5 2 2 4 3 4 1 3 1 2 4 5
4 4 5 2 3 3 4 4 3 3 2 2 3 3 3 5 3 3 4 5 2 1 3 5 2
4 4 4 4 4 4 5 3 2 1 5 1 3 1 5 5 2 2 4 4 3 1 5 3 1
2 4 5 1 1 3 1 4 2 4 4 4 3 3 4 3 1 5 2 2 3 5 2 4 2
5 3 5 2 1 3 3 1 3 3 1 2 3 1 2 1 3 1 4 3 3 4 5 3 3
1 2 1 3 4 4 4 1 2 4 4 3 3 3 1 2 1 4 3 2 2 4 3 3 3
1 3 2 4 5 1 2 2 5 3 5 1 2 5 3 2 3 3 5 1 2 5 1 1 4
4 4 1 5 4 5 4 1 4 3 2 4 4 4 2 4 1 3 4 5 1 5 2 2 1
2 5 1 4 5 1 2 1 3 2 4 4 5 3 2 1 2 5 1 4 4 1 5 1 3
1 4 2 5 2 4 2 4 4 5
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