Math 1
J.M.Basilla
Overview
Main Problem
Cryptography
General Education Mathematics
Lecture 8
Julius Magalona Basilla
Institute of Mathematics
University of the Philippines
Diliman, Quezon City
3 August 2010
Cryptography is not Coding
History of
Cryptography
Cryptography in World War I
The
communication
channel
Monoalphabetic
Substitution
The alphabet
Main Problem
Math 1
J.M.Basilla
Overview
Main Problem
Cryptography is not Coding
History of
Cryptography
Cryptography in World War I
Alice
message Bob
The
communication
channel
Monoalphabetic
Substitution
message
Oscar
?
The alphabet
The science of secret writing
Math 1
J.M.Basilla
Overview
Main Problem
The science of Secret Writing
Cryptography is not Coding
History of
Cryptography
Cryptography in World War I
The
communication
channel
Steganography
Cryptography
Monoalphabetic
Substitution
The alphabet
hiding
scrambling
Transposition
Substitution
anagram
ocw
wco
cwo
woc
cow
owc
Code
Cipher
word level
letter level
Main Problem of Coding Theory
Math 1
J.M.Basilla
Overview
Main Problem
Cryptography is not Coding
History of
Cryptography
Cryptography should not be confused with Coding Theory.
Alice
message
Noise
Bob
?
Cryptography in World War I
The
communication
channel
Monoalphabetic
Substitution
The alphabet
Noise
Main Problem of Coding Theory
Math 1
J.M.Basilla
Overview
Main Problem
Cryptography is not Coding
Cryptography should not be confused with Coding
Theory.
Storing
Alice
Information
Retrieving
Bob
Noise or Errors
Noise
History of
Cryptography
Cryptography in World War I
The
communication
channel
Monoalphabetic
Substitution
The alphabet
The sinking of Lusitania
Math 1
J.M.Basilla
Overview
Main Problem
Cryptography is not Coding
History of
Cryptography
Cryptography in World War I
I
In 1915, a German U-boat sanked Lusitania.
I
The German appeased Woodrow Wilson with a
promise of ”restricted submarine warfare”.
I
Americans remained neutral.
The
communication
channel
Monoalphabetic
Substitution
The alphabet
The Zimmermann Telegram
Math 1
J.M.Basilla
Overview
Main Problem
Cryptography is not Coding
History of
Cryptography
Cryptography in World War I
I
January 9, 1917. The German supreme high
command persuaded the then German Foreign
Minister Arthur Zimmermann to engage in an
unrestricted submarine warfare.
The
communication
channel
Monoalphabetic
Substitution
The alphabet
The Zimmermann message, decrypted and
translated
Math 1
J.M.Basilla
Overview
Main Problem
Cryptography is not Coding
History of
Cryptography
Cryptography in World War I
The
communication
channel
January 17, 1917. The British intercepted and
deciphered Zimmerman’s telegram to the German
Ambassador to the United States.
Monoalphabetic
Substitution
The alphabet
The Zimmermann message, decrypted and
translated
Math 1
J.M.Basilla
Overview
We intend to begin unrestricted warfare on the first of
February.
We shall endeavor in spite of this to keep United States
neutral. In the event of this not succeeding, we make
Mexico a proposal of alliance on the following basis: make
war together, make peace together, generous financial
support, and an understanding on our part that Mexico is
to reconquer the lost territory in Texas, New Mexico and
Arizona. The settlement in detail is left to you.
You will inform the President of Mexico of the above most
secretly, as soon as the outbreak of war with the United
States is certain and add the suggestion that he should, in
his own initiative, invite Japan to immediate adherence and
at the same time mediate between Japan and ourselves.
Please call the President’s attention to the fact that the
unrestricted employment of our submarines now offers the
prospect of compelling England to make peace within
months. Acknowledge receipt.
Zimmermann
Main Problem
Cryptography is not Coding
History of
Cryptography
Cryptography in World War I
The
communication
channel
Monoalphabetic
Substitution
The alphabet
The Americans joined Britain and France
Math 1
J.M.Basilla
I
I
I
February 1, 1917. The Germans engaged in
unrestricted submarine warfare.
February 23, 1917. Britain showed the message
intercepted in Mexico to US.
April 6, 1917. US joined Britain and France against
Germany.
Had the telegram never been intercepted or
never been published, inevitably the Germans
would have done something else that would
have brought us in eventually. But the time was
already late and, had we delayed much longer,
the Allies might have been forced to negotiate.
To that extent the Zimmermann telegram
altered the course of history...
Barbara Tuchman
American Historian,
author of The Zimmerman Telegram
Overview
Main Problem
Cryptography is not Coding
History of
Cryptography
Cryptography in World War I
The
communication
channel
Monoalphabetic
Substitution
The alphabet
The classical communication channel
Math 1
J.M.Basilla
Overview
Main Problem
Oscar
?
Cryptography is not Coding
History of
Cryptography
Cryptography in World War I
Alice
Encryption hidden message
decryption
Bob
The
communication
channel
Monoalphabetic
Substitution
The alphabet
Secure channel
key generators
The Pigpen Cipher
Free masons
Math 1
J.M.Basilla
Overview
>The alphabet are the set of characters/fundamental unit
in writing a message.
A
N
J
B
A
B
K
L
C
O
P
C
Q
D
E
F
M
N
D
O
E
R
Q
H
I
P
R
F
G
S
T
G
U
H
I
V
J
W
W
S
K
X
U
T
X
Y
L
Y
M
Z
V
Z
Main Problem
Cryptography is not Coding
History of
Cryptography
Cryptography in World War I
The
communication
channel
Monoalphabetic
Substitution
The alphabet
An Example
Math 1
J.M.Basilla
Overview
Main Problem
Pigpen Cipher
A
B
C
Cryptography is not Coding
D
E
F
G
History of
Cryptography
The
communication
channel
Cryptography in World War I
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Happy =
Carpe Diem
Monoalphabetic
Substitution
The alphabet
Calvin and Hobbes
Math 1
J.M.Basilla
Overview
Main Problem
Cryptography is not Coding
History of
Cryptography
Cryptography in World War I
The
communication
channel
Monoalphabetic
Substitution
The alphabet
Calvin:
Hobbes:
Calvin:
Hobbes:
Calvin:
”So, our secret code is ready”
”Let me see”
”I have assigned to each letter a completely random
number so that code becomes hard to break. The
letter A is 3.004.577.688, B is 28.731.5691/2”
”This must certainly be a really good code”
”Now, we only need to learn it by heart”
Main Limitation of Non mathematical
Monoalphabetic Substitution
Math 1
J.M.Basilla
Overview
Main Problem
Cryptography is not Coding
History of
Cryptography
Cryptography in World War I
I
The comics strip captures the main difficulty of Non
mathematical Monoalphabetic substitutionmemorizing the rule of substitution or the
encoding/decoding keys.
I
Cannot be made complicated nor applied to an
message with plenty of characters in the alphabet.
I
Easy to attack using frequency distribution.
The
communication
channel
Monoalphabetic
Substitution
The alphabet