An Introduction to Cryptography

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Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
An Introduction to Cryptography
Claus Aranha
twitter:caranha
Department of Computer Sciences,University of Tsukuba
December 5,2012
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Self Introduction
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
The story of Caesar and Augustus
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
The story of Caesar and Augustus
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
The story of Caesar and Augustus
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Caesar's Problem:What time to attack?
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Caesar's Problem:What time to attack?
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Caesar's Problem:What time to attack?
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Caesar's Problem:What time to attack?
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Idea 1:The Messenger
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Idea 1:The Messenger
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Idea 1:The Messenger
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Idea 2:The Code
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Idea 2:The Code
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Idea 2:The Code
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Cryptography
Cryptography!
Crypto:Secrets;
Graphy:Writing;
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Rotational Cyphers
ROTX
Code letter = Message Letter + X
(A + 1 = B)
ROT3:Claus!Fodxv
ROT8:Claus!Ktica
ROT13:Claus!Pynhf
ROT13:Pynhf!Claus
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Rotational Cyphers
ROTX
Code letter = Message Letter + X
(A + 1 = B)
ROT3:Claus!Fodxv
ROT8:Claus!Ktica
ROT13:Claus!Pynhf
ROT13:Pynhf!Claus
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Rotational Cyphers
ROTX
Code letter = Message Letter + X
(A + 1 = B)
ROT3:Claus!Fodxv
ROT8:Claus!Ktica
ROT13:Claus!Pynhf
ROT13:Pynhf!Claus
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Rotational Cyphers
ROTX
Code letter = Message Letter + X
(A + 1 = B)
ROT3:Claus!Fodxv
ROT8:Claus!Ktica
ROT13:Claus!Pynhf
ROT13:Pynhf!Claus
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Rotational Cyphers
ROTX
Code letter = Message Letter + X
(A + 1 = B)
ROT3:Claus!Fodxv
ROT8:Claus!Ktica
ROT13:Claus!Pynhf
ROT13:Pynhf!Claus
ROT13 is often used on the internet to hide Spoilers (netabare)
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
What if the enemy was more intelligent?
Dwwdfn dw gdzq wrpruurz
ROT 1:Exxego ex hear xsqsvvsa
ROT 2:Fyyfhp fy ifbs ytrtwwtb
ROT 3:Gzzgiq gz jgct zusuxxuc
ROT 22:Zsszbj zs czvm snlnqqnv
ROT 23:Attack at dawn tomorrow
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
What if the enemy was more intelligent?
Dwwdfn dw gdzq wrpruurz
ROT 1:Exxego ex hear xsqsvvsa
ROT 2:Fyyfhp fy ifbs ytrtwwtb
ROT 3:Gzzgiq gz jgct zusuxxuc
ROT 22:Zsszbj zs czvm snlnqqnv
ROT 23:Attack at dawn tomorrow
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
What if the enemy was more intelligent?
Dwwdfn dw gdzq wrpruurz
ROT 1:Exxego ex hear xsqsvvsa
ROT 2:Fyyfhp fy ifbs ytrtwwtb
ROT 3:Gzzgiq gz jgct zusuxxuc
ROT 22:Zsszbj zs czvm snlnqqnv
ROT 23:Attack at dawn tomorrow
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
What if the enemy was more intelligent?
Dwwdfn dw gdzq wrpruurz
ROT 1:Exxego ex hear xsqsvvsa
ROT 2:Fyyfhp fy ifbs ytrtwwtb
ROT 3:Gzzgiq gz jgct zusuxxuc
ROT 22:Zsszbj zs czvm snlnqqnv
ROT 23:Attack at dawn tomorrow
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
What if the enemy was more intelligent?
Dwwdfn dw gdzq wrpruurz
ROT 1:Exxego ex hear xsqsvvsa
ROT 2:Fyyfhp fy ifbs ytrtwwtb
ROT 3:Gzzgiq gz jgct zusuxxuc
...
ROT 22:Zsszbj zs czvm snlnqqnv
ROT 23:Attack at dawn tomorrow
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
What if the enemy was more intelligent?
Dwwdfn dw gdzq wrpruurz
ROT 1:Exxego ex hear xsqsvvsa
ROT 2:Fyyfhp fy ifbs ytrtwwtb
ROT 3:Gzzgiq gz jgct zusuxxuc
...
ROT 22:Zsszbj zs czvm snlnqqnv
ROT 23:Attack at dawn tomorrow
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Caesar can be more intelligent too
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Caesar can be more intelligent too
Substitution Cyphers
A
B
C
D
E
F
G
H
I
D
A
L
E
H
B
M
J
C
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Caesar can be more intelligent too
Substitution Cyphers
A
B
C
D
E
F
G
H
I
D
A
L
E
H
B
M
J
C
Rotational Cypher:
25 tries
Substitution Cypher:
400.000.000.000.000.000.000.000.000
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
How can you solve this?
Zob kllt ax lm zob zpkwb.A mz epmz zob
kllt pmcnlvb.Zptb az kpgt mld.
\A"!a,i;
\ax","lm","az"!is,on,my,of...;
\zob",\mld"!the...;
\e"!most frequent letter in english;
Statistical Analysis
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
How can you solve this?
Zob kllt ax lm zob zpkwb.A mz epmz zob
kllt pmcnlvb.Zptb az kpgt mld.
\A"!a,i;
\ax","lm","az"!is,on,my,of...;
\zob",\mld"!the...;
\e"!most frequent letter in english;
Statistical Analysis
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
How can you solve this?
Zob kllt ax lm zob zpkwb.A mz epmz zob
kllt pmcnlvb.Zptb az kpgt mld.
\A"!a,i;
\ax","lm","az"!is,on,my,of...;
\zob",\mld"!the...;
\e"!most frequent letter in english;
Statistical Analysis
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
How can you solve this?
Zob kllt ax lm zob zpkwb.A mz epmz zob
kllt pmcnlvb.Zptb az kpgt mld.
\A"!a,i;
\ax","lm","az"!is,on,my,of...;
\zob",\mld"!the...;
\e"!most frequent letter in english;
Statistical Analysis
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
How can you solve this?
Zob kllt ax lm zob zpkwb.A mz epmz zob
kllt pmcnlvb.Zptb az kpgt mld.
\A"!a,i;
\ax","lm","az"!is,on,my,of...;
\zob",\mld"!the...;
\e"!most frequent letter in english;
Statistical Analysis
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
How can you solve this?
Zob kllt ax lm zob zpkwb.A mz epmz zob
kllt pmcnlvb.Zptb az kpgt mld.
\A"!a,i;
\ax","lm","az"!is,on,my,of...;
\zob",\mld"!the...;
\e"!most frequent letter in english;
Statistical Analysis
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
What is cryptography
Plain Text:The original text;
Cyphertext:The text after coding;
Cryptosystem:A way to encrypt information;
Key:The information necessary to use a cryptosystem;
Cryptoanalysis:Trying to\break"a cyphertext;
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
The most important subject for cryptography
Most of Cryptography is pure mathematics
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
The most important subject for cryptography
Most of Cryptography is pure mathematics
Module Arithmetics
15 10 Module arithmetics are used for\cyclic"calculations.Later on you
will call them\groups".
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
The most important subject for cryptography
Most of Cryptography is pure mathematics
Statistics
What is the most frequent letter of a certain language?
What is the most frequent word of a certain language?
If three symbols appear in a row in a cyphertext,does this have meaning,
or is it coincidence?
Statistics is used heavily to calculate the\quantity of information"
available in any text.
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
The most important subject for cryptography
Most of Cryptography is pure mathematics
Combinatorics
How many variations do we have for the Rotation Cypher?(26)
How many variations do we have for the Substitation Cypher?(4x10
26
)
Combinatory analysis tells us how big problems can be.
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
The most important subject for cryptography
Most of Cryptography is pure mathematics
Other concepts
Prime numbers,Functions,geometry,etc.
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
An important Cryptosystem in real life
The ENIGMA Machine
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
An important Cryptosystem in real life
The ENIGMA Machine
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Who broke the Enigma?
Alan Turing,British Mathematician,led the
eorts that broke the Enigma cryptosystem.
He also developed early theories for Computer Science and Articial
Intelligence.Today,he is known as the Father of Computer Sciences
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Who broke the Enigma?
Alan Turing,British Mathematician,led the
eorts that broke the Enigma cryptosystem.
He also developed early theories for Computer Science and Articial
Intelligence.Today,he is known as the Father of Computer Sciences
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Where do we use cryptography today?
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Where do we use cryptography today?
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Sending information on the internet
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Personal Information
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Personal Information is important!
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Let's do Cryptography!
Each group creates their own cryptosystem;
Try to break the cryptosystem of other groups!
(create a large message rst for this)
Explain your system to everyone;
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Hints for Encoding (1)
Rotational Cyphers with words
The\Claus"Cypher:
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
C
L
A
U
S
B
E
F
G
H
I
J
K
M
N
O
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Hints for Encoding (2)
Substitution Cypher with Kana
ka
1
sa
6
ta
11
ma
16
ki
2
shi
7
chi
12
mi
17
ku
3
su
8
tsu
13
mu
18
ke
4
se
9
te
14
me
19
ko
5
so
10
to
15
mo
20
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Hints for Encoding (3)
Hidden Messages!
Here I don't explain another method.Each system shows a great
excellence.
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Hints for Encoding (3)
Hidden Messages!
Here I don't explain another method.Each system shows a great
excellence.
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
Task!
Have Fun!
Introduction
History
Cryptography
Modern Cryptography
Exercise!
Omake
For more information
Book:\The Codebreakers",by David Khan
Software:Truecrypt
Chat:CryptoCat