ISA 562 Information Security Theory & Practice

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Nov 21, 2013 (3 years and 8 months ago)

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8. Cryptography

1

ISA 562

Information Security Theory & Practice


Introduction to Cryptography

8. Cryptography

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Agenda

• Basics & Definitions

• Classical Cryptography

• Symmetric (Secret Key) Cryptography

• DES (Data Encryption Standard)

• Multiple Encryptions

• Modes of Block Cipher Operations

• Math Essential

• Asymmetric (Public Key) Cryptography

8. Cryptography

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Basic Definitions

Cryptography


Crypt = secret


Graph = writing


science / art of transforming meaningful
information into unintelligible text


Relies on mathematics (number theory, algebra)

Cryptanalysis




science / art of breaking cryptographic codes

Cryptology



science / art / study of cryptography and
cryptanalysis

8. Cryptography

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Applications of Cryptography

• Assuring document integrity

• Assuring document confidentiality

• Authenticating parties

• Document signature

• Non
-
repudiation

• Secure transactions

• Exchanging keys

• Sharing Secrets

• Digital cash

• Preserving anonymity

• Copyright protection …

8. Cryptography

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Cryptographic Services (I)

Starting from Basics

A




B


A



B








C


a) Source Integrity



b) Data Confidentiality


Normal Flow




Eavesdropping

A




B


A



B




C






C


c) Data Integrity



d) Source Authentication



Modification




Fabrication


8. Cryptography

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Cryptographic Services (II)

A




B


A



B









c



e)

Drop




f) Replay


A




B




C


f) Denial of Service

8. Cryptography

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Encryption/Decryption

Plaintext


ciphertext



Plaintext



encryption


decryption








key




key


• Plaintext:

message in original form

• Ciphertext:

message in the transformed, unrecognized form

• Encryption:

process that transforms a plaintext into a ciphertext

• Decryption:

process that transforms a ciphertext back to plaintext

• Key:


value used to control encryption/decryption.

8. Cryptography

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Cryptanalytic Attack

Attacker only knows Ciphertext



Tries to reveal plaintext and/or key


• Attacker Knows Plaintext, Ciphertext Pairs <plaintext , ciphertext>



Cryptanalysis tries to reveal the key



Relevant when plaintext is known or can be obtained


• Attacker chooses a Plaintext

and receives the Ciphertext



Cryptanalysis tries to reveal the key



Relevant when attacker can “inject” a plaintext message

8. Cryptography

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Classical Cryptography

Cryptography used by early civilizations (including
Egyptians, Greeks, Romans) for
Secrecy

Confidentiality

now includes Integrity,
Authentication & Authenticity, and in sometimes
Non
-
Repudiation.

• Early cryptography mainly encryption by
substitution and/or transposition methods



They were simple because of the lack of computing
engines



Could easily be attacked

• Same ideas in use today but with stronger properties
and powerful computing engines

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Substitution Ciphers (1)

Caesar Cipher
: fixed permutation (move 3 up in
the alphabet)

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

d e f g h i j k l m n o p q r s t u v w x y z a b c

Algorithm is:



C = ENC( P ) = P + 3 (mod 26)

For example: GMU →JPX


The secrecy is in the algorithm !

• There is one key (fixed permutation)

• Easy to break

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Substitution Ciphers (2)

Shift Cipher

similar to Caesar Cipher, but there is a cyclic shift of the 26
letters of the alphabet by key K, where

0 ≤ K < 26.

• Algorithm:

C = ENCK( P ) = P + K (mod 26)


There are 26 different keys

• Easy to break


check which of 26 possible keys returns the

a meaningful plaintext

• Decipher HAL (the computer from the movie 2001: A Space

Odyssey) using a shift cipher of one.



So the shift variable n=1.


• HAL ?

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Mono
-
Alphabetic Ciphers

Generalization: arbitrary mapping of one letter to

another

• One of N! permutations on N letters of the alphabet

• The key is the index of the permutation

• Key is secret (one of N! options)

• Example:



N = 26 letters of the English alphabet



N! = 26! ≈ 4 • 1026 ≈ 288 permutations or 309 Septillion



≈ 309,485,009,821,345,000,000,000,000 permutations

• IS IT SECURE?

Not with Frequency Analysis

8. Cryptography

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Cryptanalysis


A
ttacking Mono
-
Alphabetic Ciphers

Began in later part of the first millennium AD in the
Middle East.

• Frequency analysis is the study of the frequency
of occurrence of letters. (statistics) • First
treatise on it was written by


Ab‾uY‾us‾uf Ya‘q‾ub ibn Is
-
h‾aq ibn as
-
Sabb‾ah


ibn ‘omr‾an ibn Isma‾il al
-
Kind‾i, the “philosopher


of the Arabs.”

8. Cryptography

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Letter Frequency

Western Languages are redundant, they have a
non
-
uniform distribution of about 26 letters.

• Each symbol of ciphertext depends on only one

symbol of plaintext and one value of the
permutation key, so guessing part of the key
gives part of the plaintext.

• Attack proceeds by guessing parts of key
corresponding to most common letters, which
makes it possible to decipher an entire
message.

8. Cryptography

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Letter frequency in English

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Attacking Mono
-
Alphabetic Ciphers
in English

Appearance frequency of letters (in long texts) in a
language is well known. Appearance frequency of pairs
of letters in a language is also well known:




th, ee, oo, tt, qu, is, ae, . . . Not zq, kv, etc

Appearance frequency of certain words is also well defined:

the ≈ 6.4% a ≈ 2.1% i ≈ 0.9%

of ≈ 4.0% in ≈ 1.8% it ≈ 0.9%

and ≈ 3.2% that ≈ 1.2% for ≈ 0.8%

to ≈ 2.4% is ≈ 1.0% as ≈ 0.8%

8. Cryptography

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Attacking Mono
-
Alphabetic Ciphers

Using the appearance frequencies of letters, words,

and pairs
-
of
-
letters


accelerates the identification of

certain letter substitutions (part of the key)

• Identification of word patterns, vowels, and consonants helps in finding
parts of the text

• The identification of the remaining parts of the key now reduces the
search space dramatically (from N!)

• Using heuristics and associative word
-
completions, the rest of the key
can be easily revealed


In English

the most common letters: are E, T, A, O, I, N, S, H. more than
half of all words end in E, T, D, S. Q is always followed by U.


most common word is “THE.” and most common doublets are EE, TT,
OO, SS, LL, FF.


most common 2
-
letter combos: HE, RE, AN, TH, ER,IN.


most common 3
-
letter combos: ION, AND, ING, THE, ENT.

8. Cryptography

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Possible solutions


Do not use redundant letters, like the letter
e


Done by French writer Georges Perec in 1969. He
published a 300
-
page novel La Disparition (The
Disappearance)…translated into English by Gilbert
Adair and called “A Void”


Or use different Mono
-
Alphabetic Ciphers in
different parts of the plaintext:“Poly
-
Alphabetic
Ciphers”.
Quite strong


• Or group plaintext into blocks that go through a
transformation

8. Cryptography

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Vig`enere Cipher (I)

Blaise de Vig`enere: (1523) Created the cipher but unused
almost 200 years.


One type of Poly
-
Alphabetic Cipher The collection of
Mono
-
Alphabetic Ciphers consists of the 26 options for
Caesar Cipher (with K = 0, 1, 2, . . ., 25) where each of
the 26 is given a letter, which is the ciphertext letter that
replaces the letter ‘a’

In practice:


A table of 26 rows by 26 columns is built. Row i in the
table contains the 26 letters of the alphabet circularly
shifted by i.


A keyword is used (over and over again) to select which
of the mono
-
alphabetic ciphers to use. The cipher used
is selected by the current letter in the keyword.

8. Cryptography

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The Cipher


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

A 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

B 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 A

C C D E F G H I J K L M N O P Q R S T U V W X Y Z A B

D D E F G H I J K L M N O P Q R S T U V W X Y Z A B C

E E F G H I J K L M N O P Q R S T U V W X Y Z A B C D

F F G H I J K L M N O P Q R S T U V W X Y Z A B C D E

G G H I J K L M N O P Q R S T U V W X Y Z A B C D E F

H H I J K L M N O P Q R S T U V W X Y Z A B C D E F G

I I J K L M N O P Q R S T U V W X Y Z A B C D E F G H

J J K L M N O P Q R S T U V W X Y Z A B C D E F G H I

K K L M N O P Q R S T U V W X Y Z A B C D E F G H I J

L L M N O P Q R S T U V W X Y Z A B C D E F G H I J K

M M N O P Q R S T U V W X Y Z A B C D E F G H I J K L

N N O P Q R S T U V W X Y Z A B C D E F G H I J K L M

O O P Q R S T U V W X Y Z A B C D E F G H I J K L M N

P P Q R S T U V W X Y Z A B C D E F G H I J K L M N O

Q Q R S T U V W X Y Z A B C D E F G H I J K L M N O P

R R S T U V W X Y Z A B C D E F G H I J K L M N O P Q

S S T U V W X Y Z A B C D E F G H I J K L M N O P Q R

T T U V W X Y Z A B C D E F G H I J K L M N O P Q R S

U U V W X Y Z A B C D E F G H I J K L M N O P Q R S T

V V W X Y Z A B C D E F G H I J K L M N O P Q R S T U

W W X Y Z A B C D E F G H I J K L M N O P Q R S T U V

X X Y Z A B C D E F G H I J K L M N O P Q R S T U V W

Y Y Z A B C D E F G H I J K L M N O P Q R S T U V W X

Z Z 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

8. Cryptography

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Class Exercise using Vig`enere
Cipher


Keyword:

GMU


• Plaintext:

SECURITY


• Ciphertext:

8. Cryptography

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Attacking Vig`enere Cipher

Check whether the cipher is Mono
-
Alphabetic



Check whether the appearance frequency of letters in the ciphertext
complies with that of a Mono
-
Alphabetic cipher

Determine the length of the keyword



If two identical sequences of plaintext letters occur at a distance that
is an integer multiple of the keyword length


than the two
corresponding sequences of ciphertext letters will be identical



Detect identical sequences of ciphertext letters



Conjecture that the keyword length is the GCD (greatest common
divisor) of distances between identical sequences of ciphertext

• Neutralize shifts and break each of the suspected Mono
-
Alphabetic
Ciphers independently

8. Cryptography

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Running Key Cipher

One Time Pads

Running Key

Does not use mathematical
formula, instead uses everyday item such
as a set of books



Numbers give the book, page number, line
number, and word number

One Time Pad


Cipher only used for a small message and
then destroyed

8. Cryptography

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Transposition Methods

Letters rearranged in particular fashion

Plaintext buffered in size N bufer

Plaintext scrambled to a defiined order in buffer

Key is the transposition mapping


8. Cryptography

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Spartan Scytale

8. Cryptography

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Rail
-
Fence Cipher

Method:


Plaintext written as a sequence of diagonals and
read as a sequence of rows




m

e

m

t

d

y

t

e

t

e

o

a

a

9

8. Cryptography

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Row
-
Column Cipher



Key is



2

4

1

5

3




A

T

T

A

C

K

F

R

O

M

E

A

S

T

A

T

D

A

W

N

Ciphertext is TRSAAKETCMANTFADAOTW

8. Cryptography

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Attacking Transposition Methods

Pure Transposition Cipher easily
recognized: it has same letter frequencies
as original text

Di
-
grams and tri
-
grams also are visible

Arrange text in rectangle and move rows
and columns

8. Cryptography

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Rotor Machines

Combine Substitution and Transposition
Methods

• produce ciphers that are very difficult to
break

Rotor Machines in World War II: German
“Enigma” and Japanese “Purple”

• Breaking by the Allies was a significant
factor in the outcome of the war (Turing)

8. Cryptography

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Example of Rotor Machine