Cryptography -- Classical Styles
Anita Jones
CS451 Information Security
Copyright(C) Anita Jones
Overview
Introduction
A security model
What is cryptography?
Some classical ciphers
from days of olde …….
up to World War II
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Security problems of interest
Policies:
confidentiality - protect info content from
unwarranted observation
integrity - protect info accuracy
availability - ensure information delivery
Problems that arise in implementation:
authentication - assure identity of user (sender)
non-repudiation - protect from deniability
access control - control access to info/resources
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Attacks
interception - of information-traffic,
breaches confidentiality
interruption - of service, availability
modification - of information, i.e. loss of
integrity
fabrication - of information, destroys
authenticity
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Response?
identify key assets
evaluate threat posed to assets
implement suitable countermeasures
manage implementation
cryptography is a key technology
Note – not a “perimeter defense” technology
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Model for cryptography
Principal
Trusted 3rd Party
(arbitrates, distributes Principal
secret information)
Message
Message
Secret
Information
Security
Transform
Security
Transform
Opponent
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Secret
Information
Info channel
Issues
Transformation algorithm
What’s the secret information; How to
generate it
How to distribute secret information
Protocols -- disciplined interaction
involving all parties
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What’s cryptography
cryptography is the study of secret (crypto-)
writing (-graphy)
concerned with developing algorithms which
may be used to:
conceal the content of a message from all except
the sender & recipient (secrecy or confidentiality)
verify the correctness of a message or its sender
to the recipient (integrity & authentication)
includes protocols solving many problems
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A few terms
cryptography
the art or science of transforming an intelligible
message into one that is unintelligible, and then
transforming that message back to original form
plaintext
the original intelligible message
ciphertext
the transformed message
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A few terms
cipher
an algorithm for transforming an intelligible
message into one that is unintelligible
key
critical (secret) information used in the cipher
& known only to the sender & receiver
Symmetric – shared
Asymmetric – public/private
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A few terms
encipher (encode)
the process of converting plaintext to
ciphertext using a cipher plus key
decipher (decode)
the process of converting ciphertext back into
plaintext using a cipher plus key
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A few terms
cryptanalysis (codebreaking)
the study of methods for transforming an
unintelligible message back into an intelligible
message without knowledge of the key
code
an algorithm for transforming an intelligible
message into an unintelligible message using
a code-book
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Transformations
encryption
applying a mathematical function mapping
plaintext to ciphertext using the specified key:
C = EK(P)
decryption
applying a mathematical function mapping
ciphertext to plaintext using the specified key:
P = EK-1(C)
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P = DK(C)
More terms
cryptographic system
a single parameter family of invertible
transformations with unique inverses
where only the key is secret
the cryptographic system is typically made
public
keys, of course, are secret
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Steganography
embed message in innocuous setting
My Special Friend,
Our speaker today in class today is exciting, & I know that
the next speaker is even better. I need to report to you that
next class the teacher will give the mid-term exam. Well,
there is only one mid-term! YEAH!!! That is it for now.
I’m awful at writing, but will keep trying ………...
9/2006
Steganography
embed message in innocuous setting
My Special Friend,
Our speaker today in class today is exciting, & I know that
the next speaker is even better. I need to report to you that
next class the teacher will give the mid-term exam. Well,
there is only one mid-term! YEAH!!! That is it for now.
I’m awful at writing, but will keep trying ………...
9/2006
Two crypto techniques
Permutation
Substitution
“Staff” cipher
an early Greek transposition cipher:
cut a narrow strip of paper long enough to write
message
wind it around a staff so that adjacent edges
abut
write message horizontally down the shaft with a
character on each wrapping
unwind
Result: long sequence of seemingly random
letters
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The ole alternation trick
write message letters on alternate rows
read off cipher by row
Plain = “I CAME I SAW
I CONQUERED”
Plain: I A E S W C N U E
C M I A I O Q R D
Cipher: IAESW CNUE CMIAI OQRD
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The ole structured patterns trick
write message letters as a matrix
read off cipher by some pattern
Plain: I C A M E
I S A W I
C O N Q U
E R E D A
Cipher: diagonals, concentric circle, in and
out, etc
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The ole mirror trick
write the message backwards
Plain: I CAME I SAW I CONQUERED
Cipher: DEREU QNOCI WASIE MACI
………and speaking of J. Caesar
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Two crypto techniques
Permutation
Substitution
Caesar cipher - substitution cipher
Julius Caesar invented to transmit military
information -- 2000 years ago
Map each letter to another -- fixed offset -called the translation alphabet
Alphabets:
Plain: A B C D E F G H I J K L M N O P Q R S T U
Cipher: E F G H I J K L M N O P Q R S T U V W X Y
CipherText:
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W TI G M E P W T I E O I V G S Q M R K
Caesar cipher - substitution cipher
Julius Caesar invented to transmit military
information -- 2000 years ago
Map each letter to another -- fixed offset -called the translation alphabet
Alphabets:
Plain: A B C D E F G H I J K L M N O P Q R S T U
Cipher: E F G H I J K L M N O P Q R S T U V W X Y
CipherText:
P=
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W TI G M E P W T I E O I V G S Q M R K
S P E C I A L S P EA K E R C O M I N G
Substitution Technique
Encryption algorithm used in previous slide is
C = E(P) = (p + 4) mod(26)
More generally, any shift, k, in range 1:25
C = E(P) = (p + k) mod(26)
Decryption algorithm
p = D(C) = (c - k) mod(26)
plaintext letter P (p is its offset into the alphabet of interest;
ciphertext letter C (ditto); modulus function mod
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Cryptanalysis – break Caesar cipher
check out brute force cryptanalysis of a
Caesar cipher
What is the Key?
What is the Key size?
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Mono-alphabetic Substitution
Use any permutation of the 26 alphabetic
characters
26! (i.e. 4 x 1026) possible keys
brute force attack is cheap to execute
But, regularities of the language give clues
English, German, Hebrew, Russian – have different
characteristics in terms of letter usage
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Language regularities
can base cryptanalysis on frequency of
letter occurrence
E is most frequent, then
T, R, I, N, O, A, S, then …..
rarely are J, K, Q X Z used
E is 25 times more frequent than Q
Strategy (for a “long enough” message) is
to guess at letter value based on frequency
of appearance in ciphertext
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Language regularities - example
Ceasar (Mono alphabetic substitution) Alphabets:
Plain: A B C D E F G H I J K L M N O P Q R S T U
Cipher: E F G H I J K L M N O P Q R S T U V W X Y
CipherText:
P=
P=
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W TI G M E P W T I E O I V G S Q M R K
S P E C I A L S P EA K E R C O M I N G
S P E C I A L S P EA K E R
COMING
Crypt algorithm development
early manuscript -- Abu al-Kindi's "A
Manuscript on Deciphering Cryptographic
Messages"
published in the 9th century
stronger mono-alphabetic ciphers --some used
several replacement symbols for each letter, for
common words
nulls were developed in middle ages
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Algorithm development (cont)
Roger Bacon described methods in 1200s
Geoffrey Chaucer included several ciphers
in his writings
Arabic knowledge of cryptology described
in an encyclopedia in 1412
growing use in European diplomacy
Leon Alberti devised a cipher wheel -more on that later
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Poly-alphabetic substitution cipher
attributed to Blaise de Vigenère is
objective: improve security by using multiple
mono-alphabetic substitution alphabets
define multiple full alphabet substitutions
each letter can be replaced by many others
use a key to select which alphabet is used for each
letter of the message
i-th letter of key specifies i-th alphabet to use
use each alphabet in turn, then repeat
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Poly-alphabetic example
plaintext
S O U N D A L A R M
key
C I P H E R C I P H
ciphertext U W J U H R N I G T
A-> ABCDEFGHIJKLMNOPQRSTUVWXYZ
C -> CDEFGHIJKLMNOPQRSTUVWXYZAB
I -> IJKLMNOPQRSTUVWXYZABCDEFGH
P -> PQRSTUVWXYZABCDEFGHIJKLMNO
H -> HIJKLMNOPQRSTUVWXYZABCDEFG
E -> EFGHIJKLMNOPQRSTUVWXYZABCD
R -> RSTUVWXYZABCDEFGHIJKLMNOPQ
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'S' uses alphabet 'C' maps to 'U'
'O' uses alphabet 'I' maps to 'W'
’U' uses alphabet 'P' maps to 'J’
etc
From letters to binary
Vernam (1918) uses binary, not letters
Ci = pi x ki
pi - ith binary digit of plaintext
ki - ith binary digit of key
Ci - ith binary digit of ciphertext
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One time pad
Army Signal Corp officer, Joseph
Mauborgne improved Vernam cipher
Use random key that was truly as long as
the message
cipher output is random -- has no
statistical relationship to plaintext
problem is that sender & receiver need to
have that long key -- different for each
message
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One time pad – the ultimate substitution technique
Rotor Machines
enciphering (& deciphering) is rote, tedious,
and error prone (if done manually)
Automation permits multiple (transposition)
stages
Rotor Machine consists of
keyboard
multiple rotors, each with 26 positions
pre-wired
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Rotor machine
A
B
C
D
E
…
A
B
C
…
U
Z
Z
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Fixed wiring
Motion
Code machine
Enigma: http://webhome.idirect.com/~jproc/crypto/enigma.html
 Simulated deciphering of Enigma using “Turing Bombe”:

http://library.thinkquest.org/28005/flashed/timemachine/courseofhistory/bombeapp.shtml
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WW II crypto machines
German Enigma -- three rotors and later
more
Japanese Purple -- broken by U.S.
Yamamoto planned attack after Pearl Harbor
U.S. fleet coming out of Pearl Harbor
plans known
hundreds of Japanese ships sunk
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Next
Block Ciphers
Backup Notes cracking polyalph
original method developed by Babbage and Kasiski use repetitions in ciphertext to give
clues as to period
look for same plaintext an exact period apart which results in the same ciphertext
of course, could also be random fluke
eg.
Plaintext: TOBEORNOTTOBE
Key:
NOWNOWNOWNOW
Ciphertext: GCXRCNACPGCXR
see repeated ciphertext "GCXR"
since repeats are 9 chars apart, guess period is 3 or 9
in general find a number of duplicated sequences collect all their
distances apart, look for common factors
remembering that some will be random flukes and need
to be discarded
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Backup Notes cracking polyalph (2)
in order to break a polyalphabetic cipher must
1. determine how many alphabets -- d -- were used: See Kasiski
method
2. separate ciphertext into d sections
3. Determine if each as a monoalphabetic value (if not, have a
wrong guess) by computing the frequency balance across the cipher
text (called an Index of Coincidence)
4. solve each as a monoalphabetic cipher using
- frequency distribution,
- common double & triple letters
- word boundaries
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Issues
What do the attacks on classical
techniques target?
What is a “perfect cipher” and why?
How important is redundancy in
cryptology?
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