Encryption
Discrete Math
March 7, 2006
Harding University
Jonathan White
Outline
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Terms
Types of Attacks
Classical Techniques
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Substitution:
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Caesar
Monoalphabetic
Playfair
Shifting:
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Rail Fence Cipher
Rotor Machines (Enigma)
Outline (2)
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Data Encryption Standard (DES)
Triple DES
 Blowfish
 MD5, SHA-1
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RSA
 Quantum Computers
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Terms
Plaintext
 Ciphertext
 Cipher
 Key
 Cryptography
 Symmetric Encryption
 Asymmetric Encryption
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Terms
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Security by Obscurity
Brute Force Search Attack
Dictionary Attack
Man in the Middle Attack
Cipher Attacks
Plaintext Attacks
Steganography
Unconditional security
Computational security
Brute Force Attacks

Brute Force Searches:
Simply try every possible key
 Effort required is proportionate to the key size
 You must recognize the plaintext once you
see it!
 Typically uses no knowledge about the cipher,
the cipher text, or the plaintext, so it is very
easy to do.
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Dictionary Attacks
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For this attack, you have already encrypted a
large amount of plaintext.
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You simply search what you’ve already encrypted for
a match.
This is how most password crackers work.
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Is your password something common like:
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An English word?
A variation of your username?
Numbers or letters at the beginning or end appended to the
above?
Blank?
Guessing, along with dictionary attacks, have
proven to break ~50% of all passwords.
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Older Unix systems only allow 8 character passwords
Plaintext Attacks
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Plaintext Attacks
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Attack the language the plaintext was written
in
 Human

languages are very redundant
Ever seen Wheel of Fortune?
 ASCII
characters are also very predictable
 C++/Java/Lisp code is very redundant
 Military communications are very redundant
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Most ciphers overcome this by appending a
bit of random characters to the end of the
message
 Called
padding.
Cipher Attacks
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Attack something that is known about the cipher
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For example, if you encrypt 0 and 1 in RSA, the
ciphertext is the exact same
Ciphers typically have periodic behavior, which
can be attacked.
However, most modern ciphers have been
extensively studied and have very few potential
attacks.
No “Security by Obscurity”
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In fact, you want people to try and crack your cipher –
it just makes you look better when they can’t crack it.
Unconditional Security
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Very difficult to provide.
One of the only known unconditional secure
algorithms is a random, one time pad, key that is
as long as the message.
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Since the key is completely random, you can just add
the letters in the key and the message together and
send them. The cipher text bears no statistical
relationship between the plaintext.
You can only use the key once though.
However, how do you distribute the key?
Russian nuclear crisis.
Classical Substitution Ciphers
Where letters of the plaintext are replaced
by other letters or symbols.
 Or, if viewed as bit patterns, a sequence of
bits in the plaintext is replaced with a
sequence of bits in the plaintext.
 Very easy to use.
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They’ve been around the longest.
The key is the mapping that you used from
the plaintext to the cipher text.
Caesar Cipher
Earliest known substitution cipher.
 Used in military affairs.
 Replaces each letter in the plaintext by the
nth letter down in the alphabet, wrapping
back around.
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In this case, the key is just the shift number
that you chose.
To unencrypt, you just subtract the n from
the ciphertext to get the original.
Caesar Example
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Encrypt this message with a shift of 5:
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The brown fox ate the sheep
Plaintext
Shift
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
MEQEWXYHIRX
LDPDVWXGHQW
KCOCUVWFGPV
JBNBTUVEFOU
IAMASTUDENT
HZLZRSTCDMS
GYKYQRSBCLR
FXJXPQRABKQ
EWIWOPQZAJP
DVHVNOPYZIO
CUGUMNOXYHN
BTFTLMNWXGM
ASESKLMVWFL
ZRDRJKLUVEK
YQCQIJKTUDJ
XPBPHIJSTCI
WOAOGHIRSBH
VNZNFGHQRAG
UMYMEFGPQZF
TLXLDEFOPYE
SKWKCDENOXD
RJVJBCDMNWC
QIUIABCLMVB
PHTHZABKLUA
OGSGYZAJKTZ
Cryptanalysis of Caesar
Only have 26 possible orders.
 Very easy to defeat using brute force.
 You do need to recognize when you have
the plaintext, however.
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Monoalphabetic Cipher
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Rather than just shifting the alphabet, you could
just jumble the letters arbitrarily.
Each plaintext letter then maps to a different
ciphertext letter.
The key is then 26 characters long.
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So, we have 26! possible keys.
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But, this does not conceal the language
characteristics.
Also, tables exist for double and triple letter
frequencies such as “ing”, “th”, “ou”, etc…
These ciphers don’t change the relative letter
frequencies.
Monoalphabetic Example
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Let the key and plaintext be :
QWERTYUIOPASDFGHJKLZXCVBNM
 If we wish to replace these letters
 GO TO THE MALL
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The ciphertext is:
Playfair Cipher
A 5 x 5 matrix of letters based on a
keyword.
 Fill in letters of keyword without duplicates
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Then, just fill in the rest of the matrix with the
rest of the alphabet going in order.
 J and I are the same letter in the playfair
cipher; so, there are only 25 letters in the
alphabet.
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Playfair Encrypting/Decrypting
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Plaintext is encrypted 2 letters at a time:
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If a pair is a repeated letter, insert a filler letter like “x”
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If both letters fall in the same row, replace ach with
the letter to the right (wrapping back to start from the
end)
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Exp: “ar” encrypts as “rm”
If both letters fall in the same column, replace each
with the letter below it, wrapping bottom to top.
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Exp: balloon becomes ba lx lo on
Exp: “mu” encrypts as “cm”
Otherwise, each letter is replaced by the one in its
row in the column of the other letter of the pair.
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Exp: “hs” encrypts to “bp”, “ea” encrypts to “im”
Playfair Security
We have 25 x 25 potential combinations =
625! potential ways to encrypt.
 Widely used for many years, including
WW1.
 But, it can be broken, given a few hundred
letters.
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With a computer, this is quite simple, because
some of the plaintext structure still remains.
Transposition Ciphers
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These hide the message by rearranging
the letter order.
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The actual letters aren’t altered.
However, the ciphertext will still have the
same relative frequency as the original
text.
 These are typically incredibly quick.
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Rail Fence Cipher
Write your message horizontally across a
narrow sheet of paper.
 Wrap the paper around a circular post that
both you and the person you wish to send
the message to both posses one of.
 Then, just write down the letters you see
starting at the top of the post.
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Very insecure.
The Enigma Machine
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Used by the Germans in WW2 to
encrypt and decrypt messages.
Used a series of rotors connected
to a complex electrical circuit and
some initial letter swaps to encrypt
messages.
Produced incredibly strong
encryption for its time.
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Decryption was exactly the same as
encryption – provided you knew the
starting position.
http://www.enigmaco.de/enigma.sw
f
Enigma Machine 2
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The interesting thing about the Enigma is that the
substitution pattern changes after every keystroke.
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No longer just a simple substitution cipher.
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There are 263 possible start positions for the rotors.
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This would be relatively easy to solve.
But, this does remove a lot of the letter frequencies apparent in the
German language.
There are still 26! ways to substitute the original letters.
Altogether, (if a few mishaps hadn’t occurred), this
cipher can’t be beat by humans.
Enigma Machine 3
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Mishaps:
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Letters couldn’t encrypt to themselves.
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Repeating the same greeting in every message.
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Mother/Father/Girlfriend’s name, city, favorite soccer team…
Stolen codebooks
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Please Respond, Dear, weather reports…
Always using “X” for the space key.
Letting operators always choose their passphrase.
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Sometimes test messages were sent by lazy operators that only
used one letter.
Helps for a little while…
Stolen machines
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What really allowed the Polish and British intelligence agencies
to crack the Enigma.
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Only around 15 machines were ever captured.
Enigma Machine 4
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In order to test potential codes, the Americans
designed one of the first computers. This was
aided by Alan Turing, a British citizen.
By the end of the war, all Enigma communications
could be broken in under 3 days. However, the
Allies didn’t always use this information.
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Battle of the Bulge.
Many officials have estimated that by cracking the
Enigma, WW2 ended 1 year earlier than it would
have.