1. CSCE 790G: Computer Network Security
Chin-Tser Huang
University of South Carolina

2. Cryptography Can be characterized by
type of encryption operations used
substitution / transposition / product
number of keys used
single-key or shared / two-key or public
way in which plaintext is processed
block / stream
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3. Security of Cryptography
Unconditional security
no matter how much computer power is available, the cipher cannot be broken since the ciphertext provides insufficient information to uniquely determine the corresponding plaintext
Computational security
given limited computing resources (eg. time needed for calculations is greater than age of universe), the cipher cannot be broken
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4. Cryptographic Tools To Be Used
Shared keys
Public and private keys
Hashing functions and message digest
Nonces
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5. Symmetric Encryption Sender and receiver share a common key
All classical encryption algorithms belong to this type
Was only type prior to invention of public-key in 1970’s
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6. Basic Terminology plaintext - the original message
ciphertext - the coded message
cipher - algorithm for transforming plaintext to ciphertext
key - info used in cipher known only to sender/receiver
encipher (encrypt) - converting plaintext to ciphertext
decipher (decrypt) – restoring plaintext from ciphertext
cryptography - study of encryption principles/methods
cryptanalysis (codebreaking) - the study of principles/ methods of deciphering ciphertext without knowing key
cryptology - the field of both cryptography and cryptanalysis
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7. Types of Cryptanalytic Attacks
Ciphertext only
only know algorithm, ciphertext, and statistics
can identify plaintext
Known plaintext
know/suspect plaintext & ciphertext
Chosen plaintext
select plaintext and obtain ciphertext
Chosen ciphertext
select ciphertext and obtain plaintext
Chosen text
select either plaintext or ciphertext to encrypt or decrypt
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8. Symmetric Cipher Model
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9. Requirements Two requirements for secure use of symmetric encryption
a strong encryption algorithm
a secret key K known only to sender and receiver
Y = EK(X)
X = DK(Y)
Assume encryption algorithm is known
Imply a secure channel used to distribute key
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10. Classical Substitution Ciphers
Letters of plaintext are replaced by other letters, by numbers, or by symbols
If plaintext is viewed as a sequence of bits, then substitution involves replacing plaintext bit patterns with ciphertext bit patterns
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11. Caesar Cipher Earliest known substitution cipher
Invented by Julius Caesar
First attested use in military affairs
Replace each letter by letter three places down the alphabet
For example,
meet me after the toga party
PHHW PH DIWHU WKH WRJD SDUWB
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12. Mechanism of Caesar Cipher
Can define transformation as
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
Or assign each letter a number
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
In general, Caesar cipher can be specified as
C = E(p) = (p + k) mod (26)
p = D(C) = (C – k) mod (26)
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13. Cryptanalysis of Caesar Cipher
Only 26 possible ciphers
“A” maps to “A”, “B”, ... “Z”
Can easily break with brute-force cryptanalysis
Given ciphertext, just try all 26 ciphers
Need to recognize the original plaintext
eg. break ciphertext "GCUA VQ DTGCM"
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14. Monoalphabetic Cipher
Rather than just shifting the alphabet
Can shuffle the letters arbitrarily
Each letter in plain alphabet maps to a different random letter in cipher alphabet
Hence key is 26 letters long
For example,
Plain: abcdefghijklmnopqrstuvwxyz
Cipher: DKVQFIBJWPESCXHTMYAUOLRGZN
Plaintext: ifwewishtoreplaceletters
Ciphertext: WIRFRWAJUHYFTSDVFSFUUFYA
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15. Monoalphabetic Cipher Security
Now have a total of 26!  4 x 1026 keys
With so many keys, might think is secure
Still has problem: natural language characteristics
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16. Language Characteristics and Cryptanalysis
Letters are not equally commonly used
In English, “E” is by far the most common letter, followed by “T”, “R”, “N”, “I”, “O”, “A”, “S”
Other letters “Z”, “J”, “K”, “Q”, “X” are rarely used
Have tables of single, double & triple letter frequencies
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17. English Letter Frequencies
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18. Cryptanalysis of Caesar Cipher and Monoalphabetic Cipher
Fact: monoalphabetic substitution ciphers do not change relative letter frequencies
Discovered by Arabian scientists in 9th century
Calculate letter frequencies for ciphertext
Compare counts/plots against known values
For Caesar cipher, look for common peaks and troughs
peaks at: A-E-I triple, NO pair, RST triple
troughs at: JK, X-Z
For monoalphabetic, must identify each letter
tables of common double/triple letters help
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19. Example Cryptanalysis
Given ciphertext:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
Count relative letter frequencies
Guess “P” and “Z” are “e” and “t”
Guess “ZW” is “th” and hence “ZWP” is “the”
Proceeding with trial and error finally get:
it was disclosed yesterday that several informal but
direct contacts have been made with political
representatives of the viet cong in moscow
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20. Playfair Cipher
Not even the large number of keys in a monoalphabetic cipher provides security
One approach to improving security was to encrypt multiple letters
Playfair cipher is an example
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21. Playfair Key Matrix A 5X5 matrix of letters based on a keyword
Fill in letters of keyword (sans duplicates)
Fill rest of matrix with other letters
Eg. using the keyword MONARCHY
M O N A R
C H Y B D
E F G I/J K
L P Q S T
U V W X Z
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22. Encrypting and Decrypting
plaintext encrypted two letters at a time
if a pair is a repeated letter, insert a filler like “X” eg. “balloon” encrypts as “ba lx lo on”
if both letters fall in the same row, replace each with letter to right (wrapping back to start from end) eg. “ar” encrypts as “RM”
if both letters fall in the same column, replace each with the letter below it (again wrapping to top from bottom) eg. “mu” encrypts to “CM”
otherwise each letter is replaced by the one in its row in the column of the other letter of the pair eg. “hs” encrypts to “BP”, and “ea” to “IM” or “JM” (as desired)
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23. Security of Playfair Cipher
Security much improved over monoalphabetic
Have 26 x 26 = 676 digrams
Would need a 676 entry frequency table to analyze (verses 26 for a monoalphabetic)
Also need correspondingly more ciphertexts
Can still be broken since still has much of plaintext structure
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24. Polyalphabetic Ciphers
Use multiple cipher alphabets to improve security
Make cryptanalysis harder with more alphabets to guess and flatter frequency distribution
Use a key to select which alphabet is used for each letter of the message
Use each alphabet in turn
Repeat from start after end of key is reached
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25. Vigenère Cipher
Simplest polyalphabetic substitution cipher which effectively multiply Caesar ciphers
Key is multiple letters long K = k1 k2 ... kd
ith letter specifies ith alphabet to use
Use each key letter as a Caesar cipher key
Eg. using keyword deceptive
key: deceptivedeceptivedeceptive
plaintext: wearediscoveredsaveyourself
ciphertext:ZICVTWQNGRZGVTWAVZHCQYGLMGJ
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26. Security of Vigenère Ciphers
Have multiple ciphertext letters for each plaintext letter: obscure letter frequencies a bit
Start with letter frequencies
see if look monoalphabetic or not
if not, need to determine number of alphabets
Repetitions in ciphertext give clues to period
Find same plaintext an exact period apart which results in the same ciphertext (could also be random fluke)
Eg. repeated “VTW” in previous example suggests size of 3 or 9
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27. Autokey Cipher
To eliminate periodic nature of keyword, prefix keyword to message as key
Knowing keyword can recover the first few letters
Use these in turn on the rest of the message
Eg. given key deceptive
key: deceptivewearediscoveredsav
plaintext: wearediscoveredsaveyourself
ciphertext:ZICVTWQNGKZEIIGASXSTSLVVWLA
Still have frequency characteristics to attack
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28. One-Time Pad
If use a truly random key as long as plaintext, cipher will be secure
Unbreakable
ciphertext bears no statistical relationship to the plaintext
for any plaintext and any ciphertext there exists a key mapping one to other
Can only use the key once
Problems
overhead of making large number pf random keys
safe distribution of key
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29. Transposition Ciphers
Hide message by rearranging order of letters
Without altering the actual letters used
Can recognize these since they have the same frequency distribution as the original text
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30. Rail Fence Cipher
Write message letters out diagonally over a number of rows
Then read off cipher row by row
For example, write message out as
m e m a t r h t g p r y
e t e f e t e o a a t
and get ciphertext as
MEMATRHTGPRYETEFETEOAAT
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31. Row Transposition Ciphers
A more complex scheme
Write letters of message out in rows over a specified number of columns
Then reorder the columns according to some key before reading off the rows
Key:
Plaintext: a t t a c k p
o s t p o n e
d u n t i l t
w o a m x y z
Ciphertext: TTNAAPTMTSUOAODWCOIXKNLYPETZ
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32. Product Ciphers
Ciphers using substitutions or transpositions are not secure because of language characteristics
Hence consider using several ciphers in succession to make it harder to break
two substitutions make a more complex substitution, but still a substitution
two transpositions make a more complex transposition, but still a transposition
but a substitution followed by a transposition makes a new much harder cipher
Significance: bridge from classical to modern ciphers
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33. Rotor Machines
Before modern ciphers, rotor machines were most common product cipher
Were widely used in WW2
German Enigma, Allied Hagelin, Japanese Purple
Implement a very complex, varying substitution cipher
Use a series of cylinders, each giving one substitution, which rotate and change after each letter was encrypted
With 3 cylinders, have 263=17576 alphabets
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34. An Example of Rotor Machine
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35. Steganography An alternative to encryption Hide existence of message
using only a subset of letters/words in a longer message marked in some way
using invisible ink
hiding in LSB in graphic image or sound file
Has drawbacks
high overhead to hide relatively few info bits
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36. Next Class Block ciphers Modern symmetric encryption standard
Read Chapter 3
Have a nice long weekend!
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