Transcript Document 7482104

CSCE 790G:
Computer Network Security
Chin-Tser Huang
[email protected]
University of South Carolina
Cryptography
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Can be characterized by
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type of encryption operations used
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number of keys used
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substitution / transposition / product
single-key or shared / two-key or public
way in which plaintext is processed
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block / stream
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Security of Cryptography
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Unconditional security
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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
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given limited computing resources (eg. time
needed for calculations is greater than age of
universe), the cipher cannot be broken
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Cryptographic Tools To Be Used
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Shared keys
Public and private keys
Hashing functions and message digest
Nonces
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Symmetric Encryption
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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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Basic Terminology
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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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Types of Cryptanalytic Attacks
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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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Symmetric Cipher Model
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Requirements
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Two requirements for secure use of
symmetric encryption
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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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Classical Substitution Ciphers
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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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Caesar Cipher
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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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Mechanism of Caesar Cipher
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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
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Or assign each letter a number
a b c
0 1 2
n o
13 14
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d e f
3 4 5
p q
15 16
g h i
6 7 8
r s
17 18
j k l m
9 10 11 12
t u v w x y Z
19 20 21 22 23 24 25
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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Cryptanalysis of Caesar Cipher
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Only 26 possible ciphers
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Can easily break with brute-force
cryptanalysis
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“A” maps to “A”, “B”, ... “Z”
Given ciphertext, just try all 26 ciphers
Need to recognize the original plaintext
eg. break ciphertext "GCUA VQ DTGCM"
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Monoalphabetic Cipher
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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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Monoalphabetic Cipher Security
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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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Language Characteristics and
Cryptanalysis
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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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English Letter Frequencies
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Cryptanalysis of Caesar Cipher
and Monoalphabetic Cipher
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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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Example Cryptanalysis
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Given ciphertext:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
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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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Playfair Cipher
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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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Playfair Key Matrix
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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
C
E
L
U
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H
F
P
V
N A R
Y B D
G I/J K
Q S T
W X Z
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Encrypting and Decrypting
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plaintext encrypted two letters at a time
1.
2.
3.
4.
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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Security of Playfair Cipher
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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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Polyalphabetic Ciphers
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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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Vigenère Cipher
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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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Security of Vigenère Ciphers
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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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Autokey Cipher
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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
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Still have frequency characteristics to attack
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One-Time Pad
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If use a truly random key as long as plaintext,
cipher will be secure
Unbreakable
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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
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overhead of making large number pf random keys
safe distribution of key
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Transposition Ciphers
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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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Rail Fence Cipher
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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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Row Transposition Ciphers
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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:
3 4 2 1 5 6 7
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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Product Ciphers
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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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Rotor Machines
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Before modern ciphers, rotor machines were
most common product cipher
Were widely used in WW2
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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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An Example of Rotor Machine
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Steganography
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An alternative to encryption
Hide existence of message
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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
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high overhead to hide relatively few info bits
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Next Class
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Block ciphers
Modern symmetric encryption standard
Read Chapter 3
Have a nice long weekend!
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