Cryptography
History of Crypto
Based on Slides by
Alfred C. Weaver
References
Easy to read
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Authoritative (1652 references)
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Applied Cryptography, by Bruce Schneier
Historical
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Computer Networks, by Andrew Tanenbaum
Crypto, Stephen Levy
The Code Book, Simon Singh
AES (FIPS approved May 26, 2002)
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Info: http://csrc.nist.gov/encryption/aes/
Code: http://csrc.nist.gov/encryption/aes/
round2/r2algs-code.html
Privacy and Security
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What are they?
When do we need them?
Cryptography
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Symmetric key crypto (e.g., DES, IDEA, AES)
Public key crypto (e.g., RSA, PGP, GPG)
How powerful are they?
Digital signatures
Leads to SSL and SET
Privacy and Security
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Privacy
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data is available only to authorized users
imagine the complexity of a medical record,
with different parts visible to doctor, patient,
hospital, insurance company, social agencies,
courts, government
Security
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data is meaningless to an unauthorized user
security is achieved via cryptography
Security
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There are two kinds of security:
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one kind stops your kid brother from reading
your mail
the other kind stops major government
agencies from reading your files
We are talking about the latter
Security
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Locking a document in a safe is not
security.
Locking a document in a safe, giving the
safe to the best safecrackers in the world,
plus the design specs for the safe, plus as
many safes as they want, keyed to the
combinations they specify, and as much
time as they want...
If then they can’t open the safe, that’s
security!
Privacy and Security
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Some information is public and never
needs protection
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stock ticker
Mars Pathfinder images
airlines schedules
telephone books
university course offerings
vacation offerings
restaurant menus
electronic product catalogs
Privacy and Security
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Most e-commerce transactions need
serious security
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invoices
transactions
payments
medical records
Privacy and Security
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Weaver’s First Law states that electronic
commerce requires security algorithms
that are:
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easy to use (low hassle factor)
provably correct (low risk)
convenient (handle multiple data types)
universal (world-wide acceptance)
used only when needed (because they are
computationally expensive)
Cryptography
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Cryptography provides
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confidentiality
authentication
integrity
non-repudiation
Security achieved by
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intelligent storage on computer
encrypted transmission over the Internet
proper choice of encryption algorithm
secure management of encryption keys
Encryption
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The big picture
Plaintext
P
Ciphertext
C
Encryption
Algorithm
C=E(P)
Plaintext
P
Decryption
Algorithm
P=D(C)
D( E (P) ) = P
Cryptography
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The goal of cryptography is to protect the
data in such a way that one could freely
distribute encrypted data to everyone on
the planet, knowing that only authorized
users could reveal the plaintext
You would not intentionally do this, but
you could without fear of compromise
Caesar Cipher
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Shift the alphabet by three letters
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a becomes d
b becomes e
c becomes f, etc.
attack transmitted as dwwdfn
Suitable for Green Hornet decoder rings in
Cracker Jack boxes
Works for children, but that’s all
Substitution Cipher
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Circularly shift the alphabet by k
characters
Still no power because k < 26
Using N brute force trials, 1<=N<=25,
is guaranteed to reveal the plaintext
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P:
a
N=1: b
N=2: c
N=3: d
N=25:z
b
c
d
e
a
c
d
e
f
b
d
e
f
g
c
e
f
g
h
d
f
g
h
i
e
g
h
i
j
f
h
i
j
k
g
i
j
k
l
h
j
k
l
m
i
k
l
m
n
j
l
m
n
o
k
Monoalphabetic Substitution
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Make an arbitrary mapping between
plaintext and ciphertext
For simplicity, use just the English
alphabet
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a b c d e f g h i j k l m ...
q w e r t y u i o p a s d ...
Looks pretty hard to reverse
Monoalphabetic Substitution
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There are 26 ways to pick the first
substitution (although a=a may not be a
good one), 25 ways to pick the second, 24
ways to pick the third...
So 26! ~= 4 x 1026 possible mappings
Testing 106/sec would take 1013 years
Is it secure?
Substitution Cipher
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All natural languages have statistical
properties—in English:
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most
most
most
most
most
most
common
common
common
common
common
common
letters
digrams
trigrams
word endings
doubled letters
words
Letter Frequency
Letter
%
Letter
%
E
13.0 A
7.3
T
9.3
S
6.3
N
7.8
D
4.4
R
7.7
H
3.5
I
7.4
L
3.5
O
7.4
C
3.0
Frequency of Usage
Digrams
Trigrams
•th
•he
•at
•st
•an
•in
•ea
•nd
•er
•en
•re
•nt
•to
•es
•on
•ed
•ti
•the
•and
•tha
•hat
•ent
•ion
•for
•tio
•has
•edt
•tis
•ers
•res
•ter
•con
•ing
•men
Doubles
•ll
•tt
•ss
•ee
•pp
•oo
•rr
•ff
•cc
•dd
•nn
Endings
•e
•t
•s
•d
•n
•r
•y
Words
•the
•of
•are
•I
•and
•you
•a
•can
•to
•he
•her
•that
•in
•was
•is
•has
•it
•him
•his
Decrypting a Substitution Cipher
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Count relative frequency of letters,
digrams, trigrams, endings, doubles, and
words in the ciphertext
If you have enough encrypted text, it can
be analyzed and broken by high-speed
computers
But must have a body of encrypted text of
sufficient size to permit analysis
Substitution Ciphers
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Suppose we have a block of ciphertext
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ctbmn byctc btjds qxbns gstjc
btswx ctqtz cqvuj qjsgs tjqzz
and the text comes from an accounting
firm where we would expect the word
financial in communications
Look for pattern: _ x y _ y _ x _ _
Transposition Ciphers
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Need to break the relationship between
repeated letters in the plaintext resulting
in repeated letters in the ciphertext
Try a transposition cipher
Transposition Cipher
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Pick a word with no repeated letters
Write it horizontally
Number the columns in alphabetic order
Write the plaintext beneath it in wordwrapped rows
Read out the ciphertext in columns,
starting with column 1, then 2, ...
Transposition Cipher
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M
7
p
a
e
d
o
b
u
o
E
4
l
n
m
o
m
a
n
t
G
5
e
s
i
l
y
n
t
w
A
1
a
f
l
l
s
k
s
o
B
2
s
e
l
a
w
a
i
a
U
8
e
r
i
r
i
c
x
b
C
3
t
o
o
s
s
c
t
c
K
6
r
n
n
t
s
o
w
d
PLAINTEXT:
please transfer one
million dollars to
my swiss bank
account six two two
CIPHERTEXT:
afllsksoselawaia
toossctclnmomant
esilyntwrnntsowd
paedobuoeriricxb
Transposition Cipher
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To break it:
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must know it is a transposition cipher
look at frequency of letters
if normal frequency, code is probably transposition
cipher since each letter represents itself
guess the code word length
guess the order of columns
try all combinations of number of columns and order
of columns
complicated and difficult, but that’s what computers
are for
Transposition Cipher
I
3
m
a
l
m
N
5
o
c
a
i
T
8
v
r
w
d
E
2
e
o
a
n
R
7
a
s
r
i
C
1
r
s
e
g
O
6
m
d
a
h
M
4
y
e
t
t
PLAINTEXT:
move army across
delaware at
midnight
CIPHERTEXT:
rsegeoanmalmyett
ocaimdahasrivrwd
Jefferson Cipher Wheel
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Thomas Jefferson designed an ingenious
way to encode and decode messages
while serving as Sec. State in 1790-93
This is a reproduction at Monticello
Jefferson Wheel Cipher
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Twenty-six cylindrical wooden pieces threaded
onto an iron bar
Each wheel had all 26 characters in random
order around the circumference
Wheels are numbered 1-26 and can be
assembled in any order
Jefferson Wheel Cipher
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Assemble the 26 wheels in some order (and
remember it)
Spin wheels to align a message (up to 26
characters) on one line
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Look at any other line (say the one above or
below) and read what is there
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THOMASJEFFERSONWASAGOODMAN
JRPNFJTIAHREIDBRPFDKEJSBGJTHDKS
Transmit the encoded message
The wheel ordering must be known to the
receiver via some other method
Jefferson Wheel Cipher
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Receiver assembles wheels in proper
order
Set wheel to display the encoded message
Look at the other 25 rows—one will make
sense and that’s the message
Double Encryption
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Obviously, you can encrypt with one
scheme, then encrypt the ciphertext with
another scheme
Adds to complexity
May or may not add to security (depends
upon your choices)
Using two successive monoalphabetic
substitution ciphers is more complex, but
not more secure
One-Time Pad
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One-time pad is mathematically
unbreakable!
Choose a random bit string as a key
Convert plaintext into bitstring
Compute exclusive-or of the two strings
Ciphertext contains no redundancy
information because every combination is
equally likely
One-Time Pad
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K=10101010 10101010 10101010
P= 01100011 01100001 01110100
C=11001001 11001011 11011110
‘c’=9910=011000112
‘a’=9710=011000012
‘t’=11610=011101002
Decrypt: exclusive-or of the ciphertext with the key
reveals the plaintext
One-Time Pad
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Key must be at least as long as message
Key can not be memorized (too long), so
has to be written down and shared
between transmitted and receiver
Anything written down is dangerous
Key could be a few gigabits of random
data embedded in a music CD prefixed by
a few songs to avoid suspicion
One-Time Pad
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Generating, remembering, storing,
transferring, recalling, and using the key
are all potential vulnerabilities of the
overall end-to-end system (not the
algorithm itself)
Physical one-time pads used in WW II
One-Time Pad
key=‘cat’= 01100011 01100001 01110100
P=‘dog’= 01100100 01100100 01100111
C= 00000111 00000101 00010011
‘d’=10010=011001002
‘o’=11110=011011112
‘g’=10310=011001112
Fundamental Realization
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Anything based upon a secret (hardware
design, software details, algorithm,
techniques, locations) has a fundamental
vulnerability
Secrets don’t keep
Can bribe or torture designers and/or
users to reveal secrets
Design has to be open (public)
Thus, must minimize reliance on secrets
or sharing of secrets
Modern Cryptography
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Uses encryption with a key
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sender and receiver share the same algorithm
algorithm is public
assume eavesdropper knows the algorithm
assume eavesdropper can see all the
ciphertext
All the security is in the key, none in the
algorithm
Key is a secret, and thus a vulnerability
Two Main Classes
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Symmetric key encryption
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sender and receiver share the same key
key must remain a secret for the lifetime of
the encrypted message
Public key encryption
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uses a two-part key, one part public and one
part private
private key is never shared
encrypt with public key
decrypt with private key
private key must remain secret forever
The Big Difference
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Symmetric key is fast
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Public key is arbitrarily powerful and there
is no key to share
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sharing the key is its vulnerability
slow to compute
keys require management
So today we use both
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generate a random symmetric key and use
that to encode data
use PKC to encrypt and transmit the
symmetric key