Transcript Classical Cryptography

Cryptography
What is cryptography?
kryptos – “hidden”
 grafo – “write”


Keeping messages secret
 Usually
by making the message unintelligible
to anyone that intercepts it
The Problem
Private Message
Bob
Alice
Eavesdropping
Eve
The Solution
Private Message
Private Message
Encryption
Decryption
Scrambled Message
Bob
Alice
Eavesdropping
Eve
What do we need?
Bob and Alice want to be able to
encrypt/decrypt easily
 But no one else should be able to decrypt
 How do we do this?

 Keys!
Using Keys
Nonsense
Encryption
Plaintext
Ciphertext
Decryption
Plaintext
The Shift Cipher

We “shift” each letter over by a certain
amount
Plaintext
five red balloons
Key = 3
f+3=I
i+3=L
v+3=Y
…
Encryption
ILYH UHG EDOORRQV Ciphertext
The Shift Cipher cont.

To decrypt, we just subtract the key
ILYH UHG EDOORRQV Ciphertext
Key = 3
I-3=f
L-3=i
Y-3=v
…
five red balloons
Decryption
Plaintext
What’s wrong with the shift cipher?
Not enough keys!
 If we shift a letter 26 times, we get the
same letter back

 A shift
of 27 is the same as a shift of 1, etc.
 So we only have 25 keys (1 to 25)

Eve just tries every key until she finds the
right one
The Substitution Cipher
Plaintext

Rather than having a
fixed shift, change
every plaintext letter
to an arbitrary
ciphertext letter
a
b
c
d
e
…
z
Ciphertext
G
X
N
S
D
…
Q
The Substitution Cipher cont.
Key =
a
G
n
B
b
X
o
Y
c
N
p
Z
d
S
q
P
e
D
r
H
f
A
s
W
g
F
t
I
h
V
u
J
i
L
v
R
j
M
w
U
k
C
x
K
l
O
y
T
m
E
z
Q
five red balloons
f =A
i =L
v =R
…
Plaintext
Encryption
ALRD HDS XGOOYYBW Ciphertext
The Substitution Cipher cont.

To decrypt we just look up the ciphertext letter in
the table and then write down the matching
plaintext letter

How many keys do we have now?
 A key
is just a permutation of the letters of the
alphabet
 There are 26! permutations

403291461126605635584000000
Frequency Analysis

In English (or any language) certain letters are
used more often than others

If we look at a ciphertext, certain ciphertext
letters are going to appear more often than
others

It would be a good guess that the letters that
occur most often in the ciphertext are actually
the most common English letters
Letter Frequency



This is the letter
frequency for
English
The most
common letter
is ‘e’ by a large
margin,
followed by ‘t’,
‘a’, and ‘o’
‘J’, ‘q’, ‘x’, and
‘z’ hardly occur
at all
Frequency Analysis in Practice

Suppose this is our ciphertext
 dq
lqwurgxfwlrq wr frpsxwlqj surylglqj d eurdg vxuyhb
ri wkh glvflsolqh dqg dq lqwurgxfwlrq wr surjudpplqj.
vxuyhb wrslfv zloo eh fkrvhq iurp: ruljlqv ri frpsxwhuv,
gdwd uhsuhvhqwdwlrq dqg vwrudjh, errohdq dojheud,
gljlwdo orjlf jdwhv, frpsxwhu dufklwhfwxuh,
dvvhpeohuv dqg frpslohuv, rshudwlqj vbvwhpv,
qhwzrunv dqg wkh lqwhuqhw, wkhrulhv ri
frpsxwdwlrq, dqg duwlilfldo lqwhooljhqfh.
0.12
Relative Frequency
0.1
0.08
0.06
0.04
0.02
0
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
Letter
Ciphertext distribution
English distribution
In our ciphertext we have one letter that occurs more often than any other (h), and
6 that occur a good deal more than any others (d, l, q, r, u, and w)
There is a good chance that h corresponds to e, and d, l, q, r, u, and w correspond
to the 6 next most common English letters
Frequency Analysis cont.

If we replace ‘e’ with ‘h’ and the 6 next most
common letters with their matches, the
ciphertext becomes
 an
intro???tion to ?o?p?tin? pro?i?in? a ?roa? ??r?e?
o? t?e ?i??ip?ine an? an intro???tion to pro?ra??in?.
??r?e? topi?? ?i?? ?e ??o?en ?ro?: ori?in? o?
?o?p?ter?, ?ata repre?entation an? ?tora?e, ?oo?ean
a??e?ra, ?i?ita? ?o?i? ?ate?, ?o?p?ter ar??ite?t?re,
a??e???er? an? ?o?pi?er?, operatin? ???te??,
net?or?? an? t?e internet, t?eorie? o? ?o?p?tation,
an? arti?i?ia? inte??i?en?e.
Classical to Modern Cryptography

Classical cryptography
 Everything
up until around WWII
 Encryption/decryption done by hand

Modern cryptography
 Computers
to encrypt and decrypt
 Same principles, but automation allows
ciphers to become much more complex
The Enigma Machine


German
encryption and
decryption
machine used in
WWII
Essentially a
complex,
automated
substitution cipher
How did Enigma work?

Rotors have different
wiring connecting input
to output

Rotors move after each
keypress

The key is the initial
position of the three
rotors
Breaking the Enigma


Britain set up its cryptanalysis team in
Bletchley Park
They consistently broke German codes
throughout the war


Provided the intelligence codenamed ULTRA
Important location in the history of computing


Alan Turing
COLOSSUS
Cryptography in the Computer Age

Working with binary instead of letters

We can do things many, many times
of an Enigma machine that has 2128 pairs of
symbols on each rotor, and 20 rotors
 Think

Other than that, the basic principles are the
same as classical cryptography
Modern Ciphers

We design one relatively simple scrambling method
(called a round) and repeat it many times



Think of each round as a rotor on the Enigma
One round may be easy to break, but when you put them all
together it becomes very hard
Almost all ciphers follow one of two structures



SPN (Substitution Permutation Network)
Feistel Network
These describe the basic structure of a round
Modern Ciphers in Practice

Follow SPN/Feistel structure in general,
but with added twists for security

There are two important ciphers in the
history of modern cryptography
 DES
(Data Encryption Standard)
 AES (Advanced Encryption Standard)
DES

U.S. Government recognized the need to have a
standardized cipher for secret documents

DES was developed by IBM in 1976

Analysis of DES was the beginning of modern
cryptographic research
Controversy Surrounding DES

Development process was hidden from
public
 Suspicions
that the government had put in a
“backdoor”

Government attempted to shut down
research in cryptography
Breaking DES

The key length of DES was too short
 If
a key is 56 bits long, that means there are
256 possible keys
 “DES Cracker” machines were designed to
simply try all possible keys
Breaking DES cont.

DES was further weakened by the discovery of differential
cryptanalysis



Ideally a ciphertext should be completely random, there should be
no connection to its matching plaintext



Biham and Shamir in 1990
The most significant advance in cryptanalysis since frequency analysis
Differential analysis exploits the fact that this is never actually the case
Uses patterns between plaintext and ciphertext to discover the key
There is evidence that IBM knew about differential cryptanalysis
back when they were designing DES in 1976
Developing the AES

With DES effectively broken, a new standard
was needed

U.S. Government made it an open
application/review process this time, and
received many submissions

In 2001, after five years, the Rijndael cipher was
selected to become the Advanced Encryption
Standard
The Problem of Symmetric Key
Cryptography

Up until now we’ve been talking about symmetric
key cryptography
 Alice
and Bob are using the same key to
encrypt/decrypt

Problem: How does Bob get the key to Alice
when Eve is eavesdropping?

Up until 1976 the only solution was to physically
give Alice the key in a secure environment
Public Key Cryptography



Diffie and Hellman published a paper in 1976
providing a solution
We use one key for encryption (the public key),
and a different key for decryption (the private
key)
Everyone knows Alice’s public key, so they can
encrypt messages and send them to her
 But

only Alice has the key to decrypt those messages
No one can figure out Alice’s private key even if
they know her public key
Using Public Keys
Nonsense
Encryption
Plaintext
Ciphertext
Decryption
Plaintext
Public Key Cryptography in
Practice

The problem is that public key algorithms are too
slow to encrypt large messages
 Instead
Bob uses a public key algorithm to send Alice
the symmetric key, and then uses a symmetric key
algorithm to send the message

The best of both worlds!
 Security
of public key cryptography
 Speed of symmetric key cryptography
Sending a Message
What’s your public key?
Bob picks a
symmetric key and
encrypts it using
Alice’s public key
Alice decrypts the
symmetric key using her
private key
Then sends the
key to Alice
Bob encrypts his
message using
the symmetric
key
Then sends the
message to
Alice
hi
Alice decrypts the
message using the
symmetric key
The RSA Public Key Cipher

The most popular public key cipher is RSA, developed in
1977


Named after its creators: Rivest, Shamir, and Adleman
Uses the idea that it is really hard to factor large
numbers




Create public and private keys using two large prime numbers
Then forget about the prime numbers and just tell people their
product
Anyone can encrypt using the product, but they can’t decrypt
unless they know the factors
If Eve could factor the large number efficiently she could get the
private key, but there is no known way to do this
Are we all secure now?

Unfortunately not, there are still many problems
that need to be dealt with
 How
does Bob know that he’s really talking to Alice?
 How does Alice know that the message she receives
hasn’t been tampered with?
 How does Alice know the message was sent by Bob?

These are questions addressed by other areas
of cryptography
The End