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INTRODUCTION
to
CRYPTOGRAPHY
Fred Piper
Codes & Ciphers Ltd
12 Duncan Road, Richmond
Surrey, TW9 2JD
ENGLAND
Royal Holloway, University of London
Egham Hill, Egham
Surrey TW20 0EX
ENGLAND
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Sender
Am I happy that the whole world sees this ?
What am I prepared to do to stop them ?
What am I allowed to do to stop them ?
Recipient
Do I have confidence in :
the originator
the message contents and message stream
no future repudiation.
Network Manager
Do I allow this user on to the network ?
How do I control their privileges ?
Some Security Issues
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Cipher System
cryptogram
c
Enciphering
Algorithm
Deciphering
Algorithm
Key
k(E)
Key
k(D)
message
m
message
m
Interceptor
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The Attacker’s Perspective
Deciphering
Algorithm
Unknown Key
k(D)
Known
c
Wants
m
Note
:
k(E)
is not needed unless
it helps determine
k(D)
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Two Types of Cipher System
•
Conventional or Symmetric
k(D)
easily obtained from
k(E)
•
Public or Asymmetric
Computationally infeasible to determine
k(D)
from
k(E)
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Mortice Lock.
If you can lock
it, then you can
unlock it.
Bevelled Sprung Lock.
Anyone can lock it,
only keyholder can
unlock it.
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Types of Attack
•
Ciphertext only
•
Known plaintext
•
Chosen ciphertext
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Assumptions About Attacker (1)
Military/Government:
Try to keep details of system (including algorithm)
secret
Worst Case Conditions:
Commercial:
Assume he knows:
System (including algorithm)
All ciphertext
Some corresponding plaintext/ ciphertext
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Warning
THE FACT THAT AN ALGORITHM HAS
BEEN PUBLISHED SAYS NOTHING
ABOUT ITS STRENGTH.
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Breaking Algorithm
•
Finding a method of determining
message from cryptogram without
being given deciphering key.
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Exhaustive Key Search Attacks
•
The security depends on the secrecy of
the deciphering key.
•
One potential attack, if the algorithm is
known, is to try all possible deciphering
keys and to eliminate all incorrect ones.
•
To withstand this type of attack a large key
space is required.
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Exhaustive Key Searches
Estimating time required for key
search requires assumptions about the
attacker’ resources
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Saints or Sinners ?
Receiver
Interceptor
Sender
Who are the ‘good’ guys ?
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If Someone Wants Your Plaintext
•
Give it to them
•
Give them the decryption key
•
They may break algorithm
•
They may ‘find’ plaintext in system
•
They may ‘find’ key in system
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Practical Considerations when Implementing
Encryption
•
Key management is the difficult part
•
Keys need to be generated, distributed,
stored, changed securely
•
History shows that most cryptanalytic
attacks exploit poor implementation
and/or key management
Example: Enigma in World War 2
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Cryptography is used to provide:
1.
Confidentiality
2.
Data Integrity
3.
Entity/Origin Verification
4.
Non

Repudiation
5.
Access Control
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Choosing an Algorithm
The choice of algorithm depends upon
the application.
Applications of encryption include :
•
Data confidentiality
•
Data integrity
•
Digital Signatures.
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Misuse of Encryption
Grade
Good student
xxxxx
Bad student
xxxxx
Grades can be changed
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Classification of Techniques
•
Bit / Block operation
•
Positional dependence/independence
•
Message dependence/independence
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Vernam Cipher
Random sequence
k
1
,k
2
,…,k
n
Message
m
1
,m
2
,…,m
n
+
Ciphertext
k
1
m
1
,k
2
m
2
,…,k
n
m
n
The message and key are bit strings
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Stream Cipher
Plaintext data
Keystream
sequence
Ciphertext
Key
Sequence
Generator
XOR
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Stream Cipher
•
Enciphers bit by bit
•
Positional dependence
•
Security depends on properties of
the keystream
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Stream Ciphers
Applications
•
Widely used for military and
paramilitary applications for both data
and digitised speech
•
The main reason for their wide use is
that military communications are
often over poor channels and error
propagation is unacceptable
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Symmetric Block Cipher System
Key dependent
permutation
on
s

bit blocks
s

bit
plaintext block
s

bit
ciphertext block
Key
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Block Ciphers : Key Sizes
•
Depends on security requirement
•
Key searches on size 2
90
are
currently considered infeasible
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DES: Key Search on Internet (1997)
DES has 2
56
keys
DES key found
Search took 140 days
Search used over 10,000 computers
Peak rate: 7.10
9
keys/sec
‘Might’ have taken 32 days
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DES Breaker (1998)
Electronic Frontier Foundation
Design cost
$ 80,000
Manufacturing cost
$130,000
Test key found in
56 hours
Complete search in
220 hours
90 Billion keys per second
Design details published
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DES : Double Length Key
k = (k1,k2)
k1,k2 DES keys
E
k
(m) = E
k1
(D
k2
(E
k1
(m)))
key is 112 bits
key search with 2
112
trials is
infeasible.
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Advanced Encryption Standard
(AES)
•
Block ciphers
•
Block size 128 bits
•
Key lengths 128, 192, 256 bits
•
Must be faster than triple DES
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AES (Continued)
June 1998
:
15 candidates
August 1998
:
11
April 1999:
5
Decision
October 2000
Rijndael
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The following slides will not be
discussed but are included for
completeness
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Applications
•
Access Control
•
Authentication
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The Challenge / Response Principle
Key
Key
Random
number
Challenge
PIN

Controlled
A
A
Response
A

Encipher or OWF
Y/N
= ?
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Digital Signatures
According to ISO, the term Digital
Signature is used: ‘to indicate a
particular authentication technique
used to establish the origin of a
message in order to settle disputes of
what message (if any) was sent’.
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Digital Signatures
A signature on a message is some data
•
that validates a message and verifies its origin
•
a receiver can keep as evidence
•
a third party can use to resolve disputes.
It depends on
•
the message
•
a secret parameter only
•
available to the sender
It should be
•
easy to compute
•
(by one person only)
•
easy to verify
•
difficult to forge
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Principle of Digital Signatures
There is a (secret) number which:
•
Only one person can use
•
Is used to identify that person
•
‘Anyone’ can verify that it has been
used
NB:
Anyone who knows the value of a
number can use that number.
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Certification Authority
Aim :
To guarantee the authenticity of public keys.
Method :
The Certification Authority guarantees the
authenticity by signing a certificate containing
user’s identity and public key with its secret key.
Requirement :
All users must have an authentic copy of the
Certification Authority’s public key.
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Certification Process
Verifies
credentials
Creates
Certificate
Receives
(and checks)
Certificate
Presents Public
Key and
credentials
Generates
Key Set
Distribution
Centre
Owner
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How Does it Work?
The Certificate can accompany all Fred’s
messages
The recipient must directly or indirectly:
•
Trust the CA
•
Validate the certificate
The CA certifies
that Fred Piper’s
public key
is………..
Electronically
signed by
the CA
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Fundamental Requirement
Internal infrastructure to support
secure technological implementation
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