Transcript Why Computer Security concern for the security of information

Why Computer Security
• The past decade has seen an explosion in the
concern for the security of information
– Malicious codes (viruses, worms, etc.) caused over $28
billion in economic losses in 2003 and $67 billion in
2006!
• Security specialists markets are expanding !
– “Salary Premiums for Security Certifications
Increasing” (Computerworld 2007)
• Up to 15% more salary
• Demand is being driven not only by compliance and government
regulation, but also by customers who are "demanding more
security" from companies
– US Struggles to recruit compute security experts
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(Washington Post Dec. 23 2009)
Why Computer Security (cont’d)
• Internet attacks are increasing in frequency,
severity and sophistication
– The number of scans, probes, and attacks reported to
the DHS has increased by more than 300 percent
from 2006 to 2008.
– Karen Evans, the Bush administration's information
technology (IT) administrator, points out that most
federal IT managers do not know what advanced skills
are required to counter cyberattacks.
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Why Computer Security (cont’d)
• Virus and worms faster and powerful
– Cause over $28 billion in economic losses in 2003,
growing to over $75 billion in economic losses by 2007.
– Code Red (2001): 13 hours infected >360K machines $2.4 billion loss
– Slammer (2003): 15 minutes infected > 75K machines $1 billion loss
• Spams, phishing …
• New Internet security landscape emerging:
BOTNETS !
– Conficker/Downadup (2008): infected > 10M machines
• MSFT offering $250K reward
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Outline
• History of Security and Definitions
• Overview of Cryptography
• Symmetric Cipher
– Classical Symmetric Cipher
– Modern Symmetric Ciphers (DES and AES)
• Asymmetric Cipher
• One-way Hash Functions and Message Digest
4
The History of Computing
• For a long time, security was largely ignored in the
community
– The computer industry was in “survival mode”, struggling
to overcome technological and economic hurdles
– As a result, a lot of comers were cut and many
compromises made
– There was lots of theory, and even examples of systems
built with very good security, but were largely ignored
or unsuccessful
• E.g., ADA language vs. C (powerful and easy to use)
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Computing Today is Very Different
• Computers today are far from “survival mode”
– Performance is abundant and the cost is very cheap
– As a result, computers now ubiquitous at every facet
of society
• Internet
– Computers are all connected and interdependent
– This codependency magnifies the effects of any
failures
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Biological Analogy
• Computing today is very homogeneous.
– A single architecture and a handful of OS dominates
• In biology, homogeneous populations are in danger
– A single disease or virus can wipe them out overnight
because they all share the same weakness
– The disease only needs a vector to travel among hosts
• Computers are like the animals, the Internet
provides the vector.
– It is like having only one kind of cow in the world, and
having them drink from one single pool of water!
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The Spread of Sapphire/Slammer
Worms
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The Flash Worm
• Slammer worm infected 75,000 machines in <15
minutes
• A properly designed worm, flash worm, can take
less than 1 second to compromise 1 million
vulnerable machines in the Internet
– The Top Speed of Flash Worms. S. Staniford, D.
Moore, V. Paxson and N. Weaver, ACM WORM
Workshop 2004.
– Exploit many vectors such as P2P file sharing,
intelligent scanning, hitlists, etc.
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The Definition of Computer Security
• Security is a state of well-being of information
and infrastructures in which the possibility of
successful yet undetected theft, tampering,
and disruption of information and services is
kept low or tolerable
• Security rests on confidentiality, authenticity,
integrity, and availability
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The Basic Components
• Confidentiality is the concealment of information or
resources.
– E.g., only sender, intended receiver should “understand” message
contents
• Authenticity is the identification and assurance of the
origin of information.
• Integrity refers to the trustworthiness of data or
resources in terms of preventing improper and
unauthorized changes.
• Availability refers to the ability to use the information
or resource desired.
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Security Threats and Attacks
• A threat/vulnerability is a potential violation of
security.
– Flaws in design, implementation, and operation.
• An attack is any action that violates security.
– Active adversary
• An attack has an implicit concept of “intent”
– Router mis-configuration or server crash can also
cause loss of availability, but they are not attacks
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Friends and enemies: Alice, Bob, Trudy
• well-known in network security world
• Bob, Alice (lovers!) want to communicate “securely”
• Trudy (intruder) may intercept, delete, add messages
Alice
data
channel
secure
sender
Bob
data, control
messages
secure
receiver
data
Trudy
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Eavesdropping - Message Interception
(Attack on Confidentiality)
• Unauthorized access to information
• Packet sniffers and wiretappers
• Illicit copying of files and programs
B
A
Eavesdropper
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Integrity Attack - Tampering
With Messages
• Stop the flow of the message
• Delay and optionally modify the message
• Release the message again
B
A
Perpetrator
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Authenticity Attack - Fabrication
• Unauthorized assumption of other’s identity
• Generate and distribute objects under this
identity
A
B
Masquerader: from A
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Attack on Availability
• Destroy hardware (cutting fiber) or software
• Modify software in a subtle way (alias commands)
• Corrupt packets in transit
A
B
• Blatant denial of service (DoS):
– Crashing the server
– Overwhelm the server (use up its resource)
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Classify Security Attacks as
• Passive attacks - eavesdropping on, or
monitoring of, transmissions to:
– obtain message contents, or
– monitor traffic flows
• Active attacks – modification of data stream to:
– masquerade of one entity as some other
– replay previous messages
– modify messages in transit
– denial of service
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Group Exercise
Please classify each of the following as a
violation of confidentiality, integrity,
availability, authenticity, or some combination
of these
• John copies Mary’s homework.
• Paul crashes Linda’s system.
• Gina forges Roger’s signature on a deed.
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Outline
• Overview of Cryptography
• Symmetric Cipher
– Classical Symmetric Cipher
– Modern Symmetric Ciphers (DES and AES)
• Asymmetric Cipher
• One-way Hash Functions and Message Digest
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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) - recovering ciphertext from plaintext
• 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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Classification of Cryptography
• Number of keys used
– Hash functions: no key
– Secret key cryptography: one key
– Public key cryptography: two keys - public, private
• Type of encryption operations used
– substitution / transposition / product
• Way in which plaintext is processed
– block / stream
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Secret Key vs. Secret Algorithm
• Secret algorithm: additional hurdle
• Hard to keep secret if used widely:
– Reverse engineering, social engineering
• Commercial: published
– Wide review, trust
• Military: avoid giving enemy good ideas
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Unconditional vs. Computational Security
• Unconditional security
– No matter how much computer power is available, the
cipher cannot be broken
– The ciphertext provides insufficient information to
uniquely determine the corresponding plaintext
• Computational security
– The cost of breaking the cipher exceeds the value of
the encrypted info
– The time required to break the cipher exceeds the
useful lifetime of the info
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Brute Force Search
• Always possible to simply try every key
• Most basic attack, proportional to key size
• Assume either know / recognise plaintext
Key Size (bits)
Number of
Alternative Keys
Time required at 1
decryption/µs
Time required at 106
decryptions/µs
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232 = 4.3  109
231 µs
= 35.8 minutes
2.15 milliseconds
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256 = 7.2  1016
255 µs
= 1142 years
10.01 hours
128
2128 = 3.4  1038
2127 µs
years
= 5.4  1024
5.4  1018 years
168
2168 = 3.7  1050
2167 µs
years
= 5.9  1036
5.9  1030 years
26! = 4  1026
2  1026 µs = 6.4  1012
years
26 characters
(permutation)
6.4  106 years
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Outline
• Overview of Cryptography
• Classical Symmetric Cipher
– Substitution Cipher
– Transposition Cipher
• Modern Symmetric Ciphers (DES and AES)
• Asymmetric Cipher
• One-way Hash Functions and Message Digest
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Symmetric Cipher Model
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Requirements
• Two requirements for secure use of symmetric
encryption:
– a strong encryption algorithm
– a secret key known only to sender / receiver
Y = EK(X)
X = DK(Y)
• Assume encryption algorithm is known
• Implies a secure channel to distribute key
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Classical Substitution Ciphers
• Letters of plaintext are replaced by other
letters or by numbers or symbols
• Plaintext is viewed as a sequence of bits, then
substitution replaces plaintext bit patterns
with ciphertext bit patterns
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Caesar Cipher
• Earliest known substitution cipher
• Replaces each letter by 3rd letter on
• Example:
meet me after the toga party
PHHW PH DIWHU WKH WRJD SDUWB
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Caesar Cipher
• 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
• Mathematically give each letter a number
a b c d e f g h i j k
l
m
0 1 2 3 4 5 6 7 8 9 10 11 12
n
o
p
q
r
s
t
u
v
w
x
y
Z
13 14 15 16 17 18 19 20 21 22 23 24 25
• Then have Caesar cipher as:
C = E(p) = (p + k) mod (26)
p = D(C) = (C – k) mod (26)
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Cryptanalysis of Caesar Cipher
• Only have 25 possible ciphers
– A maps to B,..Z
• Given ciphertext, just try all shifts of letters
• Do need to recognize when have plaintext
• E.g., break ciphertext "GCUA VQ DTGCM“
• How to make it harder?
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Monoalphabetic Cipher
• Rather than just shifting the alphabet
• Could shuffle (jumble) the letters arbitrarily
• Each plaintext letter maps to a different
random ciphertext letter
• Key is 26 letters long
Plain:
abcdefghijklmnopqrstuvwxyz
Cipher: DKVQFIBJWPESCXHTMYAUOLRGZN
Plaintext:
ifwewishtoreplaceletters
Ciphertext: WIRFRWAJUHYFTSDVFSFUUFYA
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Monoalphabetic Cipher Security
• Now have a total of 26! = 4 x 1026 keys
• Is that secure?
• Problem is language characteristics
– Human languages are redundant
– Letters are not equally commonly used
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English Letter Frequencies
Note that all human languages have varying letter frequencies, though the
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number of letters and their frequencies varies.
Example Cryptanalysis
• Given ciphertext:
UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMETSXAIZ
VUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZUHSX
EPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ
• Count relative letter frequencies (see text)
• Guess P & 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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Transposition Ciphers
• Now consider classical transposition or
permutation ciphers
• These hide the message by rearranging the
letter order, without altering the actual
letters used
• Any shortcut for breaking it?
• Can recognise these since have the same
frequency distribution as the original text
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Rail Fence Cipher
• Write message letters out diagonally over a
number of rows
• Then read off cipher row by row
• E.g., 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
• Giving ciphertext
MEMATRHTGPRYETEFETEOAAT
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Product Ciphers
• Ciphers using substitutions or transpositions are
not secure because of language characteristics
• Hence consider using several ciphers in succession
to make harder, but:
– Two substitutions make another substitution
– Two transpositions make a more complex transposition
– But a substitution followed by a transposition makes a
new much harder cipher
• This is bridge from classical to modern ciphers
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Outline
• Overview of Cryptography
• Classical Symmetric Cipher
• Modern Symmetric Ciphers (DES/AES)
• Asymmetric Cipher
• One-way Hash Functions and Message Digest
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Block vs Stream Ciphers
• Block ciphers process messages in into blocks,
each of which is then en/decrypted
• Like a substitution on very big characters
– 64-bits or more
• Stream ciphers process messages a bit or byte
at a time when en/decrypting
• Many current ciphers are block ciphers, one of
the most widely used types of cryptographic
algorithms
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Block Cipher Principles
• Most symmetric block ciphers are based on a
Feistel Cipher Structure
• Block ciphers look like an extremely large
substitution
• Would need table of 264 entries for a 64-bit
block
• Instead create from smaller building blocks
• Using idea of a product cipher
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Ideal Block Cipher
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Feistel Cipher
Structure
• Process through
multiple rounds which
– partitions input block
into two halves
– perform a substitution
on left data half
– based on round function
of right half & subkey
– then have permutation
swapping halves
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Feistel
Cipher
Decryption
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DES (Data Encryption Standard)
• Published in 1977, standardized in 1979.
• Key: 64 bit quantity=8-bit parity+56-bit key
– Every 8th bit is a parity bit.
• 64 bit input, 64 bit output.
64 bit M
64 bit C
DES
Encryption
56 bits
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DES Top View
56-bit Key
64-bit
48-bitInput
K1
Generate keys
Permutation
Round 1
Round 2
…...
Round 16
Swap
Permutation
64-bit Output
Initial Permutation
48-bit K1
48-bit K2
48-bit K16
Swap 32-bit halves
Final Permutation
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DES Summary
• Simple, easy to implement:
– Hardware/gigabits/second,
software/megabits/second
• 56-bit key DES may be acceptable for noncritical applications but triple DES (DES3)
should be secure for most applications today
• Supports several operation modes (ECB CBC,
OFB, CFB) for different applications
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Avalanche Effect
• Key desirable property of encryption alg
• Where a change of one input or key bit
results in changing more than half output bits
• DES exhibits strong avalanche
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Strength of DES – Key Size
• 56-bit keys have 256 = 7.2 x 1016 values
• Brute force search looks hard
• Recent advances have shown is possible
– in 1997 on a huge cluster of computers over the
Internet in a few months
– in 1998 on dedicated hardware called “DES cracker”
by EFF in a few days ($220,000)
– in 1999 above combined in 22hrs!
• Still must be able to recognize plaintext
• No big flaw for DES algorithms
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DES Replacement
• Triple-DES (3DES)
– 168-bit key, no brute force attacks
– Underlying encryption algorithm the same, no
effective analytic attacks
– Drawbacks
• Performance: no efficient software codes for DES/3DES
• Efficiency/security: bigger block size desirable
• Advanced Encryption Standards (AES)
– US NIST issued call for ciphers in 1997
– AES was selected in Oct-2000
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AES
• Private key symmetric block cipher
• 128-bit data, 128/192/256-bit keys
• Stronger & faster than Triple-DES
• Provide full specification & design details
• Evaluation criteria
– Security: effort to practically cryptanalysis
– Cost: computational efficiency and memory
requirement
– Algorithm & implementation characteristics:
flexibility to apps, hardware/software suitability,
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simplicity
AES Shortlist
• After testing and evaluation, shortlist in Aug99:
– MARS (IBM) - complex, fast, high security margin
– RC6 (USA) - v. simple, v. fast, low security margin
– Rijndael (Belgium) - clean, fast, good security margin
– Serpent (Euro) - slow, clean, v. high security margin
– Twofish (USA) - complex, v. fast, high security margin
• Then subject to further analysis & comment
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Outlines
• Symmetric Cipher
– Classical Symmetric Cipher
– Modern Symmetric Ciphers (DES and AES)
• Asymmetric Cipher
• One-way Hash Functions and Message Digest
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Private-Key Cryptography
• Private/secret/single key cryptography uses one
key
• Shared by both sender and receiver
• If this key is disclosed communications are
compromised
• Also is symmetric, parties are equal
• Hence does not protect sender from receiver
forging a message & claiming is sent by sender
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Public-Key Cryptography
• Probably most significant advance in the 3000
year history of cryptography
• Uses two keys – a public & a private key
• Asymmetric since parties are not equal
• Uses clever application of number theoretic
concepts to function
• Complements rather than replaces private key
crypto
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Public-Key Cryptography
• Public-key/two-key/asymmetric cryptography
involves the use of two keys:
– a public-key, which may be known by anybody, and can
be used to encrypt messages, and verify signatures
– a private-key, known only to the recipient, used to
decrypt messages, and sign (create) signatures
• Asymmetric because
– those who encrypt messages or verify signatures
cannot decrypt messages or create signatures
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Public-Key Cryptography
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Public-Key Characteristics
• Public-Key algorithms rely on two keys with the
characteristics that it is:
– computationally infeasible to find decryption key
knowing only algorithm & encryption key
– computationally easy to en/decrypt messages when
the relevant (en/decrypt) key is known
– either of the two related keys can be used for
encryption, with the other used for decryption (in
some schemes)
• Analogy to delivery w/ a padlocked box
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Public-Key Cryptosystems
• Two major applications:
– encryption/decryption (provide secrecy)
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– digital signatures (provide authentication)
RSA (Rivest, Shamir, Adleman)
• The most popular one.
• Support both public key encryption and digital
signature.
• Assumption/theoretical basis:
– Factoring a big number is hard.
• Variable key length (usually 1024 bits).
• Plaintext block size.
– Plaintext must be “less or equal” than the key.
– Ciphertext block size is the same as the key length.
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What Is RSA?
• To generate key pair:
– Pick large primes (>= 512 bits each) p and q
– Let n = p*q, keep your p and q to yourself!
– For public key, choose e that is relatively prime to
ø(n) =(p-1)(q-1), let pub = <e,n>
– For private key, find d that is the multiplicative
inverse of e mod ø(n), i.e., e*d = 1 mod ø(n), let priv =
<d,n>
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RSA Example
1.
Select primes: p=17 & q=11
2.
Compute n = pq =17×11=187
3.
Compute ø(n)=(p–1)(q-1)=16×10=160
4.
Select e : gcd(e,160)=1; choose e=7
5.
Determine d: de=1 mod 160 and d < 160 Value is
d=23 since 23×7=161= 10×160+1
6.
Publish public key KU={7,187}
7.
Keep secret private key KR={23,17,11}
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How Does RSA Work?
• Given pub = <e, n> and priv = <d, n>
– encryption: c = me mod n, m < n
– decryption: m = cd mod n
– signature: s = md mod n, m < n
– verification: m = se mod n
• given message M = 88 (nb. 88<187)
• encryption:
C = 887 mod 187 = 11
• decryption:
M = 1123 mod 187 = 88
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Is RSA Secure?
• Factoring 1024-bit number is very hard!
• But if you can factor big number n then given public
key <e,n>, you can find d, hence the private key by:
– Knowing factors p, q, such that, n = p*q
– Then ø(n) =(p-1)(q-1)
– Then d such that e*d = 1 mod ø(n)
• Threat
– Moore’s law
– Refinement of factorizing algorithms
• For the near future, a key of 1024 or 2048 bits
needed
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Symmetric (DES) vs. Public Key (RSA)
• Exponentiation of RSA is expensive !
• AES and DES are much faster
– 100 times faster in software
– 1,000 to 10,000 times faster in hardware
• RSA often used in combination in AES and DES
– Pass the session key with RSA
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Outline
• History of Security and Definitions
• Overview of Cryptography
• Symmetric Cipher
– Classical Symmetric Cipher
– Modern Symmetric Ciphers (DES and AES)
• Asymmetric Cipher
• One-way Hash Functions and Message Digest
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Confidentiality => Authenticity ?
• Symmetric cipher ?
– Shared key problem
– Plaintext has to be intelligible/understandable
• Asymmetric cipher?
– Too expensive
– Plaintext has to be intelligible/understandable
– Desirable to cipher on a much smaller size of data
which uniquely represents the long message
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Hash Functions
• Condenses arbitrary message to fixed size
h = H(M)
• Usually assume that the hash function is
public and not keyed
• Hash used to detect changes to message
• Can use in various ways with message
• Most often to create a digital signature
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Hash Functions & Digital Signatures
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Requirements for Hash Functions
1.
Can be applied to any sized message M
2. Produces fixed-length output h
3. Is easy to compute h=H(M) for any message M
4. Given h is infeasible to find x s.t. H(x)=h
•
One-way property
5. Given x is infeasible to find y s.t. H(y)=H(x)
•
Weak collision resistance
6. Is infeasible to find any x,y s.t. H(y)=H(x)
•
Strong collision resistance
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Birthday Problem
• How many people do you need so that the probability of
having two of them share the same birthday is > 50% ?
• Random sample of n birthdays (input) taken from k (365,
output)
• kn total number of possibilities
• (k)n=k(k-1)…(k-n+1) possibilities without duplicate birthday
• Probability of no repetition:
– p = (k)n/kn  1 - n(n-1)/2k
• For k=366, minimum n = 23
• n(n-1)/2 pairs, each pair has a probability 1/k of having the
same output
• n(n-1)/2k > 50%  n>k1/2
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How Many Bits for Hash?
• m bits, takes 2m/2 to find two with the same
hash
• 64 bits, takes 232 messages to search
(doable)
• Need at least 128 bits
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General Structure of Secure Hash Code
• Iterative compression function
– Each f is collision-resistant, so is the resulting
hashing
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MD5: Message Digest Version 5
input Message
Output 128 bits Digest
• Until recently the most widely used hash algorithm
– in recent times have both brute-force & cryptanalytic
concerns
• Specified as Internet standard RFC132175
MD5 Overview
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MD5 Overview
1. Pad message so its length is 448 mod 512
2. Append a 64-bit original length value to message
3. Initialise 4-word (128-bit) MD buffer (A,B,C,D)
4. Process message in 16-word (512-bit) blocks:
–
Using 4 rounds of 16 bit operations on message block &
buffer
–
Add output to buffer input to form new buffer value
5. Output hash value is the final buffer value
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Processing of Block mi - 4 Passes
mi
MDi
ABCD=fF(ABCD,mi,T[1..16])
A
C
D
B
ABCD=fG(ABCD,mi,T[17..32])
ABCD=fH(ABCD,mi,T[33..48])
ABCD=fI(ABCD,mi,T[49..64])
+
MD i+1
+
+
+
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Secure Hash Algorithm
• SHA is specified as the hash algorithm in the
Digital Signature Standard (DSS), NIST, 1993
• Input message must be < 264 bits
– not really a problem
• Message is processed in 512-bit blocks
sequentially
• Message digest is 160 bits
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SHA-1 verses MD5
• Brute force attack is harder (160 vs 128 bits for
MD5)
• A little slower than MD5 (80 vs 64 steps)
– Both work well on a 32-bit architecture
• Both designed as simple and compact for
implementation
• Cryptanalytic attacks
– MD4/5: vulnerability discovered since its design
– SHA-1: no until recent 2005 results raised concerns on
its use in future applications
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Revised Secure Hash Standard
• NIST have issued a revision in 2002
• Adds 3 additional hash algorithms
• SHA-256, SHA-384, SHA-512
– Collectively called SHA-2
• Designed for compatibility with increased
security provided by the AES cipher
• Structure & detail are similar to SHA-1
• Hence analysis should be similar, but security
levels are rather higher
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Backup Slides
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Cryptanalysis Scheme
• Ciphertext only:
– Exhaustive search until “recognizable plaintext”
– Need enough ciphertext
• Known plaintext:
– Secret may be revealed (by spy, time), thus <ciphertext,
plaintext> pair is obtained
– Great for monoalphabetic ciphers
• Chosen plaintext:
– Choose text, get encrypted
– Pick patterns to reveal the structure of the key
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One-Time Pad
• If a truly random key as long as the message is
used, the cipher will be secure - One-Time pad
• E.g., a random sequence of 0’s and 1’s XORed to
plaintext, no repetition of keys
• Unbreakable since ciphertext bears no
statistical relationship to the plaintext
• For any plaintext, it needs a random key of the
same length
– Hard to generate large amount of keys
• Have problem of safe distribution of key
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Rotor Machines
• Before modern ciphers,
rotor machines were
most common complex
ciphers in use
• Widely used in WW2
– German Enigma, Allied
Hagelin, Japanese Purple
• Implemented a very
complex, varying
substitution cipher
85
Substitution-Permutation Ciphers
• Substitution-permutation (S-P) networks
[Shannon, 1949]
– modern substitution-transposition product cipher
• These form the basis of modern block ciphers
• S-P networks are based on the two primitive
cryptographic operations
– substitution (S-box)
– permutation (P-box)
• provide confusion and diffusion of message
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Confusion and Diffusion
• Cipher needs to completely obscure statistical
properties of original message
• A one-time pad does this
• More practically Shannon suggested S-P networks
to obtain:
• Diffusion – dissipates statistical structure of
plaintext over bulk of ciphertext
• Confusion – makes relationship between
ciphertext and key as complex as possible
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Bit Permutation (1-to-1)
Input:
1 2
0 0
3
1
4
0
32
1
…….
1 bit
Output
1
0
1
1
22
6
13 32
……..
1
3
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Per-Round Key Generation
Initial Permutation of DES key
C i-1 28 bits
D i-1 28 bits
Circular Left Shift
Circular Left Shift
One
round
Round 1,2,9,16:
single shift
Others: two bits
Permutation
with Discard
48 bits
Ki
Ci
28 bits
Di
28 bits
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A DES Round
32 bits Ln
32 bits Rn
E
One Round
Encryption
48 bits
Mangler
Function
48 bits
Ki
S-Boxes
P
32 bits
32 bits Ln+1
32 bits Rn+1
90
Mangler Function
4 4 4 4 4 4 4 4
6
6
6
6
6
+
+
+
+
+
6
+
6
+
6
6
6
6
6
6
6
6
+
S1 S2 S3 S4 S5 S6 S7 S8
4 4 4 4 4 4 4 4
6
The permutation produces
“spread” among the
chunks/S-boxes!
Permutation
91
Bits Expansion (1-to-m)
Input:
1
0
2
0
3
1
4
0
5
1…….
32
1
Output
1
0
0
1
0
1
0
1
1
2
3
4
5
6
7
8
……..
1
0
48
92
S-Box (Substitute and Shrink)
• 48 bits ==> 32 bits. (8*6 ==> 8*4)
• 2 bits used to select amongst 4 substitutions
for the rest of the 4-bit quantity
2 bits
row
4 bits
column
I1
I2
I3
I4
I5
I6
Si
i = 1,…8.
O1
O2
O3
O4
93
S-Box Examples
Each row and column contain different numbers.
0
1
2
3
4
5
6
7
8
0
14
4
13
1
2
15
11
8
3
1
0
15
7
4
14
2
13
1
10
2
4
1
14
8
13
6
2
11
15
3
15
12
8
2
4
9
1
7
5
Example: input: 100110 output: ???
94
9…. 15
Padding Twist
• Given original message M, add padding bits
“10*” such that resulting length is 64 bits less
than a multiple of 512 bits.
• Append (original length in bits mod 264),
represented in 64 bits to the padded message
• Final message is chopped 512 bits a block
95
Why Does RSA Work?
• Given pub = <e, n> and priv = <d, n>
– n =p*q, ø(n) =(p-1)(q-1)
– e*d = 1 mod ø(n)
– xed = x mod n
– encryption: c = me mod n
– decryption: m = cd mod n = med mod n = m mod n = m
(since m < n)
– digital signature (similar)
96
Using Hash for Authentication
Assuming share a key KAB
• Alice to Bob: challenge rA
• Bob to Alice: MD(KAB|rA)
• Bob to Alice: rB
• Alice to Bob: MD(KAB|rB)
• Only need to compare MD results
97
Using Hash to Encrypt
• One-time pad with KAB
– Compute bit streams using MD, and K
• b1=MD(KAB), bi=MD(KAB|bi-1), …
–  with message blocks
– Is this a real one-time pad ?
– Add a random 64 bit number (aka IV)
b1=MD(KAB|IV), bi=MD(KAB|bi-1), …
98
MD5 Process
• As many stages as the number of 512-bit
blocks in the final padded message
• Digest: 4 32-bit words: MD=A|B|C|D
• Every message block contains 16 32-bit words:
m0|m1|m2…|m15
– Digest MD0 initialized to:
A=01234567,B=89abcdef,C=fedcba98, D=76543210
– Every stage consists of 4 passes over the message
block, each modifying MD
• Each block 4 rounds, each round 16 steps
99
Different Passes...
Each step i (1 <= i <= 64):
• Input:
– mi – a 32-bit word from the message
With different shift every round
– Ti – int(232 * abs(sin(i)))
Provided a randomized set of 32-bit patterns, which
eliminate any regularities in the input data
– ABCD: current MD
• Output:
– ABCD: new MD
100
MD5 Compression Function
• Each round has 16 steps of the form:
a = b+((a+g(b,c,d)+X[k]+T[i])<<<s)
• a,b,c,d refer to the 4 words of the buffer,
but used in varying permutations
– note this updates 1 word only of the buffer
– after 16 steps each word is updated 4 times
• where g(b,c,d) is a different nonlinear
function in each round (F,G,H,I)
101
MD5 Compression Function
102
Functions and Random Numbers
• F(x,y,z) == (xy)(~x  z)
– selection function
• G(x,y,z) == (x  z) (y ~ z)
• H(x,y,z) == xy z
• I(x,y,z) == y(x  ~z)
103
Basic Steps for SHA-1
Step1: Padding
Step2: Appending length as 64 bit unsigned
Step3: Initialize MD buffer 5 32-bit words
Store in big endian format, most significant bit in low address
A|B|C|D|E
A = 67452301
B = efcdab89
C = 98badcfe
D = 10325476
E = c3d2e1f0
104
Basic Steps...
Step 4: the 80-step processing of 512-bit blocks
– 4 rounds, 20 steps each.
Each step t (0 <= t <= 79):
– Input:
• Wt – a 32-bit word from the message
• Kt – a constant.
• ABCDE: current MD.
– Output:
• ABCDE: new MD.
105