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
1
(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.
2
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
3
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)
5
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
6
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!
7
The Spread of Sapphire/Slammer
Worms
8
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.
9
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
10
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.
11
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
12
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
13
Eavesdropping - Message Interception
(Attack on Confidentiality)
• Unauthorized access to information
• Packet sniffers and wiretappers
• Illicit copying of files and programs
B
A
Eavesdropper
14
Integrity Attack - Tampering
With Messages
• Stop the flow of the message
• Delay and optionally modify the message
• Release the message again
B
A
Perpetrator
15
Authenticity Attack - Fabrication
• Unauthorized assumption of other’s identity
• Generate and distribute objects under this
identity
A
B
Masquerader: from A
16
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)
17
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
18
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.
19
Outline
• Overview of Cryptography
• Symmetric Cipher
– Classical Symmetric Cipher
– Modern Symmetric Ciphers (DES and AES)
• Asymmetric Cipher
• One-way Hash Functions and Message Digest
20
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
21
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
22
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
23
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
24
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
32
232 = 4.3  109
231 µs
= 35.8 minutes
2.15 milliseconds
56
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
25
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
26
Symmetric Cipher Model
27
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
28
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
29
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
30
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)
31
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?
32
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
33
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
34
English Letter Frequencies
Note that all human languages have varying letter frequencies, though the
35
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
36
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
37
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
38
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
39
Outline
• Overview of Cryptography
• Classical Symmetric Cipher
• Modern Symmetric Ciphers (DES/AES)
• Asymmetric Cipher
• One-way Hash Functions and Message Digest
40
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
41
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
42
Ideal Block Cipher
43
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
44
Feistel
Cipher
Decryption
45
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
46
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
47
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
48
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
49
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
50
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
51
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,
52
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
53
Outlines
• Symmetric Cipher
– Classical Symmetric Cipher
– Modern Symmetric Ciphers (DES and AES)
• Asymmetric Cipher
• One-way Hash Functions and Message Digest
54
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
55
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
56
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
57
Public-Key Cryptography
58
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
59
Public-Key Cryptosystems
• Two major applications:
– encryption/decryption (provide secrecy)
60
– 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.
61
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>
62
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}
63
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
64
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
65
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
66
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
67
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
68
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
69
Hash Functions & Digital Signatures
70
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
71
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
72
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
73
General Structure of Secure Hash Code
• Iterative compression function
– Each f is collision-resistant, so is the resulting
hashing
74
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
76
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
77
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
+
+
+
78
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
79
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
80
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
81
Backup Slides
82
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
83
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
84
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
86
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
87
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
88
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
89
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
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