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 will grow to over $75 billion by 2007

• Security specialists markets are expanding !– “ Full-time information security professionals will

rise almost 14% per year around the world, going past 2.1 million in 2008” (IDC report)

Why Computer Security (cont’d)

• Internet attacks are increasing in frequency, severity and sophistication

• Denial of service (DoS) attacks– Cost $1.2 billion in 2000– 1999 CSI/FBI survey 32% of respondents detected

DoS attacks directed to their systems– Thousands of attacks per week in 2001– Yahoo, Amazon, eBay, Microsoft, White House,

etc., attacked

Why Computer Security (cont’d)• Virus and worms faster and powerful

– Melissa, Nimda, Code Red, Code Red II, Slammer …– 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 !

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

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)

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

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!

The Spread of Sapphire/Slammer Worms

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.

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

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.

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

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

securesender

securereceiver

channel data, control messages

data data

Alice Bob

Trudy

Eavesdropping - Message Interception (Attack on

Confidentiality)• Unauthorized access to information• Packet sniffers and wiretappers• Illicit copying of files and programs

A B

Eavesdropper

Integrity Attack - Tampering With Messages

• Stop the flow of the message• Delay and optionally modify the message• Release the message again

A B

Perpetrator

Authenticity Attack - Fabrication

• Unauthorized assumption of other’s identity• Generate and distribute objects under this

identity

A B

Masquerader: from A

Attack on Availability• Destroy hardware (cutting fiber) or software• Modify software in a subtle way (alias commands)• Corrupt packets in transit

• Blatant denial of service (DoS):– Crashing the server– Overwhelm the server (use up its resource)

A B

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

Outline• Overview of Cryptography• Symmetric Cipher

– Classical Symmetric Cipher– Modern Symmetric Ciphers (DES and AES)

• Asymmetric Cipher• One-way Hash Functions and Message

Digest

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

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

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

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 – Only one-time pad scheme qualifies

• 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

Brute Force Search

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 = 5.4 1024 years

5.4 1018 years

168 2168 = 3.7 1050 2167 µs = 5.9 1036 years

5.9 1030 years

26 characters (permutation)

26! = 4 1026 2 1026 µs = 6.4 1012 years

6.4 106 years

• Always possible to simply try every key • Most basic attack, proportional to key size • Assume either know / recognise plaintext

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

Symmetric Cipher Model

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

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

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

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 numbera 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)

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?

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

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

English Letter Frequencies

Note that all human languages have varying letter frequencies, though the 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

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

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 ciphertextMEMATRHTGPRYETEFETEOAAT

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

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

Outline• Overview of Cryptography• Classical Symmetric Cipher• Modern Symmetric Ciphers (DES/AES)• Asymmetric Cipher• One-way Hash Functions and Message

Digest

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

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

Ideal Block Cipher

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

Feistel Cipher Structure• Feistel cipher implements Shannon’s S-P

network concept– based on invertible product cipher

• 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

Feistel Cipher

Structure

Feistel Cipher

Decryption

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.

DESEncryption

64 bit M 64 bit C

56 bits

DES Top View

Permutation

Permutation

Swap

Round 1

Round 2

Round 16

Generate keysInitial Permutation48-bit K1

48-bit K2

48-bit K16

Swap 32-bit halves

Final Permutation

64-bit Output

48-bit K164-bit Input56-bit Key

…...

DES Summary• Simple, easy to implement:

– Hardware/gigabits/second, software/megabits/second

• 56-bit key DES may be acceptable for non-critical applications but triple DES (DES3) should be secure for most applications today

• Supports several operation modes (ECB CBC, OFB, CFB) for different applications

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

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

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– Rijndael was selected as the AES in Oct-2000

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, simplicity

AES Shortlist• After testing and evaluation, shortlist in Aug-

99: – 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

Outlines• Symmetric Cipher

– Classical Symmetric Cipher– Modern Symmetric Ciphers (DES and AES)

• Asymmetric Cipher• One-way Hash Functions and Message

Digest

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

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

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

Public-Key Cryptography

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

Public-Key Cryptosystems

• Two major applications:– encryption/decryption (provide secrecy)– 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 512 bits).• Variable plaintext block size.

– Plaintext must be “smaller” than the key.– Ciphertext block size is the same as the key length.

What Is RSA?• To generate key pair:

– Pick large primes (>= 256 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>

RSA Example1. Select primes: p=17 & q=112. Compute n = pq =17×11=1873. Compute ø(n)=(p–1)(q-1)=16×10=1604. Select e : gcd(e,160)=1; choose e=75. Determine d: de=1 mod 160 and d < 160 Value

is d=23 since 23×7=161= 10×160+16. Publish public key KU={7,187}7. Keep secret private key KR={23,17,11}

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

Is RSA Secure?• Factoring 512-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

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

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

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

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

Hash Functions & Digital Signatures

Requirements for Hash Functions1. Can be applied to any sized message M2. Produces fixed-length output h3. Is easy to compute h=H(M) for any message M4. Given h is infeasible to find x s.t. H(x)=h

• One-way property5. Given x is infeasible to find y s.t. H(y)=H(x)

• Weak collision resistance6. Is infeasible to find any x,y s.t. H(y)=H(x)

• Strong collision resistance

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

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

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

General Structure of Secure Hash Code

• Iterative compression function– Each f is collision-resistant, so is the resulting hashing

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 RFC1321

MD5 Overview

MD5 Overview1. 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

Processing of Block mi - 4 Passes

ABCD=fF(ABCD,mi,T[1..16])

ABCD=fG(ABCD,mi,T[17..32])

ABCD=fH(ABCD,mi,T[33..48])

ABCD=fI(ABCD,mi,T[49..64])

mi

+ + + +

A B C D

MDi

MD i+1

Secure Hash Algorithm• Developed by NIST, specified in the Secure

Hash Standard (SHS, FIPS Pub 180), 1993• SHA is specified as the hash algorithm in

the Digital Signature Standard (DSS), NIST

General Logic• Input message must be < 264 bits

– not really a problem• Message is processed in 512-bit blocks

sequentially• Message digest is 160 bits• SHA design is similar to MD5, a little

slower, but a lot stronger

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 SHA-1: no until recent 2005 results raised concerns

on its use in future applicationson its use in future applications

Revised Secure Hash Standard• NIST have issued a revision FIPS 180-2 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

Backup Slides

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

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

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

Bit Permutation (1-to-1)

…….

……..

1 2 3 4 32

22 6 13 32 3

Input:

Output

0 0 1 0 1

1 0 1 1 1

1 bit

Per-Round Key Generation

28 bits 28 bits

48 bitsKi

Oneround

Circular Left Shift Circular Left Shift

28 bits 28 bits

Permutationwith Discard

Initial Permutation of DES key

C i-1 D i-1

C i D i

Round 1,2,9,16: single shiftOthers: two bits

A DES Round

48 bits

32 bits

32 bits Ln 32 bits Rn

32 bits Ln+1 32 bits Rn+1

E

S-Boxes

P

48 bitsKi

One RoundEncryption

ManglerFunction

Mangler Function4444444 4

6666666 6

+ + +++ ++ +

6666666 6

S8S1 S2 S7S3 S4 S5 S6

4444444 4

Permutation

The permutation produces “spread” among the chunks/S-boxes!

Bits Expansion (1-to-m)

…….

……..

1 2 3 4 5 32Input:

Output

0 0 1 0 1 1

1 2 3 4 5 6 7 8 48

1 0 0 1 0 1 0 1 1 0

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 bitsrow

S i

i = 1,…8.

I1I2I3I4I5I6

O1O2O3O4

4 bitscolumn

S-Box Examples

0 1 2 3 4 5 6 7 8 9…. 15

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

Each row and column contain different numbers.

Example: input: 100110 output: ???

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

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)– xed = x mod n– encryption: c = me mod n– decryption: m = cd mod n = med mod n = m mod

n = m (since m < n)– digital signature (similar)

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), …

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

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

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)

MD5 Compression Function

Functions and Random Numbers

• F(x,y,z) == (xy)(~x z)– selection function

• G(x,y,z) == (x z) (y ~ z)• H(x,y,z) == xy z• I(x,y,z) == y(x ~z)

Basic Steps for SHA-1Step1: PaddingStep2: Appending length as 64 bit unsignedStep3: Initialize MD buffer 5 32-bit wordsStore in big endian format, most significant bit in low address

A|B|C|D|EA = 67452301B = efcdab89C = 98badcfeD = 10325476E = c3d2e1f0

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.