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### Backup Slides Confidentiality)

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

- Jobs and salaries for technology professionals have lessened in recent years. BUT …
- 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): 10 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 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

Alice

Bob

data, control messages

channel

secure

sender

secure

receiver

data

data

Trudy

Eavesdropping - Message Interception (Attack on Confidentiality)

- Unauthorized access to information
- Packet sniffers and wiretappers
- Illicit copying of files and programs

B

A

Eavesdropper

Integrity Attack - Tampering With Messages Confidentiality)

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

B

A

Perpetrator

Authenticity Attack - Fabrication Confidentiality)

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

B

A

Masquerader: from A

B Confidentiality)

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)

Classify Security Attacks as Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

- 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

Cryptanalysis Scheme Confidentiality)

- 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

Unconditional vs. Computational Security Confidentiality)

- 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 Confidentiality)

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

Outline Confidentiality)

- 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 Confidentiality)

Requirements Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

- 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)

Cryptanalysis of Caesar Cipher Confidentiality)

- 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"

Monoalphabetic Cipher Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

Note that all human languages have varying letter frequencies, though the number of letters and their frequencies varies.

Example Cryptanalysis Confidentiality)

- 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

One-Time Pad Confidentiality)

- 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

Transposition Ciphers Confidentiality)

- 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 Confidentiality)

- 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

Product Ciphers Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

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

Block vs Stream Ciphers Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

Substitution-Permutation Ciphers Confidentiality)

- 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

Confusion and Diffusion Confidentiality)

- 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

Feistel Cipher Structure Confidentiality)

- 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 Confidentiality)

Feistel Cipher Decryption Confidentiality)

DES (Data Encryption Standard) Confidentiality)

- 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

DES Top View Confidentiality)

56-bit Key

64-bit Input

48-bit K1

Generate keys

Permutation

Initial Permutation

48-bit K1

Round 1

48-bit K2

Round 2

…...

48-bit K16

Round 16

Swap 32-bit halves

Swap

Final Permutation

Permutation

64-bit Output

Cipher Iterative Action : Confidentiality)

Input: 64 bits

Key: 48 bits

Output: 64 bits

Key Generation Box :

Input: 56 bits

Output: 48 bits

DES StandardOne round (Total 16 rounds)

DES Box Summary Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

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

- Asymmetric Cipher
- One-way Hash Functions and Message Digest

Private-Key Cryptography Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

Public-Key Characteristics Confidentiality)

- 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 Confidentiality)

- Two major applications:
- encryption/decryption (provide secrecy)
- digital signatures (provide authentication)

RSA (Rivest, Shamir, Adleman) Confidentiality)

- 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? Confidentiality)

- 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 Example Confidentiality)

- Select primes: p=17 & q=11
- Computen = pq =17×11=187
- Computeø(n)=(p–1)(q-1)=16×10=160
- Select e : gcd(e,160)=1; choose e=7
- Determine d: de=1 mod 160 and d < 160 Value is d=23 since 23×7=161= 10×160+1
- Publish public key KU={7,187}
- Keep secret private key KR={23,17,11}

How Does RSA Work? Confidentiality)

- 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

Why Does RSA Work? Confidentiality)

- 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)

Is RSA Secure? Confidentiality)

- 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) Confidentiality)

- 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 Confidentiality)

- 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 ? Confidentiality)

- Symmetric cipher ?
- Plaintext has to be intelligible/understandable

- Asymmetric cipher?
- Straightforward use provides no authenticity
- Coupled encryption
- Too expensive
- Requires intelligible text, otherwise message size doubles

Hash Functions Confidentiality)

- 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 Confidentiality)

Requirements for Hash Functions Confidentiality)

- Can be applied to any sized message M
- Produces fixed-length output h
- Is easy to compute h=H(M) for any message M
- Given h is infeasible to find x s.t. H(x)=h
- One-way property

- Given x is infeasible to find y s.t. H(y)=H(x)
- Weak collision resistance

- Is infeasible to find any x,y s.t. H(y)=H(x)
- Strong collision resistance

Birthday Problem Confidentiality)

- 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? Confidentiality)

- 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 Confidentiality)

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

Using Hash to Encrypt Confidentiality)

- 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), …

- Compute bit streams using MD, and K

General Structure of Secure Hash Code Confidentiality)

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

MD5: Message Digest Version 5 Confidentiality)

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 Confidentiality)

MD5 Overview Confidentiality)

- Pad message so its length is 448 mod 512
- Append a 64-bit original length value to message
- Initialise 4-word (128-bit) MD buffer (A,B,C,D)
- 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

- Output hash value is the final buffer value

Processing of Block Confidentiality)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

Secure Hash Algorithm Confidentiality)

- 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 Confidentiality)

- 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 Confidentiality)

- 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

Revised Secure Hash Standard Confidentiality)

- 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

Bit Permutation (1-to-1) Confidentiality)

1 2 3 4 32

…….

0 0 1 0 1

Input:

1 bit

Output

……..

1 0 1 1 1

22 6 13 32 3

Per-Round Key Generation Confidentiality)

Initial Permutation of DES key

C i-1

D i-1

28 bits

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

C i

D i

28 bits

28 bits

A DES Round Confidentiality)

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

6 Confidentiality)

6

6

6

6

6

6

6

6

6

6

6

6

6

6

6

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

4

S1

S2

S3

S4

S5

S6

S7

S8

+

+

+

+

+

+

+

+

Permutation

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

Bits Expansion (1-to-m) Confidentiality)

1 2 3 4 5 32

Input:

…….

0 0 1 0 1 1

Output

……..

10 0 1 0 1 0 110

1 2 3 4 5 6 7 8 48

2 bits Confidentiality)

row

I1

I2

I3

I4

I5

I6

S

O1

O2

O3

O4

i

4 bits

column

= 1,…8.

i

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

S-Box Examples Confidentiality)

Each row and column contain different numbers.

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

Example: input: 100110 output: ???

Padding Twist Confidentiality)

- 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

MD5 Process Confidentiality)

- 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... Confidentiality)

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

- mi – a 32-bit word from the message
- Output:
- ABCD: new MD

MD5 Compression Function Confidentiality)

- 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 Confidentiality)

Functions and Random Numbers Confidentiality)

- 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-1 Confidentiality)

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

Basic Steps... Confidentiality)

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.

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