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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 !

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Why computer security l.jpg

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 (Washington Post Dec. 23 2009)


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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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  • 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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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



data, control messages










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Eavesdropping - Message Interception (Attack on Confidentiality)

  • Unauthorized access to information

  • Packet sniffers and wiretappers

  • Illicit copying of files and programs





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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





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Authenticity Attack - Fabrication

  • Unauthorized assumption of other’s identity

  • Generate and distribute objects under this identity



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

  • 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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  • 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


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  • 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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  • 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



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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


    Plaintext: ifwewishtoreplaceletters



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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 number of letters and their frequencies varies.


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Example Cryptanalysis

  • Given ciphertext:




  • 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



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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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  • 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



56 bits


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DES Top View

56-bit Key

64-bit Input

48-bit K1

Generate keys


Initial Permutation

48-bit K1

Round 1

48-bit K2

Round 2


48-bit K16

Round 16

Swap 32-bit halves


Final Permutation


64-bit Output


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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


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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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  • 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


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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


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  • 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)

    • digital signatures (provide authentication)


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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

  • 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}


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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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  • 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

  • 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


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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 RFC1321


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MD5 Overview


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MD5 Overview

  • 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


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Processing of Block mi - 4 Passes















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


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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)

1 2 3 4 32


0 0 1 0 1


1 bit



1 0 1 1 1

22 6 13 32 3


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Per-Round Key Generation

Initial Permutation of DES key

C i-1

D i-1

28 bits

28 bits

Circular Left Shift

Circular Left Shift



Round 1,2,9,16:

single shift

Others: two bits


with Discard

48 bits


C i

D i

28 bits

28 bits


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A DES Round

32 bits Ln

32 bits Rn


One Round


48 bits



48 bits




32 bits

32 bits Ln+1

32 bits Rn+1


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Mangler Function

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


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Bits Expansion (1-to-m)

1 2 3 4 5 32



0 0 1 0 1 1



10 0 1 0 1 0 110

1 2 3 4 5 6 7 8 48


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2 bits














4 bits


= 1,…8.


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


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S-Box Examples

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: ???


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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


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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)


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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


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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), …


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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


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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


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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)


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MD5 Compression Function


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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)


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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 = 67452301

B = efcdab89

C = 98badcfe

D = 10325476

E = c3d2e1f0


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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.


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