introduction ece 498yh / cs 498yh: computer security
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Introduction
ECE 498YH / CS 498YH: Computer Security
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Administrative Aspects
• Course web page:– http://www.crhc.uiuc.edu/~yihchun/498– Not up yet
• Syllabus:– Midterm date TBA. Please report any conflicts.– Don’t cheat
• Project:– Systems security project– Probably network routing or spam
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Computer Security: 10,000’ View
Material borrowed from Matt Bishop’s sample slides for Computer Security:
Art and Science
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Basic Components
• Confidentiality– Keeping data and resources hidden
• Integrity– Data integrity (integrity)– Origin integrity (authentication)
• Availability– Enabling access to data and resources
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Classes of Threats• Disclosure
– Snooping• Deception
– Modification, spoofing, repudiation of origin, denial of receipt
• Disruption– Modification
• Usurpation– Modification, spoofing, delay, denial of service
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Policies and Mechanisms
• Policy says what is, and is not, allowed– This defines “security” for the site/system/etc.
• Mechanisms enforce policies• Composition of policies
– If policies conflict, discrepancies may create security vulnerabilities
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Goals of Security• Prevention
– Prevent attackers from violating security policy• Detection
– Detect attackers’ violation of security policy• Recovery
– Stop attack, assess and repair damage– Continue to function correctly even if attack
succeeds
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Trust and Assumptions
• Underlie all aspects of security• Policies
– Unambiguously partition system states– Correctly capture security requirements
• Mechanisms– Assumed to enforce policy– Support mechanisms work correctly
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Types of Mechanisms
secure precise broad
set of reachable states set of secure states
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Assurance
• Specification– Requirements analysis– Statement of desired functionality
• Design– How system will meet specification
• Implementation– Programs/systems that carry out design
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Operational Issues• Cost-Benefit Analysis
– Is it cheaper to prevent or recover?• Risk Analysis
– Should we protect something?– How much should we protect this thing?
• Laws and Customs– Are desired security measures illegal?– Will people do them?
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Human Issues
• Organizational Problems– Power and responsibility– Financial benefits
• People problems– Outsiders and insiders– Social engineering
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Tying Together
Threats
Policy
Specification
Design
Implementation
Operation
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Key Points• Policy defines security, and mechanisms enforce
security– Confidentiality– Integrity– Availability
• Trust and knowing assumptions• Importance of assurance• The human factor
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Chapter 9: Basic Cryptography
• Classical Cryptography• Public Key Cryptography• Cryptographic Checksums
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Overview• Classical Cryptography
– Cæsar cipher– Vigènere cipher– DES
• Public Key Cryptography– Diffie-Hellman– RSA
• Cryptographic Checksums– HMAC
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Cryptosystem• Quintuple (E, D, M, K, C)
– M set of plaintexts– K set of keys– C set of ciphertexts– E set of encryption functions e: M K C– D set of decryption functions d: C K M
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Example• Example: Cæsar cipher
– M = { sequences of letters }– K = { i | i is an integer and 0 ≤ i ≤ 25 }
– E = { Ek | k K and for all letters m,
Ek(m) = (m + k) mod 26 }
– D = { Dk | k K and for all letters c,
Dk(c) = (26 + c – k) mod 26 }
– C = M
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Attacks• Opponent whose goal is to break cryptosystem is the
adversary– Assume adversary knows algorithm used, but not key
• Three types of attacks:– ciphertext only: adversary has only ciphertext; goal is to
find plaintext, possibly key– known plaintext: adversary has ciphertext,
corresponding plaintext; goal is to find key– chosen plaintext: adversary may supply plaintexts and
obtain corresponding ciphertext; goal is to find key
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Basis for Attacks• Mathematical attacks
– Based on analysis of underlying mathematics• Statistical attacks
– Make assumptions about the distribution of letters, pairs of letters (digrams), triplets of letters (trigrams), etc.Called models of the language
– Examine ciphertext, correlate properties with the assumptions.
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Classical Cryptography• Sender, receiver share common key
– Keys may be the same, or trivial to derive from one another
– Sometimes called symmetric cryptography• Two basic types
– Transposition ciphers– Substitution ciphers– Combinations are called product ciphers
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Transposition Cipher• Rearrange letters in plaintext to produce
ciphertext• Example (Rail-Fence Cipher)
– Plaintext is HELLO WORLD– Rearrange as
HLOOLELWRD
– Ciphertext is HLOOL ELWRD
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Attacking the Cipher
• Anagramming– If 1-gram frequencies match English
frequencies, but other n-gram frequencies do not, probably transposition
– Rearrange letters to form n-grams with highest frequencies
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Substitution Ciphers
• Change characters in plaintext to produce ciphertext
• Example (Cæsar cipher)– Plaintext is HELLO WORLD– Change each letter to the third letter following it
(X goes to A, Y to B, Z to C)Key is 3, usually written as letter ‘D’
– Ciphertext is KHOOR ZRUOG
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Attacking the Cipher
• Exhaustive search– If the key space is small enough, try all possible
keys until you find the right one– Cæsar cipher has 26 possible keys
• Statistical analysis– Compare to 1-gram model of English
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Cæsar’s Problem
• Key is too short– Can be found by exhaustive search– Statistical frequencies not concealed well
They look too much like regular English letters
• So make it longer– Multiple letters in key– Idea is to smooth the statistical frequencies to
make cryptanalysis harder
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Vigènere Cipher• Like Cæsar cipher, but use a phrase• Example
– Message THE BOY HAS THE BALL– Key VIG– Encipher using Cæsar cipher for each letter:
key VIGVIGVIGVIGVIGVplain THEBOYHASTHEBALLcipher OPKWWECIYOPKWIRG
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Attacking the Cipher
• Approach– Establish period; call it n
Look for repetitions in ciphertext– Break message into n parts, each part being
enciphered using the same key letter Just like attacking Cæsar
– Solve each part You can leverage one part from another
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One-Time Pad• A Vigenère cipher with a random key at least as long as
the message– Provably unbreakable– Why? Look at ciphertext DXQR. Equally likely to
correspond to plaintext DOIT (key AJIY) and to plaintext DONT (key AJDY) and any other 4 letters
– Warning: keys must be random, or you can attack the cipher by trying to regenerate the key Approximations, such as using pseudorandom
number generators to generate keys, are not random
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Overview of the DES• A block cipher:
– encrypts blocks of 64 bits using a 64 bit key– outputs 64 bits of ciphertext
• A product cipher– basic unit is the bit– performs both substitution and transposition
(permutation) on the bits• Cipher consists of 16 rounds (iterations) each with a round
key generated from the user-supplied key
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Round Key Generation• 48-bit round keys are
selected based on permutations of the key
• Each key bit shows up in around 14 round keys
Image Source: Wikipedia
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Feistel Structure• Each “round” processes
half of the block• Easy to invert, even if f is
hard to invert (why?)
Image Source: Wikipedia
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The f Function• E is the expansion
function: replicates some of the input bits
• S boxes are implemented as a lookup table– Designed to be
nonlinear• P is a permutation
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Controversy
• Considered too weak– Diffie, Hellman said in a few years technology
would allow DES to be broken in days Design using 1999 technology published
– Design decisions not public S-boxes may have backdoors
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Undesirable Properties• 4 weak keys
– They are their own inverses• 12 semi-weak keys
– Each has another semi-weak key as inverse• Complementation property
– DESk(m) = c DESk(m) = c• S-boxes exhibit irregular properties
– Distribution of odd, even numbers non-random– Outputs of fourth box depends on input to third box
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Differential Cryptanalysis• A chosen ciphertext attack
– Requires 247 plaintext, ciphertext pairs• Revealed several properties
– Small changes in S-boxes reduce the number of pairs needed
– Making every bit of the round keys independent does not impede attack
• Linear cryptanalysis improves result– Requires 243 plaintext, ciphertext pairs
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DES Modes• Electronic Code Book Mode (ECB)
– Encipher each block independently
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What’s Wrong With ECB
• Electronic Code Book Mode (ECB)– Encipher each block independently
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DES Modes• Electronic Code Book Mode (ECB)
– Encipher each block independently• Cipher Block Chaining Mode (CBC)
– Xor each block with previous ciphertext block– Requires an initialization vector for the first one
• Encrypt-Decrypt-Encrypt Mode (2 keys: k, k)– c = DESk(DESk
–1(DESk(m)))• Encrypt-Encrypt-Encrypt Mode (3 keys: k, k, k)
– c = DESk(DESk (DESk(m)))
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CBC Mode Encryption
init. vector m1
DES
c1
m2
DES
c2
sent sent
…
…
…
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CBC Mode Decryption
init. vector c1
DES
m1
…
…
…
c2
DES
m2
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Self-Healing Property• Initial message
– 3231343336353837 3231343336353837 3231343336353837 3231343336353837
• Received as (underlined 4c should be 4b)– ef7c4cb2b4ce6f3b f6266e3a97af0e2c 746ab9a6308f4256 33e60b451b09603d
• Which decrypts to– efca61e19f4836f1 3231333336353837 3231343336353837 3231343336353837
– Incorrect bytes underlined– Plaintext “heals” after 2 blocks
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Current Status of DES• Design for computer system, associated software that
could break any DES-enciphered message in a few days published in 1998
• Several challenges to break DES messages solved using distributed computing
• NIST selected Rijndael as Advanced Encryption Standard, successor to DES– Designed to withstand attacks that were successful on
DES
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Public Key Cryptography• Two keys
– Private key known only to individual– Public key available to anyone
Public key, private key inverses
• Idea– Confidentiality: encipher using public key,
decipher using private key– Integrity/authentication: encipher using private
key, decipher using public one
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Requirements1. It must be computationally easy to encipher or
decipher a message given the appropriate key2. It must be computationally infeasible to derive
the private key from the public key3. It must be computationally infeasible to
determine the private key from a chosen plaintext attack
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Diffie-Hellman
• Compute a common, shared key– Called a symmetric key exchange protocol
• Based on discrete logarithm problem– Given integers n and g and prime number p,
compute k such that n = gk mod p– Solutions known for small p– Solutions computationally infeasible as p grows
large
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Algorithm• Constants: prime p, integer g ≠ 0, 1, p–1
– Known to all participants• Anne chooses private key kAnne, computes public key
KAnne = gkAnne mod p• To communicate with Bob, Anne computes Kshared =
KBobkAnne mod p• To communicate with Anne, Bob computes Kshared =
KAnnekBob mod p– It can be shown these keys are equal
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Example• Assume p = 53 and g = 17• Alice chooses kAlice = 5
– Then KAlice = 175 mod 53 = 40• Bob chooses kBob = 7
– Then KBob = 177 mod 53 = 6• Shared key:
– KBobkAlice mod p = 65 mod 53 = 38– KAlicekBob mod p = 407 mod 53 = 38
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RSA
• Exponentiation cipher• Relies on the difficulty of determining the number
of numbers relatively prime to a large integer n
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Background• Totient function (n)
– Number of positive integers less than n and relatively prime to n Relatively prime means with no factors in common
with n• Example: (10) = 4
– 1, 3, 7, 9 are relatively prime to 10• Example: (21) = 12
– 1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19, 20 are relatively prime to 21
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Algorithm• Choose two large prime numbers p, q
– Let n = pq; then (n) = (p–1)(q–1)– Choose e < n such that e is relatively prime to
(n).– Compute d such that ed mod (n) = 1
• Public key: (e, n); private key: d• Encipher: c = me mod n• Decipher: m = cd mod n
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Example: Confidentiality• Take p = 7, q = 11, so n = 77 and (n) = 60• Alice chooses e = 17, making d = 53• Bob wants to send Alice secret message HELLO (07 04
11 11 14)– 0717 mod 77 = 28– 0417 mod 77 = 16– 1117 mod 77 = 44– 1117 mod 77 = 44– 1417 mod 77 = 42
• Bob sends 28 16 44 44 42
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Example• Alice receives 28 16 44 44 42• Alice uses private key, d = 53, to decrypt message:
– 2853 mod 77 = 07– 1653 mod 77 = 04– 4453 mod 77 = 11– 4453 mod 77 = 11– 4253 mod 77 = 14
• Alice translates message to letters to read HELLO– No one else could read it, as only Alice knows her
private key and that is needed for decryption
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Example: Integrity/Authentication• Take p = 7, q = 11, so n = 77 and (n) = 60• Alice chooses e = 17, making d = 53• Alice wants to send Bob message HELLO (07 04 11 11 14) so Bob
knows it is what Alice sent (no changes in transit, and authenticated)– 0753 mod 77 = 35– 0453 mod 77 = 09– 1153 mod 77 = 44– 1153 mod 77 = 44– 1453 mod 77 = 49
• Alice sends 35 09 44 44 49
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Example• Bob receives 35 09 44 44 49
• Bob uses Alice’s public key, e = 17, n = 77, to decrypt message:
– 3517 mod 77 = 07
– 0917 mod 77 = 04
– 4417 mod 77 = 11
– 4417 mod 77 = 11
– 4917 mod 77 = 14
• Bob translates message to letters to read HELLO
– Alice sent it as only she knows her private key, so no one else could have enciphered it
– If (enciphered) message’s blocks (letters) altered in transit, would not decrypt properly
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Example: Both• Alice wants to send Bob message HELLO both enciphered and
authenticated (integrity-checked)– Alice’s keys: public (17, 77); private: 53– Bob’s keys: public: (37, 77); private: 13
• Alice enciphers HELLO (07 04 11 11 14):– (0753 mod 77)37 mod 77 = 07– (0453 mod 77)37 mod 77 = 37– (1153 mod 77)37 mod 77 = 44– (1153 mod 77)37 mod 77 = 44– (1453 mod 77)37 mod 77 = 14
• Alice sends 07 37 44 44 14
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Security Services
• Confidentiality– Only the owner of the private key knows it, so
text enciphered with public key cannot be read by anyone except the owner of the private key
• Authentication– Only the owner of the private key knows it, so
text enciphered with private key must have been generated by the owner
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More Security Services
• Integrity– Enciphered letters cannot be changed
undetectably without knowing private key• Non-Repudiation
– Message enciphered with private key came from someone who knew it
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Warnings• Encipher message in blocks considerably larger
than the examples here– If 1 character per block, RSA can be broken
using statistical attacks (just like classical cryptosystems)
– Attacker cannot alter letters, but can rearrange them and alter message meaningExample: reverse enciphered message of
text ON to get NO
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Cryptographic Checksums• Mathematical function to generate a set of k bits
from a set of n bits (where k ≤ n).– k is smaller then n except in unusual
circumstances• Example: ASCII parity bit
– ASCII has 7 bits; 8th bit is “parity”– Even parity: even number of 1 bits– Odd parity: odd number of 1 bits
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Definition
• Cryptographic checksum h: AB:1. For any x A, h(x) is easy to compute2. For any y B, it is computationally infeasible to find
x A such that h(x) = y3. It is computationally infeasible to find two inputs x,
x A such that x ≠ x and h(x) = h(x)– Alternate form (stronger): Given any x A, it is
computationally infeasible to find a different x A such that h(x) = h(x).
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Collisions• If x ≠ x and h(x) = h(x), x and x are a collision
– Pigeonhole principle: if there are n containers for n+1 objects, then at least one container will have 2 objects in it.
– Application: if there are 32 files and 8 possible cryptographic checksum values, at least one value corresponds to at least 4 files
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Keys• Keyed cryptographic checksum: requires
cryptographic key– DES in chaining mode: encipher message, use
last n bits. Requires a key to encipher, so it is a keyed cryptographic checksum.
• Keyless cryptographic checksum: requires no cryptographic key– MD5 and SHA-1 are best known; others include
MD4, HAVAL, and Snefru
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HMAC• Make keyed cryptographic checksums from keyless
cryptographic checksums• h keyless cryptographic checksum function that takes data
in blocks of b bytes and outputs blocks of l bytes. k is cryptographic key of length b bytes– If short, pad with 0 bytes; if long, hash to length b
• ipad is 00110110 repeated b times• opad is 01011100 repeated b times• HMAC-h(k, m) = h(k opad || h(k ipad || m))
exclusive or, || concatenation
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Key Points• Two main types of cryptosystems: classical and public key• Classical cryptosystems encipher and decipher using the
same key– Or one key is easily derived from the other
• Public key cryptosystems encipher and decipher using different keys– Computationally infeasible to derive one from the other
• Cryptographic checksums provide a check on integrity