Introduction

ECE 498YH / CS 498YH: Computer Security

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

Computer Security: 10,000’ View

Material borrowed from Matt Bishop’s sample slides for Computer Security:

Art and Science

Basic Components

• Confidentiality– Keeping data and resources hidden

• Integrity– Data integrity (integrity)– Origin integrity (authentication)

• Availability– Enabling access to data and resources

Classes of Threats• Disclosure

– Snooping• Deception

– Modification, spoofing, repudiation of origin, denial of receipt

• Disruption– Modification

• Usurpation– Modification, spoofing, delay, denial of service

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

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

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

Types of Mechanisms

secure precise broad

set of reachable states set of secure states

Assurance

• Specification– Requirements analysis– Statement of desired functionality

• Design– How system will meet specification

• Implementation– Programs/systems that carry out design

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?

Human Issues

• Organizational Problems– Power and responsibility– Financial benefits

• People problems– Outsiders and insiders– Social engineering

Tying Together

Threats

Policy

Specification

Design

Implementation

Operation

Key Points• Policy defines security, and mechanisms enforce

security– Confidentiality– Integrity– Availability

• Trust and knowing assumptions• Importance of assurance• The human factor

Chapter 9: Basic Cryptography

• Classical Cryptography• Public Key Cryptography• Cryptographic Checksums

Overview• Classical Cryptography

– Cæsar cipher– Vigènere cipher– DES

• Public Key Cryptography– Diffie-Hellman– RSA

• Cryptographic Checksums– HMAC

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

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

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

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.

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

Transposition Cipher• Rearrange letters in plaintext to produce

ciphertext• Example (Rail-Fence Cipher)

– Plaintext is HELLO WORLD– Rearrange as

HLOOLELWRD

– Ciphertext is HLOOL ELWRD

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

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

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

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

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

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

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

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

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

Feistel Structure• Each “round” processes

half of the block• Easy to invert, even if f is

hard to invert (why?)

Image Source: Wikipedia

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

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

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

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

DES Modes• Electronic Code Book Mode (ECB)

– Encipher each block independently

What’s Wrong With ECB

• Electronic Code Book Mode (ECB)– Encipher each block independently

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)))

CBC Mode Encryption

init. vector m1

DES

c1

m2

DES

c2

sent sent

…

…

…

CBC Mode Decryption

init. vector c1

DES

m1

…

…

…

c2

DES

m2

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

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

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

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

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

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

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

RSA

• Exponentiation cipher• Relies on the difficulty of determining the number

of numbers relatively prime to a large integer n

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

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

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

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

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

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

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

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

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

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

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

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).

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

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

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

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