1

Counter-measures

Threat Monitoring Cryptography as a security tool

Encryption Digital Signature Key distribution

2

Threat Monitoring

Check for suspicious patterns of activity i.e., several incorrect password attempts may

signal password guessing Audit log

Records time, user, & type of all accesses to object

Useful for recovery from violation, developing better security measures

Scan system periodically for security holes Done when the computer is relatively unused

3

Threat Monitoring (Cont.)

Check for: Short or easy-to-guess passwords Unauthorized setuid programs Unauthorized programs in system

directories Unexpected long-running processes Improper directory protections Improper protections on system data files Dangerous entries in the program search

path (Trojan horse) Changes to system programs: monitor

checksum values

4

Cryptography

Cryptography: a set of mathematical functions with a set of nice properties. A common mechanism for enforcing policies.

Encrypt clear text into cipher text, and vice versa

plaintext plaintextciphertext

KA

encryptionalgorithm

decryption algorithm

Alice’s encryptionkey

Bob’s decryptionkey

KB

5

Properties of Good Encryption Techniques

Encryption scheme depends not on secrecy of algorithm but on parameter of algorithm called encryption key

Extremely difficult for an intruder to determine the encryption key

6

Cryptography Algorithms

Symmetric key algorithm: one shared by a pair of users used for both encryption and decryption.

Asymmetric or public/private key algorithms are based on each user having two keys:

public key – in public private key – key known only to

individual user

7

Symmetric Key Cryptography

Symmetric key crypto: Bob and Alice share same (symmetric) key: K

plaintextciphertext

KA-B

encryptionalgorithm

decryption algorithm

A-B

KA-B

plaintextmessage, m

K (m)A-B

K (m)A-B

m = K ( ) A-B

Q: how do Bob and Alice agree on key value?

8

Symmetric Key Cryptography: Substitution Ciper

Substituting one thing for another monoalphabetic cipher: substitute one letter

for anotherplaintext: abcdefghijklmnopqrstuvwxyz

ciphertext: mnbvcxzasdfghjklpoiuytrewq

Plaintext: bob. i love you. alice

ciphertext: nkn. s gktc wky. mgsbc

E.g.:

Q: How hard to break this simple cipher?• Brute force• Other

9

Symmetric Key Crypto: DES

initial permutation 16 identical “rounds” of

function application, each using different 48 bits of key

final permutation

DES operation

DES: Data Encryption StandardUS encryption standard [NIST 1993]

10

How Secure is DES?

DES Challenge: 56-bit-key-encrypted phrase (“Strong cryptography makes the world a safer place”) decrypted (brute force) in 4 months in 1997

No known “backdoor” decryption approach

Making DES more secure: use three keys sequentially (3-DES)

on each datum use cipher-block chaining

11

AES: Advanced Encryption Standard

new (Nov. 2001) symmetric-key NIST standard, replacing DES

processes data in 128 bit blocks 128, 192, or 256 bit keys brute force decryption (try each

key) taking 1 sec on DES, takes 149 trillion years for AES

12

Public Key Cryptography

symmetric key crypto

requires sender, receiver know shared secret key

Q: how to agree on key in first place (particularly if never “met”)?

public key cryptography

radically different approach [Diffie-Hellman76, RSA78]

sender, receiver do not share secret key

public key known to all

private key known only to an individual

13

Public Key Cryptography

plaintextmessage, m

ciphertextencryptionalgorithm

decryption algorithm

Bob’s public key

plaintextmessageK (m)

B+

K B+

Bob’s privatekey

K B-

m = K (K (m))B+

B-

14

Public Key Encryption Algorithms

need K ( ) and K ( ) such thatB B

given public key K , it should be impossible to compute private key KB

B

Requirements:

1

2

RSA: Rivest, Shamir, Adelson algorithm

+ -

K (K (m)) = m BB

- +

+

-

15

RSA: Choosing Keys

1. Choose two large prime numbers p, q. (e.g., 1024 bits each)

2. Compute n = pq, z = (p-1)(q-1)

3. Choose e (with e<n) that has no common factors with z. (e, z are “relatively prime”).

4. Choose d such that ed-1 is exactly divisible by z. (in other words: ed mod z = 1 ).

5. Public key is (n,e). Private key is (n,d).

K B+ K B

-

16

RSA: Encryption, decryption

0. Given (n,e) and (n,d) as computed above

1. To encrypt bit pattern, m, compute

c = m mod n

e (i.e., remainder when m is divided by n)e

2. To decrypt received bit pattern, c, compute

m = c mod n

d (i.e., remainder when c is divided by n)d

m = (m mod n)

e mod n

dMagichappens!

c

17

RSA Example:

Bob chooses p=5, q=7. Then n=35, z=24.e=5 (so e, z relatively prime).d=29 (so ed-1 exactly divisible by z).

letter m me c = m mod ne

l 12 1524832 17

c m = c mod nd

17 481968572106750915091411825223071697 12

cdletter

l

encrypt:

decrypt:

18

RSA: Why it works

(m mod n)e mod n = m mod nd ed

Useful number theory result: If p,q prime and n = pq, then:

x mod n = x mod ny y mod (p-1)(q-1)

= m mod n

ed mod (p-1)(q-1)

= m mod n1

= m

(using number theory result above)

(since we chose ed to be divisible by(p-1)(q-1) with remainder 1 )

19

RSA: Another Important Property

The following property will be very useful later:

K (K (m)) = m BB

- +K (K (m))

BB+ -

=

use public key first, followed by private key

use private key first,

followed by public key

Result is the same!

20

Usage of Cryptography

Encryption (for confidentiality) Digital Signature Key distribution

21

Digital Signatures

Cryptographic technique analogous to hand-written signatures.

sender (Bob) digitally signs document, establishing he is document owner/creator.

verifiable, nonforgeable: recipient (Alice) can prove to someone that Bob, and no one else (including Alice), must have signed document

Digital Signature: signed (encrytped) message digest

22

Message Digests

Goal: fixed-length, easy- to-compute digital “fingerprint”

apply hash function H to m, get fixed size message digest, H(m).

Hash function properties: many-to-1 produces fixed-size msg

digest (fingerprint) given message digest x,

computationally infeasible to find m’ such that x = H(m’)

large message

m

H: HashFunction

H(m)

23

large message

mH: Hashfunction H(m)

digitalsignature(encrypt)

Bob’s private

key K B-

+

Bob sends digitally signed message:

Alice verifies signature and integrity of digitally signed message:

KB(H(m))-

encrypted msg digest

KB(H(m))-

encrypted msg digest

large message

m

H: Hashfunction

H(m)

digitalsignature(decrypt)

H(m)

Bob’s public

key K B+

equal ?

Digital Signature: Example

24

Functionality of Digital signature

Functionality: Prove Bob signed the message Message has not been modified

Questions: Why sign message digest instead of

message? What if Bob wants m to be confidential?

Question: can you use symmetric cryptography for digital signature?

25

Hash Function Algorithms

MD5 (Message-Digest algorithm 5) hash function widely used (RFC 1321) computes 128-bit message digest in 4-

step process. Designed by Rivest, 1992 Found security flaws in 1996, more

serious flaws found in 2004. SHA-1 (Secure Hash Algorithm) is also used.

US standard [NIST, FIPS PUB 180-1] 160-bit message digest Shown possible to break it faster than

brute-force, 2005

26

Comparison of Symmetric & Asymmetric Cryptography

Symmetric cryptography Easy to compute

Asymmetric cryptography Computationally expensive Good theoretical bounds Provide more functionalities than

encryption (e.g., digital signature)