Network systems security by mort anvari lecture7

Key Management Asymmetric encryption helps address key distribution problems  Two aspects  distribution of public keys  use of public-key encryption to distribute secret keys... 9/16

Key Management

Network Systems Security

Mort Anvari

Key Management

 Asymmetric encryption helps address key

distribution problems

 Two aspects

 distribution of public keys

 use of public-key encryption to distribute secret keys

9/16/2004 3

Distribution of Public Keys

 Four alternatives of public key distribution

 Public announcement

 Publicly available directory

 Public-key authority

 Public-key certificates

Public Announcement

 Users distribute public keys to recipients or

broadcast to community at large

 E.g append PGP keys to email messages or post to news groups or email list

 Major weakness is forgery

 anyone can create a key claiming to be someone

else and broadcast it

 can masquerade as claimed user before forgery is discovered

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Publicly Available Directory

 Achieve greater security by registering keys with a public directory

 Directory must be trusted with

properties:

 contains {name, public-key} entries

 participants register securely with directory

 participants can replace key at any time

 directory is periodically published

 directory can be accessed electronically

 Still vulnerable to tampering or forgery

Public-Key Authority

 Improve security by tightening control over distribution of keys from directory

 Has properties of directory

 Require users to know public key for the directory

 Users can interact with directory to

obtain any desired public key securely

 require real-time access to directory when keys are needed

9/16/2004 7

Public-Key Authority

Public-Key Certificates

real-time access to public-key authority

key

 usually with other info such as period of

validity, authorized rights, etc

Public-Key or Certificate Authority (CA)

the CA’s public key

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Public-Key Certificates

Distribute Secret Keys

Using Asymmetric Encryption

 Can use previous methods to obtain

public key of other party

 Although public key can be used for

confidentiality or authentication,

asymmetric encryption algorithms are

too slow

 So usually want to use symmetric

encryption to protect message contents

 Can use asymmetric encryption to set up

a session key

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Simple Secret Key

Distribution

 A generates a new temporary public key pair

 A sends B the public key and A’s identity

 B generates a session key K s and sends

encrypted K s (using A’s public key) to A

 A decrypts message to recover K s and both use

Problem with

Simple Secret Key

Distribution

 An adversary can intercept and

impersonate both parties of protocol

 A generates a new temporary public key pair {KU a ,

KR a } and sends KU a || ID a to B

 Adversary E intercepts this message and sends KU e ||

ID a to B

 B generates a session key K s and sends encrypted K s

(using E’s public key)

 E intercepts message, recovers K s and sends

encrypted K s (using A’s public key) to A

 A decrypts message to recover K s and both A and B unaware of existence of E

9/16/2004 13

Distribute Secret Keys

Using Asymmetric Encryption

 if A and B have securely exchanged public-keys

?

Problem with Previous

Scenario

by N2

 An adversary can intercept

message (4) and replay an old

message or insert a fabricated

message

9/16/2004 15

Order of Encryption Matters

 What can be wrong with the following

protocol?

AB: N

BA: E KUa [E KRb [K s ||N]]

 An adversary sitting between A and B can get

a copy of secret key Ks without being caught

by A and B!

Diffie-Hellman Key

Exchange

 First public-key type scheme proposed

 By Diffie and Hellman in 1976 along with

advent of public key concepts

 A practical method for public exchange of

secret key

 Used in a number of commercial products

 cannot be used to exchange an arbitrary message

 Value of key depends on the participants (and their private and public key information)

 Based on exponentiation in a finite (Galois)

field (modulo a prime or a polynomial) - easy

 Security relies on the difficulty of computing discrete logarithms (similar to factoring) – hard

Primitive Roots

 From Euler’s theorem: aø(n) mod n=1

 Consider am mod n=1, GCD(a,n)=1

 must exist for m= ø(n) but may be smaller

 once powers reach m, cycle will repeat

 If smallest is m= ø(n) then a is called a

primitive root

 if p is prime, then successive powers of

a “generate” the group mod p

 Not every integer has primitive roots

9/16/2004 19Primitive Root Example:

Power of Integers Modulo 19

Discrete Logarithms

 Inverse problem to exponentiation is to find the

discrete logarithm of a number modulo p

 Namely find x where a x = b mod p

 Written as x=log a b mod p or x=ind a,p (b)

 If a is a primitive root then discrete logarithm

always exists, otherwise may not

 3 x = 4 mod 13 has no answer

 2 x = 3 mod 13 has an answer 4

 While exponentiation is relatively easy, finding

discrete logarithms is generally a hard problem

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Diffie-Hellman Setup

 All users agree on global parameters

 large prime integer or polynomial q

 α which is a primitive root mod q

 Each user (e.g A) generates its key

 choose a secret key (number): x A < q

 compute its public key: y A = α xA mod q

 Each user publishes its public key

= yA xB mod q (which B can compute)

= yB xA mod q (which A can compute)

 KAB is used as session key in symmetric encryption scheme between A and B

 Attacker needs xA or xB, which requires solving discrete log

9/16/2004 23

Diffie-Hellman Example

Next Class

 Hashing functions

 Message digests