Public-Key Encryption and Key Management in Cryptography and Network Security, Study notes of Design and Analysis of Algorithms

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Cryptography and

Cryptography and

Network Security

Network Security

Chapter 10

Chapter 10

Key Management

Key Management



public-key encryption helps address

public-key encryption helps address

key

key

distribution problems

distribution problems



have two aspects of this:

have two aspects of this:



distribution of public keys

distribution of public keys



use of public-key encryption to

use of public-key encryption to distribute

distribute

secret keys

secret keys

Public Announcement

Public Announcement



users distribute public keys to recipients or

users distribute public keys to recipients or

broadcast to community at large

broadcast to community at large



eg. append PGP keys to email messages or

eg. append PGP keys to email messages or

post to news groups or email list

post to news groups or email list



major weakness is forgery

major weakness is forgery



anyone can create a key claiming to be

anyone can create a key claiming to be

someone else and broadcast it

someone else and broadcast it



until forgery is discovered can masquerade as

until forgery is discovered can masquerade as

claimed user

claimed user

Publicly Available Directory

Publicly Available Directory



can obtain greater security by registering

can obtain greater security by registering

keys with a public directory

keys with a public directory



directory must be trusted with properties:

directory must be trusted with properties:



contains {name,public-key} entries

contains {name,public-key} entries



participants register securely with directory

participants register securely with directory



participants can replace key at any time

participants can replace key at any time



directory is periodically published

directory is periodically published



directory can be accessed electronically

directory can be accessed electronically



still vulnerable to tampering or forgery

still vulnerable to tampering or forgery

Public-Key Authority

Public-Key Authority

Public-Key Certificates

Public-Key Certificates



certificates allow key exchange without

certificates allow key exchange without

real-time access to

real-time access to

public-key authority

public-key authority



a certificate

a certificate

binds

binds

identity

identity

to

to

public key

public key



usually with other info such as period of

usually with other info such as period of

validity, rights of use etc

validity, rights of use etc



with all contents

with all contents

signed

signed

by a trusted

by a trusted

Public-Key or Certificate Authority (CA)

Public-Key or Certificate Authority (CA)



can be verified by anyone who knows the

can be verified by anyone who knows the

public-key authorities public-key

public-key authorities public-key

Public-Key D

Public-Key D

istribution of Secret

istribution of Secret

Keys

Keys



use previous methods to obtain public-key

use previous methods to obtain public-key



can use for secrecy or authentication

can use for secrecy or authentication



but public-key algorithms are slow

but public-key algorithms are slow



so usually want to use private-key

so usually want to use private-key

encryption to protect message contents

encryption to protect message contents



hence need a session key

hence need a session key



have several alternatives for negotiating a

have several alternatives for negotiating a

suitable session

suitable session

Simple Secret Key

Simple Secret Key

Distribution

Distribution



proposed by Merkle in 1979

proposed by Merkle in 1979



A generates a new temporary public key pair

A generates a new temporary public key pair



A sends B the public key and their identity

A sends B the public key and their identity



B generates a session key K sends it to A

B generates a session key K sends it to A

encrypted using the supplied public key

encrypted using the supplied public key



A decrypts the session key and both use

A decrypts the session key and both use



problem is that an opponent can intercept

problem is that an opponent can intercept

and impersonate both halves of protocol

and impersonate both halves of protocol

Hybrid Key Distribution

Hybrid Key Distribution



retain use of private-key KDC

retain use of private-key KDC



shares secret master key with each user

shares secret master key with each user



distributes session key using master key

distributes session key using master key



public-key used to distribute master keys

public-key used to distribute master keys



especially useful with widely distributed users

especially useful with widely distributed users



rationale

rationale



performance

performance



backward compatibility

backward compatibility

Diffie-Hellman Key Exchange

Diffie-Hellman Key Exchange



first public-key type scheme proposed

first public-key type scheme proposed



by Diffie & Hellman in 1976 along with the

by Diffie & Hellman in 1976 along with the

exposition of public key concepts

exposition of public key concepts



note: now know that

note: now know that

Williamson

Williamson

(UK CESG)

(UK CESG)

secretly proposed the concept in 1970

secretly proposed the concept in 1970



is a practical method for public exchange

is a practical method for public exchange

of a secret key

of a secret key



used in a number of commercial products

used in a number of commercial products

Diffie-Hellman Setup

Diffie-Hellman Setup



all users agree on global parameters:

all users agree on global parameters:



large prime integer or polynomial

large prime integer or polynomial

q

q



a

a being a primitive root mod

being a primitive root mod q

q



each user (eg. A) generates their key

each user (eg. A) generates their key



chooses a secret key (number):

chooses a secret key (number): x

x

A

A

< q

< q



compute their

compute their public key

public key :

y

y

AA

a

a

x

x

A

A

mod q

mod q



each user makes public that key

each user makes public that key

y

y

A

A

Diffie-Hellman Key Exchange

Diffie-Hellman Key Exchange



shared session key for users A & B is K

shared session key for users A & B is K

AB

AB

K

K

AB

AB

=

=

a

a

x

x

A.A.

x

x

BB

mod q

mod q

= y

= y

A

A

x

x

B

B

mod q (which

mod q (which B

B can compute)

can compute)

= y

= y

BB

xx

AA

mod q (which

mod q (which A

A can compute)

can compute)



K

K

AB

AB

is used as session key in private-key

is used as session key in private-key

encryption scheme between Alice and Bob

encryption scheme between Alice and Bob



if Alice and Bob subsequently communicate,

if Alice and Bob subsequently communicate,

they will have the

they will have the same

same key as before, unless

key as before, unless

they choose new public-keys

they choose new public-keys



attacker needs an x, must solve discrete log

attacker needs an x, must solve discrete log

Key Exchange Protocols

Key Exchange Protocols



users could create random private/public

users could create random private/public

D-H keys each time they communicate

D-H keys each time they communicate



users could create a known private/public

users could create a known private/public

D-H key and publish in a directory, then

D-H key and publish in a directory, then

consulted and used to securely

consulted and used to securely

communicate with them

communicate with them



both of these are vulnerable to a meet-in-

both of these are vulnerable to a meet-in-

the-Middle Attack

the-Middle Attack



authentication of the keys is needed

authentication of the keys is needed

Weakness

Weakness



In this simple example, it would be possible by brute force to

In this simple example, it would be possible by brute force to

determine the secret key 160. In particular, an attacker E can

determine the secret key 160. In particular, an attacker E can

determine the determine the



common key by discovering a solution to the equation 3

common key by discovering a solution to the equation 3



a

a



mod 353 = 40 or the equation 3

mod 353 = 40 or the equation 3



b

b



mod 353 = 248. The brute-force approach is to

mod 353 = 248. The brute-force approach is to



calculate powers of 3 modulo 353, stopping when the result equals

calculate powers of 3 modulo 353, stopping when the result equals

either 40 or 248. The desired answer is reached with the exponent

either 40 or 248. The desired answer is reached with the exponent



value of 97, which provides 3

value of 97, which provides 3



97

97



mod 353 = 40.

mod 353 = 40.



With larger numbers, the problem becomes impractical.

With larger numbers, the problem becomes impractical.