Overview of Key Establishment Overview of Key Establishment Techniques:Techniques:

Key Distribution, Key Agreement and PKIKey Distribution, Key Agreement and PKI

Wade Trappe

Lecture OverviewLecture Overview

We now begin our look at building protocols using the basic tools that we have discussed.

The discussion in this lecture will focus on issues of key establishment and the associated notion of authentication

These protocols are not real, but instead are meant to serve just as a high-level survey

Later lectures will go into specific protocols and will uncover practical challenges faced when implementing these protocols

Key Establishment: The problemKey Establishment: The problem

Securing communication requires that the data is encrypted before being transmitted.

Associated with encryption and decryption are keys that must be shared by the participants.

The problem of securing the data then becomes the problem of securing the establishment of keys.

Task: If the participants do not physically meet, then how do the participants establish a shared key?

Two types of key establishment:– Key Agreement– Key Distribution

Key DistributionKey Distribution

Key Agreement protocols: the key isn’t determined until after the protocol is performed.

Key Distribution protocols: one party generates the key and distributes it to Bob and/or Alice (Shamir’s 3pass, Kerberos).

Shamir’s Three-Pass Protocol:– Alice generates and Bob generates . – A key K is distributed by:

Alice BobpmodKK a1

pmodKK b12

pmodKK1a

23

pmodKK1b

3

Bob Calculates:

*pZa *

pZb

Basic TTP Key Distribution Basic TTP Key Distribution

KDC

Ka

Kb

Step 1Step 2

1. A Sends: {Request || IDA || IDB || N1}2. KDC Sends: EKa[ KAB|| {Request || IDA || IDB || N1}||EKb(KAB, IDA)]

Step 3Step 4

3. A Sends: EKb(KAB, IDA)

Step 5

4. B Sends: EKAB(N2) 5. A Sends: EKAB(f(N2))

Key AgreementKey Agreement In many scenarios, it is desirable for two parties to exchange messages in order to establish a shared secret that may be used

to generate a key. The Diffie-Hellman (DH) protocol is a basic tool used to establish shared keys in two-party communication. Two parties, A and B, establish a shared secret by:

The security of the DH scheme is based upon the intractibility of the Diffie-Hellman Problem:

The Diffie-Hellman scheme can be extended to work on arbitrary groups (e.g. Elliptic Curves).

Given a prime p, a generator g of , and elements and , it is computationally difficult to find .

*pZ pmodga pmodgb

pmodgab

pmodgpmodg:Bpmodgpmodg:A

pmodg:ABpmodg:BA

abbaabab

ba

Intruder In The MiddleIntruder In The Middle

The Intruder-in-the-Middle attack on Diffie-Hellman is based upon the following strategy to improve one’s chess ranking:– Eve challenges two grandmasters, and uses GM1’s moves against GM2.

Eve can either win one game, or tie both games.

Eve has and can perform the Intruder-in-the-Middle attack by:

Alice BobEvepmodga pmodgb

pmodgz pmodgzCalculates

pmodgKza

AE pmodgKzb

BE

Calculates

Calculates

BEAE K,K

Decrypts data with KBE

Decrypts data with KAE, uses data and encrypts with KBE

Encrypts data with KAE

DATAEAEK DATAE

BEK

Begins DH Begins DH

*pZz

Station-to-Station ProtocolStation-to-Station Protocol

Digital signatures can be used to prevent this protocol failure (STS Protocol).

A digital signature is a scheme that ties a message and its author together.– Private sig( ) function and Public ver( ) function.

Alice Bobpmodga

abBK

b g,gsigE,pmodg

baAK g,gsigE

pmodgKba

Calculates

pmodgKab

Calculates

Decrypts to get:

abB g,gsig

Verifies sig Verifies sig

Distribution of Public KeysDistribution of Public Keys

There are several techniques proposed for the distribution of public keys:– Public announcement– Publicly available directory– Public key authority– Public key certificates

Public AnnouncementPublic Announcement

Idea: Each person can announce or broadcast their public key to the world.

Example: People attach their PGP or RSA keys at the end of their emails.

Weakness: – No authenticity: Anyone can forge such an announcement– User B could pretend to be User A, but really announce User B’s public

key.

Public Directory ServicePublic Directory Service

Idea: Have a public directory or “phone book” of public keys. This directory is under the control/maintenance of a trusted third party (e.g. the government).

Involves:– Authority maintains a directory of {name, PK}– Each user registers public key. Registration should involve

authentication.– A user may replace or update keys. – Authority periodically publishes directory or updates to directory.– Participants can access directory through secure channel.

Weaknesses:– If private key of directory service is compromised, then opponent

can pretend to be directory service.– Directory is a single point of failure.

Public Key AuthorityPublic Key Authority

Idea: More security is achieved if the authority has tighter control over who gets the keys.

Assumptions:– Central authority maintains a dynamic directory of public keys of

all users.– Central authority only gives keys out based on requests.– Each user knows the public key of the authority.

Weaknesses:– Public Key Authority is a single point of failure.– User has to contact PK Authority, thus the PK Authority can be a

bottleneck for service.

Public Key Authority, protocolPublic Key Authority, protocol

PK Auth

ABStep 1Step 2

1. A Sends: {Request || Time1}2. PK Auth: EdAuth[ eB|| {Request || Time1}]

Step 3Step 6

3. A Sends B: EeB(IDA||N1)

Step 7

4 and 5. B does steps 1 and 2.

6. B Sends: EeA(N1||N2)

Step 4

Step 5

7. A Sends: EeB(N2)

Public Key CertificatesPublic Key Certificates

Idea: Use certificates! Participants exchange keys without contacting a PK Authority in a way that is reliable.

Certificates contain:– A public key (created/verified by a certificate authority).– Other information.

Certificates are given to a participant using the authority’s private key.

A participant conveys its key information to another by transmitting its certificate.

Other parties can verify that the certificate was created/verified by the authority.

Weakness:– Requires secure time synchronization.

Public Key Certificates, overview Public Key Certificates, overview

Cert Auth

A B

Give eA securely to CA

CertA = EdAuth{Time1||IDA||eA}

CertACert B

Securely give eB to CA

CertB = EdAuth{Time2||IDB||eB}

Requirements:•Any participant can read a certificate to determine the name and public key of the certificate’s owner.•Any participant can verify that the certificate originated from the certificate authority and is not counterfeit.•Only the certificate authority can create and update certificates.•Any participant can verify the currency of the certificate.

X.509 PK CertificatesX.509 PK Certificates

X.509 is a very commonly used public key certificate framework.

The certificate structure and authentication protocols are used in:– IP SEC– SSL– SET

X.509 Certificate Format:– Version 1/2/3– Serial is unique within the CA– First and last time of validity

Version

Cert Serial #

Algorithm & Parms

Issuer Name

Validity Time: Not before/after

Subject Name

PK Info: Algorithm, Parms, Key

. . .Signature (w/ hash)

X.509 Certificate ChainingX.509 Certificate Chaining

Its not feasible to have one CA for a large group of users.

Suppose A knows CA X1, B knows CA X2. If A does not know X2’s PK then CertX2(B) is useless to A.

If X1 and X2 have certified each other then A can get B’s PK by:– A obtains CertX1(X2)– A obtains CertX2(B)– Because B has a trusted copy of

X2’s PK, A can verify B’s certificate and get B’s PK.

Certificate Chain:– {CertX1(X2)|| CertX2(B)}

Procedure can be generalized to more levels.

A B

X1 X2

{CertX1(X2)|| CertX2(B)}

CertX1(X2) CertX2(X1)