Computer SecurityKey Management

Introduction

We distinguish between a session key and a interchange key (long term key).

The session key is associated with a session; the long term key with a principal.

Basic key exchange

C = trusted third party• A C: {request for ksession for Bob}kA

• C A: {ksession}kA, {ksession}kB

• A B: {ksession}kB

Now A and B share ksession .

Basic key exchange -- problems

With whom is Bob sharing a key? Replay attacks: Eve may highjack a session.

Classical cryptography key exchange

C = trusted third party• A C: { A||B|| rand1 }

• C A: { A||B||rand1||ksession , {A ||ksession}kB } kA

• A B: {A ||ksession}kB

• B A: {rand2}ksession

• A B: {rand2-1}ksession

rand1 and rand2 are called nonces.

Classical cryptography key exchange

Discussion on attacks.Intercept & highjack sessions, Use of Timestamps.

KerberosTicket : TAB = B || { A||A’s address||valid time||kAB||t}kB

t is a timestamp, kB is a key that B shares with an

authentication server,

AAB = { A||generation time}kAB is an authenticator for A.

1. A C: A || B2. C A: {kAB}kA || TAB

3. A B: G || AAB || TAB

4. B A: A || {kAG}kAB || TAG

5. A G: AAG||TAG

6. G A: {t+1}kAG

Kerberos

Discussion.How are principals (Alice,Bob) authenticated?

Key exchange with Public Key Cryptography

First try. A B: { ksession }eB

Key exchange with Public Key Cryptography

A fix A B: A, { { ksession }dA }eB

where dA is the private key of A.

Bob decrypts the received and uses the public key of A to obtain ksession from { ksession }dA.

But how does B get to know A’s key?

A man-in-the-middle attack

The attacker E succeeds in convincing A that B’s public key is eE and not eB..

1. A C: request for B’s public key –intercepted by E2. E C: request for B’s public key

3. C E: eB

4. E A: eE

5. A B: {ksession}eE -- intercepted by E

6. E B: {ksession}eB

(we did this attack in our Midterm 2)

Public Key Infrastructuresthe X.509 Authentication Framework

X.509 is based on certificate signature chains.Certificates are digitally signed by Certifying authorities and link a Public key to its owner.See textbook for details on X.509v3 certificates.

Public Key Infrastructures Certificate signature chains

Let X<<Y>> represent a certificate that X generated for the subject Y, eg X authenticated (digitally signed) the Public Key of Y.X<<Y>> represents the explicit trust that X has in (the public key of) Y (he wouldn’t otherwise certify it!).

Public Key Infrastructures Certificate signature chains

A certificate chain:X1<< X2 >> || X2<< X3 >> || . . . || Xn-1<< Xn >> represents the implicit trust of X1 in Xn:X1 trusts X2, who in turn trusts X3, who in turn trusts X3, . . . , and Xn-1 trusts Xn.PKI’s are based on implicit trust.

The structure of a PKI trust graphs

A PKI is determined by its: Certifying Authorities (CAs) Subjects Implicit trust relationships.

The trust graph of a PKI is the graph whose nodes are the CAs and the subjects and whose edges are the explicit trust relationships. Implicit trust relationships are represented by paths in the trust graph.

The structure of a PKI Trust graphs

The trust graph for the X.509 PKI is essentially a graph tree, with leafs the subjects.

The root CA is called the Root of the PKI. The X.509 PKI is scalable: the length of a trust

certificate chain is logarithmic in the size of the graph.

Trust graphs

C1

DavidCarol

C2

Alice Bob

Root CA

With a tree-graphs we have 1. Scalable solutions 2. Single point of failures

PKIs

Forest – cross-certifying Root CAs Other graph solutions PGPs Merkle Authentication Tree

PGP certificate chainsProvides privacy for electronic mail.The public key of an entity B is certified by “friends” who know him, say E,F,G. PGP certificate for A: E,F,G <<B>>PGP

Suppose we have the following chain:A,J <<J>>PGP || K,J,E <<E>>PGP || E,H <<H>>PGP ||

I,H,G <<G>>PGP || E,F,G,B <<B>>PGP ||

Then A PGP-trust B.

For more details see: http://www.cs.fsu.edu/~burmeste/ACM11temp.pdf

Merkle Authentication TreeTime stamping

Certificates can be kept as data in files, This reduces the problem of forging certificates to

the problem of data integrity.

Merkle Authentication Tree

Let Yi be an identifier and its associated public key. f : D D D a function that maps pairs of bit strings to a bit

string, where D is the set of bit strings. h: N N D be a cryptographic hash function, where N is

the set of natural numbers. h(i,j) = f (h (i, i+j /2) , h (i+j /2+1 , j) if i < j

f (Yi ,Yij) otherwise.

Merkle Authenticatiomn Tree h(1,4)

Y4

h(4,4)h(3,3)h(2,2)h(1,1)

h(3,4)h(1,2)

Y2 Y3Y1

The root value h(1,4) must be known and the file publicly available.

Merkle Authenticatiomn Tree

Suppose that Y1,Y2 ,…,Yn are in a file, and that user 3

wants to validate Y3.

Compute:• h(3,3) = f (Y3,Y3), • h(3,4) = f (h(3,3),h(4,4)), (assume that h(4,4) is available)• h(1,4) = f (h(1,2),h(3,4)). (assume that h(1,2) is available)

If h(1,4) is stored in a public file thenY3 can be validated

(time-stamped).

Merkle Authentication Tree

The hashes needed to validate a certificate for Yi are

called the authentication path of that certificate. The authentication path for Y3 is:

C3 = {Y3, h(4,4),h(1,2))}.