Cryptography

Lecture 10

Stefan Dziembowskiwww.dziembowski.net

stefan@dziembowski.net

Plan

1. Qualified signatures

2. PKI and trust management

3. Introduction to the key establishment protocols

Remember the slide from the previous lectures?

P5

P1

P3P2

P4

pk1

pk2

pk3

pk4

pk5

public register:

sk3

sk5

sk4sk1

sk2

Question:How to maintain the public register?

1. We start with the case when the public keys are used for signing that is legally binding.

2. Then we consider other cases.

But pk is not my public key!

A problem

Alice Bob

(m, σ =Signsk(m))

skA pkA

m є {0,1}*

Judge

I got (m,σ) from AliceIt’s not true!

I never signed m!

Vrfy(pk,m,σ) = yesso you cannot repudiate signing m...

Solution: certification authoritiesA simplified view:

comes with her ID and pkAlice

(pkCert,skCert)

checks the ID of Alice and issues a certificate:

SignskCert(“pkAlice is a public key of Alice”)

Alice

Now, everyone can verify that pkAlice is a public key of Alice. So Alice can attach it to every signature

Certification Authority

really everyone?

What is needed to verify the certificate

To verify the certificate coming from Cert one needs:

1. to know the public key of the Cert

2. to trust Cert.

It is better if Cert also keeps a document:

“I, Alice certify that pkAlice is my public key”

with a written signature of Alice.

How does it look from the legal point of view?

What matters at the end is if you can convince the judge.

Many countries have now a special law regulating these things.

In Italy it is:

Decreto Legislativo 7 marzo 2005, n. 82"Codice dell'amministrazione digitale"

pubblicato nella Gazzetta Ufficiale n. 112 del 16 maggio 2005 - Supplemento Ordinario n. 93

This law defines the conditions to become an official certification authority (in Italian: certificatore).

A certificate issued by such an authority is called a qualified certificate (in Italian: certificato qualificato)

A signature obtained this way is called a qualified digital signature (in Italian: firma elettronica qualificata).

The qualified signature is equivalent to the written one!

Some of the Italian Certificate Authorities:

Banca Monte dei Paschi di Siena S.p.A. (dal 03/08/2004)Lombardia Integrata S.p.A. (dal 17/08/2004)Banca Intesa S.p.A. (dal 09/09/2004 - Società soggetta a cambio di denominazione

sociale; ora Intesa Sanpaolo S.p.A.)Banca di Roma S.p.A. (dal 09/09/2004)(cessata attività dal 13/02/2008 - certificatore sostitutivo: nessuno)CNIPA (dal 15/03/2001)I.T. Telecom S.r.l. (dal 13/01/2005)Comando Trasmissioni e Informazioni Esercito (dal 10/04/2003 - già Comando C4

- IEW - cessata attività dal 21/09/2007 - certificatore sostitutivo: nessuno)Consorzio Certicomm (dal 23/06/2005)

.

.

.

So, what to do if you want to issue the qualified signatures?

You have to go to one of this companies and get a qualified certificate (it costs!).

The certificate is valid just for some given period.

What if the secret key is lost?

1. In this case you have to revoke the certificate.Every authority maintains a list of revoked certificates.

2. The certificates come with some insurance.

In many case one doesn’t want to use the qualified signatures

1. The certificates cost.

2. It’s risky to use them:

How do you know what your computer is really signing?Computers have viruses, Trojan horses, etc.

You can use external (trusted) hardware but it should have a display (so you can see what is signed).

Remember: qualified signatures are equivalent to the written ones!

Practical solution

In many cases the qualified signatures are an overkill.

Instead, people use non-qualified signatures.

Here, the certificates are distributed using a public-key infrastructure (PKI).

Users can certify keys of the other users

P1 P3P2

pk3pk1 pk2

knows pk2 knows pk3

“trusts” P2

P2 certifies that pk3 is a public key of P3 signature of P2

P1 believesthat pk3 is a

public key of P3

this should be done only if P2 really met P3 in person and verified his identity

P1 P3P2

pk3pk1 pk2

knows pk2 knows pk3

“trusts” P2

P4

pk4

knows pk4

“trusts” P3

P2 certifies that pk3 is a public key of P3 signature of P2

P3 certifies that pk4 is a public key of P4 signature of P3

P1 believesthat pk3 is a

public key of P3

P1 P3P2

pk3pk1 pk2

knows pk2 knows pk3

“trusts” P2

P4

pk4

P2 certifies that pk3 is a public key of P3 signature of P2

P3 certifies that pk4 is a public key of P4 signature of P3

P1 believesthat pk3 is a

public key of P3

“trusts” P3

knows pk4

P4

pk4

“trusts” P4

P4 certifies that pk5 is a public key of P5 signature of P4

This is called acertificate chain

knows pk5

A problem

What if P1 does not know P3?How can he trust him?

Answer: P2 can recommend P3 to P1.

P1 P3P2

pk3pk1 pk2

knows pk2 knows pk3

“trusts” P2

P4

pk4

“trusts” P3

knows pk4

A question: is trust transitive?

P1 P3P2

pk3pk1 pk2

“trusts” P2 “trusts” P3

P1 P3P2

pk3pk1 pk2

“trusts” P3

Does:

imply:

?

Example

P1 P3P2

pk3pk1 pk2

trusts thatP2 is a very

honest person

P1 P3P2

pk3pk1 pk2

doesn’t trust that P3

is honest, because he thinks that P2 is honest but naive

trusts thatP3 is a very

honest person

I can recommend P3

Moral

Trust is not transitive:

“P1 trusts in the certificates issued by P2”

is not the same as saying:

“P1 trusts that if

P2 says you can trust the certificates issued by P3

then

one can trust the certificates issued by P3”

Recommendation levelslevel 1 recommendation:

A: ”you can trusts in all the certificates issued by B”

level 2 recommendation:

A : “you can trust that all the level 1 recommendations issued by B”

level 3 recommendation:

B : “you can trust that all the level 2 recommendations issued by B”

and so on. . .

Recursively:

level i+1 recommendation:

A : “you can trust that all the level i recommendations issued by B”

P1 P3P2 P4

P1 P3P2 P4

trusts the certificates issued by P4

Now, if:

then

Of course the recommendations also need to be signed.

Starts to look complicated...

P2 issues

a recommendationof level 2 for P3

P3 issues

a recommendationof level 1 for P4

P2 trust

in all the recommendations

issued by P2

How is it solved in practice?

In popular standard is X.509 the recommendation is included into a certificate.

Here the level of recommendations is bounded using a field called basic constraints.

X.509 is used for example in SSL.

SSL is implemented is implemented in every popular web-browser.

So, let’s look at it.

this field limits the recommendation

depth(here it’s unlimited)

Concrete example

Let’s go to the Banca Di Roma website

a certificatechain

the second certificate wassigned by ”Verisign Primary Authority” for“Verisign Inc”.

(it’s not strange, we willdiscuss it)

Look here

The third certificatewas issued by Verisign Inc.for Banca di Roma

The typical pictureweb browser knows these certificates

Verisign DigiCert Entrust . . .

VerisignEurope

VerisignUSA

VerisignItaly

Banca di Roma

a certificate path

Implicit assumptions:

• the author of the browser is honest,• nobody manipulated the browser

CA1

CA2

CA3

CAn

client

cert1

cert2

cert3

certn-1

certn

Moreover:

each certi has a number di denoting a maximal depth of certificate chain from this point (this limits the recommendation depth)

That is, we need to have:

di ≥ n - i

All these certificates have tohave a flag “Is a Certification Authority”

switched on.

d1

d2

d3

dn

Is it so important to check it?

Yes!

For example: the last element in the chain can be anybody (who paid to Verising for a certificate).

For sure we do not want to trust the certificates issued by anyone.

So, what happens when a user contacts the bank?

Alice

sends(cert1,..., certn)

If Alice’s browser knows cert1 it canverify the chain and read the public key of the bank from certn

Bank

What happens if the certification path is invalid?

For example if the first certificate in the path is not known to the user.

Experiment: let’s delete the Verisign certificate for the configuration of the browser...

What happens?

Suppose Alice and Bob want to authenticate to each other...

Alice Bobinternet

Observation: authentication itself is not very useful.More useful: key establishment

Protocols for key establishment

Suppose Alice and Bob want to establish a fresh session key in an authentic way.

When is it possible?

• Using symmetric cryptography: Alice and Bob can use some trusted server S.

• Using asymmetric cryptography: e.g. using PKI.

Symmetric cryptography

The server can help Alice and Bob to establish a session key.

(in reality it’s not so trivial to design a secure protocol)

Alice Bob

server S

share a private keyKAS

share a private keyKBS

The public-key cryptography

Alice

sends(cert1,..., certn)

If they accepted the certificate paths they can establish a session key:

1. Alice selects a random key K. 2. Alice encrypts K with Bob’s public key, and sign is it with her private

key, and sends it to Bob.3. Bob verifies the signature and decrypts the K.

Again: in reality it’s not that simple...

Bob

sends(cert’1,..., cert’n)

What if one of the parites doesn’t have a certificate?

Typical situation in real life...

E.g. a bank can verify authenticity of Alice by asking her for a secret password.

This password is provided to her (in a physical way) when she opened an account.

How to prevent the dictionary attacks?

Not so trivial...

Designing the key establishment protocols

It is an active area of research.

It’s more complicated than one may think...

On the next slides we show some common errors.

An idea (1)

Alice Bob

server S

key shared by Alice and the server: KAS

key shared by Bob and the server: KBS

(A,B)

EncKAS(KAB),EncKBS(KAB)

(EncKBS(KAB),A)

selects a random KAB

An attack

Alice Bob

server S

key shared by Alice and the server: KAS

key shared by Bob and the server: KBS

(A,B)

EncKAS(KAB),EncKBS(KAB)

(EncKBS(KAB),A)

selects a random KAB

(EncKBS(KAB),D)

I’m talking to D

An idea (2)

Alice Bob

server S

key shared by Alice and the server: KAS

key shared by Bob and the server: KBS

(A,B)

EncKAS(KAB,B),EncKBS(KAB,A)

EncKBS(KAB,A)

selects a random KAB

A replay attack

Alice Bob

(A,B)

EncKAS(K’AB,B),EncKBS(K’AB,A)

EncKBS(K’AB,A)

the adversary stores the values that the server sent in the previous session and replays them.

So, the key is not fresh...

How to protect against the replay attacks?

Nonce – “number used once”.

Nonce is a random number generated by one party and returned to that party to show that a message is newly generated.

An idea (3): Needham Schreoder 1972.

Alice Bob

server S

key shared by Alice and the server: KAS

key shared by Bob and the server: KBS

(A,B,NA)

EncKAS(KAB, B, NA, EncKBS(KAB,A))

EncKBS(KAB,A)

selects a random KAB

EncKAB(NB – 1)

EncKAB(NB)

An attack on Needham Schroeder

Bob

EncKBS(K’AB,A)

EncK’AB(NB – 1)

EncK’AB(NB)

Assume that an old session key K’AB is known to the adversary.

If e.g. K’AB is used as one-time pad this may happen...

The final solution

Alice Bob

server S

key shared by Alice and the server: KAS

key shared by Bob and the server: KBS

(A,B,NA,NB)

EncKAS(KAB, B, NA) EncKBS(KAB, A, NB)

selects a random KAB

EncKBS(KAB, A, NB)

(B,NB)

Other desirable features

1. Forward-security:if an adversary breaks into the machine at some time t the previous session keys remain secret.

2. Deniability:A user can always deny that he sent some message.

3. Resistance to denial-of-service attacks(don’t put to much work on the server!).

Another (real-life) problemAlice and Bob may use different versions of the protocol.

Therefore at the beginning of the protocol they have to agree on the ciphers that they will use.

How to do agree in a secure way?

AliceBob

Alice:I prefer to use AES, but I can also use DES

Alice:I can onlyuse DES,

Bob:I can onlyuse DES,

Bob:I prefer to use AES, but I can also use DES

They’ll end up using DES!

Protocols used in practice

• Symmetric: Kerberos

• Asymmetric: SSL, SSH, IPSec...