Modern Cryptography
www.dziembowski.net/Studenti/BISS09
Lecture 8
Public-Key Infrastructure
Stefan Dziembowski
University of Rome
La Sapienza
BiSS 2009
Bertinoro International
Spring School
2-6 March 2009
Plan
1. Qualified signatures
2. PKI and trust management
3. Introduction to the key
establishment protocols
Remember the slide from the previous
lectures?
public register:
P3
P2
pk1
sk3
sk2
pk2
pk3
pk4
pk5
P4
P1
sk4
sk1
P5
sk5
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.
A problem
skA
pkA
m є {0,1}*
(m, σ =Signsk(m))
Alice
Bob
It’s not true!
I never signed m!
I got (m,σ) from Alice
Vrfy(pk,m,σ) = yes
so you cannot repudiate signing m...
But pk is not my public key!
Judge
Solution: certification authorities
A simplified view:
(pkCert,skCert)
comes with her ID and pkAlice
Certification Authority
Alice
checks the ID of Alice and
issues a certificate:
SignskCert(“pkAlice is a public key of Alice”)
Now, everyone can verify that pkAlice is a public key of Alice.
So Alice can attach it to every signature
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.
Plan
1. Qualified signatures
2. PKI and trust management
3. Introduction to the key
establishment protocols
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.
The certificates are distributed using a public-key
infrastructure (PKI).
Users can certify keys of the other users
knows pk2
knows pk3
P2
P1
pk1
P3
pk3
pk2
“trusts” P2
P2 certifies that pk3 is a public key of P3
signature of P2
P1 believes
that pk3 is a
public key of P3
this should be done only if P2 really met P3 in person and verified his identity
knows pk2
P1
pk1
knows pk3
P2
P3
pk3
pk2
knows pk4
P4
pk4
“trusts” P2
“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 believes
that pk3 is a
public key of P3
knows pk2
P1
pk1
knows pk3
P2
P3
pk3
pk2
knows pk4
P4
pk4
knows pk5
P5
pk4
“trusts” P2
“trusts” P3
This is called a
certificate chain
“trusts” P4
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
P4 certifies that pk5 is a public key of P5
signature of P4
P1 believes
that pk3 is a
public key of P3
A problem
knows pk2
P1
pk1
knows pk3
P2
P3
pk3
pk2
knows pk4
P4
pk4
“trusts” P2
“trusts” P3
What if P1 does not know P3?
How can he trust him?
Answer: P2 can recommend P3 to P1.
A question: is trust transitive?
Does:
P1
pk1
P2
P3
pk3
pk2
“trusts” P2
“trusts” P3
P2
P3
imply:
P1
pk1
pk3
pk2
“trusts” P3
?
Example
P1
pk1
P2
pk2
trusts that
P2 is a very
honest person
P1
pk1
P2
pk2
I can recommend P3
P3
pk3
trusts that
P3 is a very
honest person
P3
pk3
doesn’t trust that P3
is honest, because he thinks that
P2 is honest but naive
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 levels
level 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”
Now, if:
P2
P1
P3
P4
P2 trust
P2 issues
P3 issues
in all the
recommendations issued
by P2
a recommendation
of level 2 for P3
a recommendation
of level 1 for P4
then
P1
P2
P3
P4
trusts the certificates issued by P4
Of course the recommendations also need to be signed.
Starts to look complicated...
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 webbrowser.
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 certificate
chain
the second certificate was
signed by ”Verisign
Primary Authority” for
“Verisign Inc”.
(it’s not strange, we will
discuss it)
Look here
The third certificate
was issued by
Verisign Inc.
for
Banca di Roma
The typical picture
web browser knows these certificates
Verisign
DigiCert
Entrust
...
Implicit assumptions:
Verisign
Europe
Verisign
USA
Verisign
Italy
Banca di Roma
•
•
•
the author of the browser is honest,
the author of the browser is competent
nobody manipulated the browser
a certificate path
is it
always
true?
d1
CA1
cert1
d2
CA2
cert2
d3
CA3
cert3
certn-1
dn
All these certificates have to
have a flag “Is a Certification Authority”
switched on.
CAn
certn
client
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
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)
Bank
If Alice’s browser knows cert1 it can
verify the chain and read the public key of
the bank from certn
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?
Another popular PKI
Pretty Good Privacy (PGP) – every user can act
as a certification authority.
Hence the name:
Web of Trust
Plan
1. Qualified signatures
2. PKI and trust management
3. Introduction to the key
establishment protocols
Suppose Alice and Bob want to authenticate to
each other...
Alice
internet
Observation: authentication itself is not very useful.
More useful: key establishment
Bob
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
share a private key
KAS
Alice
server S
share a private key
KBS
Bob
The server can help Alice and Bob to establish a session key.
(in reality it’s not so trivial to design a secure protocol)
The public-key cryptography
sends
(cert1,..., certn)
Alice
sends
(cert’1,..., cert’n)
Bob
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...
What if one of the parties 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)
key shared by Alice and
the server: KAS
key shared by Bob and
the server: KBS
server S
(“A,B”)
selects a random KAB
EncKAS(KAB),
EncKBS(KAB)
(EncKBS (KAB),”A”)
Alice
Bob
An attack
key shared by Alice and
the server: KAS
key shared by Bob and
the server: KBS
server S
(A,B)
selects a random KAB
EncKAS(KAB),
EncKBS(KAB)
(EncKBS(KAB),”A”)
Alice
I’m talking
to D
(EncKBS (KAB),”D”)
Bob
An idea (2)
key shared by Alice and
the server: KAS
key shared by Bob and
the server: KBS
server S
(A,B)
selects a random KAB
EncKAS(KAB,”B”),
EncKBS(KAB,”A”)
EncKBS(KAB,”A”)
Alice
Bob
A replay attack
the adversary stores the
values that the server sent in
the previous session and
replays them.
So, the key is not fresh...
(A,B)
EncKAS(K’AB,”B”),
EncKBS(K’AB,”A”)
EncKBS(K’AB,”A”)
Alice
Bob
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.
key shared by Alice and
the server: KAS
key shared by Bob and
the server: KBS
server S
(“A,B”,NA)
selects a random KAB
EncKAS(KAB, “B”, NA, EncKBS(KAB,”A”))
EncKBS(KAB,”A”)
Alice
EncKAB(NB)
EncKAB(NB – 1)
Bob
An attack on Needham Schroeder
Assume that an old session key K’AB is known to the adversary.
EncKBS(K’AB,”A”)
EncK’AB(NB)
Bob
EncK’AB(NB – 1)
The final solution
key shared by Alice and
the server: KAS
key shared by Bob and
the server: KBS
server S
(“A,B”,NA,NB)
selects a random KAB
EncKAS(KAB, “B”, NA)
EncKBS(KAB, “A”, NB)
(“B”,NB)
Alice
EncKBS(KAB, “A”, NB)
Bob
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) problem
Alice 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?
Alice:
I prefer to use
AES, but I can
also use DES
Alice
Bob:
I can only
use DES,
They’ll end up using DES!
Alice:
I can only
use DES,
Bob:
I prefer to use
AES, but I can
also use DES
Bob
Protocols used in practice
• Symmetric: Kerberos
• Asymmetric: SSL, SSH, IPSec...
©2009 by Stefan Dziembowski. Permission to make digital or hard copies of part or all of
this material is currently granted without fee provided that copies are made only for
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