Authenticated Key Exchange

1
Authenticated Key Exchange

• Definitions
• MAP
• matching conversations
• oracles
• (I)KA
• AKEP2
• AKEP2 Security
• Session Keys
• Perfect Forward Secrecy
• Adversary Attacks

Presented By Ashley Bruno Blayne White
2
Key Establishment Protocols

• Cryptographic protocols that establish keys for
  use by other protocols
• examples AKEP2, MAP1, Diffie-Hellman,
  Station-to-station

3
Definitions

• Principal a party wishing to establish shared
  keys
• Nonce a random or pseudo-random number issued in
  an authentication protocol to ensure that old
  communications cannot be reused in replay attacks

4
Definitions (cont'd)

• MAC (ie. Message Authentication Code) the result
  of a hash function that combines a message with a
  key
• Freshness a key is fresh if it can be guaranteed
  to be new (Menezes, van Oorschot and Vanstone,
  1997)

(probably no longer fresh)
5
Oracles

• An I/O device that responds to every query with
  a random response chosen uniformly from it's
  output domain. if given the same input query, the
  same output response is given.

6
Oracle Freshness

• An oracle is fresh if
• It has accepted a session key
• Its session key has not been given a Reveal query
  (oracle is unopened)
• There is no opened oracle with whom it has a
  matching conversation that has accepted the
  session key.

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Mutual Entity Authentication

• Provides assurance to both entities of the
  identity of the other entity involved
• If a pair of oracles has matching conversations,
  then both oracles accept.
• The probability of an oracle accepting when it
  does not have a matching conversation with
  another oracle is negligible.

8
Matching Conversations

• A conversation consists of all messages sent and
  received by an oracle.
• Matching Conversations occur when the
  conversations of both parties are the same when
  all messages are faithfully delivered from the
  sender oracle to the receiver oracle, with the
  exception of the last message, since the
  initiator cannot know if this last message was
  received by its partner.

9
(Implicit) Key Authentication

• Provides assurance that no entity other than a
  specifically identified entity can gain access to
  the key.
• Independent of the actual possession of such key
  by the second party, or knowledge of such actual
  possession by the first party

10
Perfect Forward Secrecy
It is still desirable to design protocols where
past sessions remain secure. Perfect forward
secrecy compromise of long-term keys does not
compromise past session keys. Forward secrecy
indicates that the secrecy of old keys is carried
forward into the future.
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Authenticated Key Exchange Protocol 2

• A three-pass protocol
• Uses symmetric authentication
• Uses keyed hash functions instead of encryption
• Does not rely on a trusted third party (TTP)
• Provides mutual entity authentication and
  (implicit) key authentication
• Provides Perfect Forward Secrecy

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AKEP2

• A and B are principals
• A and B share two long term symmetric keys K, K'
• each protocol run generates fresh nonces na, nb
• uses a keyed hash function (MAC) hk and a keyed
  one-way function h'k'

13
AKEP2
na
A
B
A sends a challenge nonce to B.
hk(B,A,na,nb), nb
A
B

• B resonds with hk(B,A,na,nb) and sends it's own
  challenge nonce.
• k is the shared key k h'k'(nb)

hk(A,nb)
A
B
A responds to the challenge nonce with hk(A,nb)
to B
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AKEP2 Security

• The intent is to authenticate the principals
  involved and distribute a session key which will
  consist of a principal's private output
• At the end of a secure AKE any adversary should
  not be able to distinguish a fresh session key
  from a random element.

15
AKE Security Session Keys

• The compromise of one of these keys should have
  minimal consequences.
• It should not subvert subsequent authentication.
• It should not leak information about other
  session keys.

16
AKEP2 Security

• Protocol II is secure if it is a secure mutual
  authentication protocol. This requires
• That two oracles, in the absence of an active
  adversary, always accept
• The advantage of a probabilistic polynomial
  adversary is negligible.
• The current security definitions give the
  adversary very strong abilities in corrupting the
  parties, but they limit his ability to utilize
  those powers.

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Attacks allowed by current definitions

• Key-compromise impersonation the adversary
  reveals a long-term secret key of a party and
  then impersonates others to this party.
• An adversary reveals the ephemeral secret key of
  a party who initiates an AKE session and
  impersonates the other participant of this
  session.

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Attacks allowed (cont'd)

• Two honest parties execute matching sessions,
  while the adversary reveals ephemeral secret keys
  of both parties and tries to learn the session
  key.
• Two honest parties execute matching sessions,
  while the adversary reveals long-term keys of
  both parties prior to the session execution and
  tries to learn the session key.

However, all four of these attacks are not
considered violations of protocol security!
19
Authenticated Key Exchange

• M. Bellare and P. Rogaway.Entity Authentication
  and key distribution Advances in Cryptology -
  Crypto 93 Proceedings, Lecture Notes in Computer
  Science Vol. 773, D. Stinson ed, Springer-Verlag,
  1994.
• Brian LaMacchia, Kristen Lauter, Anton Mityagin.
  Stronger Security of Authenticated Key Exchange.