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A Calculus for Cryptographic Protocols: The Spi Calculus

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cAB. cAS. cSB. Second example: channel establishment. We ... cAB. Advantage: Channel cAB is a public channel ... cAB. Channel cAB, cSB, cAS are public channels ... – PowerPoint PPT presentation

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Title: A Calculus for Cryptographic Protocols: The Spi Calculus


1
A Calculus for Cryptographic Protocols The Spi
Calculus
  • Speaker David Bañeres Besora
  • Author Martín Abadi

2
Index
  • Examples pi-calculus
  • Why Spi-calculus?
  • Syntax and semantic of Spi-calculus
  • Examples Spi-calculus
  • Improves in Spi-calculus
  • Conclusions

3
  • Examples pi-calculus
  • Why Spi-calculus?
  • Syntax and semantic of Spi-calculus
  • Examples Spi-calculus
  • Improves in Spi-calculus
  • Conclusions

4
First example sharing a channel
  • We can use pi calculus for describing some
    security protocols

5
First example sharing a channel
  • This protocol has two properties
  • Authenticity
  • An attacker cannot change the message M and sent
    it to B.
  • B knows that the message can be only from A
  • Secrecy
  • The Message M cannot be read in transit from A to
    B.

6
Second example channel establishment
  • We use a server for sending the channel

7
Second example channel establishment
  • We use a server for sending the channel

8
Second example channel establishment
  • We use a server for sending the channel.
  • We have also the properties of authenticity and
    secrecy.
  • Its not needed that A and B know the name of the
    channel before sending the message M.
  • But, A and B must know channels to the server

9
  • Examples pi-calculus
  • Why Spi-calculus?
  • Syntax and semantic of Spi-calculus
  • Examples Spi-calculus
  • Improves in Spi-calculus
  • Conclusions

10
Can we use pi-calculus for cryptography?
  • We can use pi-calculus when we send hidden
    messages through a channel

11
Spi-Calculus (Martín Abadi)
  • Spi-Calculus is an extension of pi-calculus
  • It supports cryptographic operations
  • We can describe security protocols
    (authentication, electronic commerce, ...)

12
  • Examples pi-calculus
  • Why Spi-calculus?
  • Syntax and semantic of Spi-calculus
  • Examples Spi-calculus
  • Improves in Spi-calculus
  • Conclusions

13
Syntax of Spi-Calculus
  • Terms
  • Known grammar of pi-calculus
  • New element

14
Syntax of Spi-Calculus
  • Processes
  • Known grammar of pi-calculus

15
Syntax of Spi-Calculus
  • Processes
  • New elements

16
Syntax of Spi-Calculus
  • Processes
  • New elements
  • Match
  • if M and N are the same then the execution
    continues,
  • otherwise the execution is stuck
  • Pair splitting
  • if M is equal to (N,L) then the execution is

17
Syntax of Spi-Calculus
  • Processes
  • New elements
  • Integer case
  • if M is 0 then the execution continues in P
  • if M is suc(N) then the execution is
  • otherwise the execution is stuck
  • Shared-key decryption
  • The process tries to decrypt L with the key N
  • If L is MN then we replace the variable M for
    x
  • otherwise the process is stuck

18
Semantic of Spi-Calculus
  • Reaction (?)
  • Reduction (gt)
  • Replication
  • Match
  • Let
  • Zero
  • Suc
  • Decrypt
  • Structural equivalence (?)
  • Structural Reduction

19
Semantic of Spi-Calculus
  • Known semantic notions
  • Structural equivalence
  • Commitment Relation
  • Strong Bisimilarity
  • New (for testing)
  • Barbed equivalence (? ?)
  • Barbed bisimulation
  • Barbed congruence

20
  • Examples pi-calculus
  • Why Spi-calculus?
  • Syntax and semantic of Spi-calculus
  • Examples Spi-calculus
  • Improves in Spi-calculus
  • Conclusions

21
Sharing the encryption key
  • Advantage Channel cAB is a public channel
  • Disadvantage Both processes must know the
    encryption key

22
Sharing the encryption key
23
Key establishment
  • We use a server for sending the key

24
Key establishment
cAS
cSB
cAB
  • Channel cAB, cSB, cAS are public channels
  • Process B doesnt know the encryption key until
    the server sends it.

25
Key establishment
26
Key establishment
27
Key establishment
28
A complete authentication example
  • We have N processes and one server

29
A complete authentication example
30
  • Examples pi-calculus
  • Why Spi-calculus?
  • Syntax and semantic of Spi-calculus
  • Examples Spi-calculus
  • Improves in Spi-calculus
  • Conclusions

31
Hashing, public key and digital signatures
  • We need to add more primitives to the grammar
  • Hashing
  • Public key
  • Digital signatures

32
Digital signature of a message
  • We can use pi calculus for describing some
    security protocols

33
Digital signature of a message
M
A
B
34
Conclusions
  • Pi-calculus is useful for describing processes
    that transmit information using a channel.
  • We cannot use Pi-calculus for cryptographic
    processes
  • Spi-calculus has a complete grammar for describe
    this processes
  • We can use Spi-calculus for shared-key, public
    key, digital signatures and hash functions.

35
References
  • M. Abadi and A.D. Gordon. A Calculus for
    Cryptographic Protocols The Spi Calculus.
    Research Report. January 1998
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