A Calculus for Cryptographic Protocols: The Spi Calculus

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A Calculus for Cryptographic Protocols The Spi
Calculus

• Speaker David Bañeres Besora
• Author Martín Abadi

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Index

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

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

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First example sharing a channel

• We can use pi calculus for describing some
  security protocols

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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.

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Second example channel establishment

• We use a server for sending the channel

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Second example channel establishment

• We use a server for sending the channel

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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

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

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Can we use pi-calculus for cryptography?

• We can use pi-calculus when we send hidden
  messages through a channel

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Spi-Calculus (Martín Abadi)

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

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

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Syntax of Spi-Calculus

• Terms
• Known grammar of pi-calculus

• New element

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Syntax of Spi-Calculus

• Processes
• Known grammar of pi-calculus

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Syntax of Spi-Calculus

• Processes
• New elements

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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

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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

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Semantic of Spi-Calculus

• Reaction (?)
• Reduction (gt)
• Replication
• Match
• Let
• Zero
• Suc
• Decrypt
• Structural equivalence (?)
• Structural Reduction

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Semantic of Spi-Calculus

• Known semantic notions
• Structural equivalence
• Commitment Relation
• Strong Bisimilarity
• New (for testing)
• Barbed equivalence (? ?)
• Barbed bisimulation
• Barbed congruence

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

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Sharing the encryption key

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

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Sharing the encryption key
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Key establishment

• We use a server for sending the key

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Key establishment
cAS
cSB
cAB

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

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Key establishment
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Key establishment
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Key establishment
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A complete authentication example

• We have N processes and one server

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

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Hashing, public key and digital signatures

• We need to add more primitives to the grammar
• Hashing
• Public key
• Digital signatures

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Digital signature of a message

• We can use pi calculus for describing some
  security protocols

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Digital signature of a message
M
A
B
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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.

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References

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