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Trust calculus for PKI

Trust calculus for PKI. Roman Novotný , Milan Vere ščák. Outline. PKI Maurer deterministic model Maurer probabilistic model Maurer PKI on P2P Roman continues with modeling in real world. Public key infrastructure (PKI).

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Trust calculus for PKI

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  1. Trust calculus for PKI Roman Novotný, Milan Vereščák

  2. Outline • PKI • Maurer deterministic model • Maurer probabilistic model • Maurer PKI on P2P • Roman continues with modeling in real world

  3. Public key infrastructure (PKI) • PKI – complex distributed systems of the end entities, CA, certificates, RA • Public key cryptography • Certificate issuance • Certificate validation • Certificate revocation • CA – trusted third party

  4. Public key certification • Alice knows the public key of X (for verifying the certificate) and is convinced of its authenticity. • Alice trusts X to be honest and to correctly authenticate the owner of a public key before signing it. X (CA) Alice Bob

  5. Simple example • If Alice does not know an authentic copy of X's public key, the first condition can be satisfied by using a certificate for X's public key issued by another entity Y. Y (CA) X (CA) Alice Bob

  6. Maurer PKI deterministic model Requirements: • Generality and expressive power. • Precise Semantics. • Evaluation order independence. • Efficient implementation. • Scalability. • Easy usability.

  7. Maurer model • Special type of logic • syntax: 4 formulas (statements) • Semantics: 2 inference rules

  8. Example 1

  9. Example 2

  10. Probablistic Maurer model • True/false (trust/distrust) • This model measures validity on continuos scale from 0 to 1 • Every statement has assigned confidence parameter

  11. Example

  12. PKI based on P2P network • Based on Chord: scalable p2p lookup protocol • Chord p2p network consists of nodes • maps given key onto a node • Node identifier (e.g. IP address of node) • Key (e.g. filename) • Hash function maps both the key and the node identifier into m-bit identifier

  13. Algorithm for lookup • The mapping principle: each key is assigned to the first existing node whose identifier is greater than or equal to the identifier of the key. • Each node has finger table with m entries pointing to m nodes

  14. Searching • Requires maximum LogN steps, where N is a number of nodes

  15. Views • Nodes are used for storing statements • privateView: a set of private statements that are not accessible from other nodes, only local node can access them. • publicView: a set of message tokens that are accessible to other nodes. • Message tokens consist of encrypted message and index key associated to that particular message.

  16. Public messages • Public messages • Certificate messages Cert(X, PX, Y, PY) • Recommendation messages Rec(X, PX, Y, i) • Private messages • Authenticity statements Aut(X, PX) • Trust statements Trust(X, i) • Distributing is done according to p2p lookup protocol and retrieving also using a Maurer inference rules

  17. Advantages of P2P model • load distribution: Hash function distributes message tokens (public messages) uniformly among the nodes. • scalability: We need Log(N) steps to retrieve or publicate a message token of the total number of N nodes. • fault resistance: This is because of decentralized character of this model.

  18. Improvement of model • Binding between public keys and certification informations • Time – aware model • Validity template

  19. Statements • Authenticity of binding - Aut(A,X,P,I) • Trust – Trust(A,X,D,I) • Certificates – Cert(X,Y,P,I) • Trust Transfers – Tran(X,Y,P,I) • Certification Validity Templates – Val(A,C,t) • Transfer Validity Templates – Val(A,T,t)

  20. Derivation of new statements

  21. X.509 and model • Set of property – subject’s name, issuer, signature algorithm • Time interval – validity – not before, not after • Certification revocation list – Cert(X,0,L,I), where 0 – empty set

  22. Thanks for your attention

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