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Trust calculus for PKI

This document outlines the concept of Trust within Public Key Infrastructure (PKI), focusing on Maurer’s deterministic and probabilistic models. It explores the complexities of PKI as a distributed system involving entities like Certificate Authorities (CAs) and certificate validation processes. The paper delves into P2P network applications in PKI, illustrating how trust is established and maintained using probabilistic measures. Finally, it highlights improvements and expansions of the model to enhance scalability, fault resistance, and the binding of public keys to certification information.

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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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