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. Alice X (CA) 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. Alice Y (CA) Bob X (CA)

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 Finger table of node 8Finger table of node 42 istart-idN8.finger[i]istart-idN8.finger[i] 18+1=9N14142+1=43N48 28+2=10N14242+2=43N48 38+4=12N14342+4=46N48 48+8=16N21442+8=50N51 58+16=24N32542+16=58N1 68+32=40N42642+32=10N14

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 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