Trust calculus for PKI

Roman Novotný, Milan Vereščák

Outline

PKI Maurer deterministic model Maurer probabilistic model Maurer PKI on P2P Roman continues with modeling in real world

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

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

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)

Maurer PKI deterministic model

Requirements: Generality and expressive power. Precise Semantics. Evaluation order independence. Efficient implementation. Scalability. Easy usability.

Maurer model

Special type of logic syntax: 4 formulas (statements) Semantics: 2 inference rules

Example 1

Example 2

Probablistic Maurer model

True/false (trust/distrust) This model measures validity on continuos

scale from 0 to 1 Every statement has assigned confidence

parameter

Example

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

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 8 Finger table of node 42

i start-id N8.finger[i] i start-id N8.finger[i]

1 8+1=9 N14 1 42+1=43 N48

2 8+2=10 N14 2 42+2=43 N48

3 8+4=12 N14 3 42+4=46 N48

4 8+8=16 N21 4 42+8=50 N51

5 8+16=24 N32 5 42+16=58 N1

6 8+32=40 N42 6 42+32=10 N14

Searching

Requires maximum LogN steps, where N is a number of nodes

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.

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

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.

Improvement of model

Binding between public keys and certification informations

Time – aware model Validity template

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)

Derivation of new statements

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

Thanks for your attention