Vulnerability analysis of certificate graphs

  • Authors:
  • Eunjin (EJ) Jung;Mohamed G. Gouda

  • Affiliations:
  • Department of Computer Science, University of Iowa, Iowa City, IA 52242, USA.;Department of Computer Science, University of Texas, Austin, TX 78712, USA

  • Venue:
  • International Journal of Security and Networks
  • Year:
  • 2006

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Abstract

A certificate system can be represented by a directed graph,called a certificate graph, where each node represents a user thathas a public key and a private key and each edge (u, v) representsa certificate that is signed by the private key of u and containsthe public key of v. Two types of damage can be done in acertificate graph when the private key of a node u in the graph isrevealed to an adversary: explicit and implicit. The explicitdamage is that the adversary can impersonate node u to other nodesin the graph (until it is known to other nodes that the private keyof u is revealed). The implicit damage is that the adversary canimpersonate nodes other than u to other nodes in the graph. In thispaper, we define a metric called vulnerability that measures thescope of explicit and implicit damage that may occur in acertificate graph when the private key of a node in the graph isrevealed to an adversary. Using this metric, we analyse thevulnerability of different classes of certificate graphs. Forexample, in the case of (m, k)-star certificate graphs, thevulnerability is 1−(k−1)/2mk, whereas in the case of(d, h)-tree certificate graphs, the vulnerability is approximately1−h/dh. For the same number of nodes, (m, k)-starcertificate graphs can be made less vulnerable than (d, h)-treecertificate graphs. We present three algorithms that compute thevulnerability of an arbitrary certificate graph, and use thesealgorithms to show that certificate dispersal and stricteracceptance criteria reduce the vulnerability of certificategraphs.