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Abstract: Authentication using a path of trusted intermediaries, each able to authenticate the next one in the path, is a well-known technique for authenticating entities in a large-scale system. Recent work has extended this technique to include multiple paths in an effort to bolster authentication, but the success of this approach may be unclear in the face of intersecting paths, ambiguities in the meaning of certificates, and interdependencies in the use of different keys. Several authors have thus proposed metrics to evaluate the confidence afforded by a set of paths. In this paper, we develop a set of guiding principles for the design of such metrics. We motivate our principles by showing how previous approaches fail with respect to them and what the consequences to authentication might be. We then propose a direction for constructing metrics that come closer to meeting our principles and thus, we believe, to being satisfactory metrics for authentication.