  This paper deals with the evaluation of trust in public-key infrastructures.
Different trust models have been proposed to interconnect the various PKI
components in order to propagate the trust between them. In this paper we
provide a new polynomial algorithm using linear algebra to assess trust
relationships in a network using different trust evaluation schemes. The
advantages are twofold: first the use of matrix computations instead of graph
algorithms provides an optimized computational solution; second, our algorithm
can be used for generic graphs, even in the presence of cycles. Our algorithm
is designed to evaluate the trust using all existing (finite) trust paths
between entities as a preliminary to any exchanges between PKIs. This can give
a precise evaluation of trust, and accelerate for instance cross-certificate
validation.
