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.