With the advent in the 1980’s of truly global hierarchical naming (via the Domain Name Service), security researchers realized that the trust relationships needed to authenticate principals would often not follow the naming hierarchy. The most successful non-hierarchical authentication schemes are based on X.509 and RFC 5280, as used for example in TLS and Authenticode. These are extremely widely deployed, and are trusted for most people’s everyday use of the Internet. Unfortunately several incidents in the last few years have proved that this trust is misplaced. We explore the weaknesses of this machinery, helped by a large database of X.509 certificates, and we offer an analysis technique and a suggestion for how the trust could be enhanced.