Most currently deployed Public Key Infrastructures (PKIs) are hierarchically oriented and rely on a centralized design. Hierarchical PKIs may be appropriate solutions for many usage-scenarios, but there exists the viable alternative of the 'Web of Trust'. In a web of trust, each user of the system can choose for himself whom he elects to trust, and whom not. After contrasting the properties of web-of-trust based PKIs to those of hierarchical PKIs, an introduction to webs of trust and to quantitative trust calculations is given. The paper concludes with the presentation of an efficient, sub-exponential algorithm that allows heuristic computations of trust paths in a web of trust.