Establishing authentic channels has become a common operation on the Internet and electronic commerce would not be possible without it. Because traditionally authentication is based on identifying users, the success of electronic commerce causes rapid erosion of their privacy. Privacy-friendly authentication, such as group signatures or anonymous credential systems, could mitigate this issue minimizing the information released during an authentication operation. Unfortunately, privacy-friendly authentication systems are not yet deployed. One reason is their sophistication and feature richness, which is complicating their understanding. By providing a calculus for analyzing and comparing the requirements and goals of privacy-friendly authentication systems, we contribute to a better understanding of such technologies. Our calculus extends the one by Maurer and Schmid [18], by introducing: (1) pseudonyms to enable pseudonymous authentication, (2) a pseudonym annotation function denoting the information an entity reveals about itself, and (3) event-based channel conditions to model conditional release of information used for privacy-friendly accountability.