This report on the state of the art and future directions of public-key cryptography is published in accordance with the terms of reference of the European Institute for System Security (EISS). The EISS was founded in 1988 by cabinet resolution of the state government of Baden-W}rttemberg and its basic task is scientific research and knowledge transfer in the field of security in telecommunications and computer and information systems. This report gives the results of an EISS workshop on public-keycryptography and contains seven chapters: an introduction, the scope of the workshop, the topics chosen, classification and description of the most prominent public-key systems, the dependence of public-key cryptography on computational number theory, mistakes and problems with public-key systems, and a projection of needs and requirements for public-key systems. It is addressed to all members of the computer science community: systems developers, researchers, decision makers, standardization committees, patent offices, and users and customers of secure computer systems.