This report on the state of the art and future directions ofpublic-key cryptography is published in accordance with theterms of reference of the European Institute for SystemSecurity (EISS). The EISS was founded in 1988 by cabinetresolution of the state government of Baden-W}rttemberg andits basic task is scientific research and knowledge transferin the field of security in telecommunications and computerand information systems.This report gives the results of an EISS workshop onpublic-keycryptography and contains seven chapters: anintroduction, the scope of the workshop, the topics chosen,classification and description of the most prominentpublic-key systems, the dependence of public-keycryptography on computational number theory, mistakes andproblems with public-key systems, and a projection of needsand requirements for public-key systems.It is addressed to all members of the computer sciencecommunity: systems developers, researchers, decision makers,standardization committees, patent offices, and users andcustomers of secure computer systems.