Moderately Hard Functions: From Complexity to Spam Fighting

A key idea in cryptography is using hard functions in order to obtain secure schemes. The theory of hard functions (e.g. one-way functions) has been a great success story, and the community has developed a fairly strong understanding of what types of cryptographic primitives can be achieved under which assumption. We explore the idea of using moderately hard functions in order to achieve many tasks for which a perfect solution is impossible, for instance, denial-of-service. We survey some of the applications of such functions and in particular describe the properties moderately hard functions need for fighting unsolicited electronic mail. We suggest several research directions and (re)call for the development of a theory of such functions.