The notion of security for probabilistic cryptosystems

Reviewer: Graham K. Jenkins

This paper was originally written in 1986, and must therefore be regarded as somewhat dated. It is commendable, however, for its lucid explanations of several different public-key scenarios. The paper introduces the notions of one- and three-pass systems for the establishment of secure communications sessions. Three formal definitions of security for public-key cryptosystems are then examined, two from Goldwasser and Micali and one from Yao. It is shown that all three are, in fact, equivalent; the mathematical basis for this claim is presented in some detail. Support for the work in this paper came from the US Army Research Office, the National Science Foundation, and IBM and General Electric grants. The reader might, in consequence, expect its content to have some immediate practical application. It is indeed unfortunate that such an expectation is not realized. Those engaged in theoretical studies relating to public-key cryptosystems, though, may find that this paper provides a valuable introduction to the subject.