Introduction to Secure Computation

Abstract

The objective of this paper 1 is to give an elementary introduction to fundamental concepts, techniques and results of Secure Computation. Topics covered include classical results for general secure computation by Yao, Goldreich & Micali & Wigderson, Kilian, Ben-Or & Goldwasser & Wigderson, and Chaum & Crépeau & Damgaard. We also introduce such concepts as oblivious transfer, security against malicious attacks and verifiable secret sharing, and for some of these important primitives we discuss realization. This paper is organized as follows. Part I deals with oblivious transfer and secure (general) two-party computation. Part II discusses secure general multi-party computation and verifiable secret sharing. Part III addresses information theoretic security and presents detailed but elementary explanations of some recent results in Verifiable Secret Sharing and Multi-Party Computation. The importance of theory and general techniques often lies in the fact that the true nature of security is uncovered and that this henceforth enables to explore what is "possible at all". This then motivates the search for concrete and often specialized realizations that are more efficient. Nevertheless, many principles developed as part of the general theory are fundamental to the design of practical solutions as well.