A general completeness theorem for two party games

MIT for Two-Party Games We consider 2-party cryptographic games of the following form. Alice and Bob choose inputs i and j, respectively, from some finite domain D. At the end of the game, Alice and Bob learn the value of l'(i, j), for some function F. We establish a necessary and sufficient condition on F and D, under which one can implement oblivious transfer. Bob should learn the value of C(i, j), where C' is some circuit agreed upon by Alice and Bob, but learn nothing else about i. Alice should learn nothing about j. 1 Research on secure t we-party circuit comput a-tion has proceeded along two lines. We can base secure two-party circuit computation on various unproven computational complexity assumptions [12, 1, 2], or on " idealized implementations " of simpler two-party games [8]. This paper follows the latter approach. 1 Introduction. Finite cryptographic games. 1.1 General background. Secure two-party games. In this paper, we outline how one can base a wide range of secure t we-party games on any one of a large class of finite two-party games. Many two-party games can be implemented using secure t we-party circuit evaluation[ll], which we informally describe as follows: Alice and Bob choose two inputs, i and j, respectively, and have agreed upon some circuit C. At the end of the game, *Research supported in part by a NSF postdoctoral fellowship. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise , or to republish, requires a fee and/or specific permission. By finite cryptographic games, we refer to two-party games in which Alice and Bob's inputs are from some finite domain. An example is one-out-oj-two oblivious transfer (l–2 OT) [7]. 1–2 OT can be specified as follows: Alice has two input bits, SO and SI, and Bob has a single input bit c. At the end of this game, Bob should learn the value of SC, but obtain no additional information about ST, an d Alice should learn nothing about c. Chor and Kushilevitz [5, 9] consider the following class of finite t we-player games: Alice and Bob choose inputs i and …