A Synchronous Model for Multi-Party Computation and the Incompleteness of Oblivious Transfer.
Dennis Hofheinz, Jörn Müller‐Quade · 2004
This work develops a composable notion of security in a synchronous communication network to analyze cryptographic primitives and protocols in a reliable network with guaranteed delivery. In such a synchronous model the abort of protocols must be handled explicitly. It is shown that a version of global bit commitment which allows to identify parties that did not give proper input cannot be securely realized with the primitives oblivious transfer and broadcast. This proves that the primitives oblivious transfer and broadcast are not complete in our synchronous model of security. In the synchronous model presented ideal functionalities as well as parties can be equipped with a “shell” which can delay communication until the adversary allows delivery or the number of rounds since the shell received the message exceeds a specified threshold. This additionally allows asynchronous specification of ideal functionalities and allows to model a network where messages are not necessarily delivered in the right order. If these latency times are chosen to be infinite the network is no more reliable and becomes completely asynchronous. In the full version [HMQ04] of this paper, it is shown that a large class of protocols which are secure in the asynchronous settings [Can01, CLOS02] can be transformed into secure realizations in the new model by choosing infinite latency times.