Common use of Split Functionality sF Clause in Contracts

Split Functionality sF. The split functionality is a generic construction based upon an ideal functionality: Its description can be found on Figure 1. In the initialization stage, the adversary adaptively chooses disjoint subsets of the honest parties (with a unique session identifier that is fixed for the duration of the protocol). More precisely, the protocol starts with a session identifier sid. Then, the initialization stage generates some random values which, combined together and with sid, create the new session identifier sid′, shared by all parties which have received the same values – that is, the parties of the disjoint subsets. The important point here is that the subsets create a partition of the players, thus forbidding commu- nication among the subsets. During the computation, each subset H activates a separate instance of the functionality F. All these functionality instances are independent: The executions of the protocol for each subset H can only be related in the way the adversary chooses the inputs of the players it controls. The parties Pi ∈ H provide their own inputs and receive their own outputs (see the first item of “computation” in Figure 1), whereas the adversary plays the role of all the parties Pj ∈/ H (see the second item).

Split Functionality sF. The split functionality is a generic construction based upon an ideal functionality: Its description can be found on Figure 1. In the initialization stage, the adversary adaptively chooses disjoint subsets of the honest parties (with a unique session identifier identi er that is fixed xed for the duration of the protocol). More precisely, the protocol starts with a session identifier identi er sid. Then, the initialization stage generates some random values which, combined together and with sid, create the new session identifier sid′identi er sid', shared by all parties which have received the same values – that is, the parties of the disjoint subsets. The important point here is that the subsets create a partition of the players, thus forbidding commu- nication among the subsets. During the computation, each subset H activates a separate instance of the functionality F. F . All these functionality instances are independent: The executions of the protocol for each subset H can only be related in the way the adversary chooses the inputs of the players it controls. The parties Pi ∈ H provide their own inputs and receive their own outputs (see the first rst item of “computation” computation in Figure 1), whereas the adversary plays the role of all the parties Pj ∈/ H (see the second item).