(Unconditional) Secure Multiparty Computation with Man-in-the-middle Attacks

In secure multi-party computation n parties jointly evaluate an n-variate function f in the presence of an adversary which can corrupt up till t parties. All honest parties are required to receive their correct output values, irrespective of how the corrupted parties under the control of the adversary behave. The adversary should not be able to learn anything more about the input values of the honest parties, then what can be inferred from the input and output values of the corrupted parties and structure of the function. Almost all the works that have appeared in the literature so far assume the presence of authenticated channels between the parties. This assumption is far from realistic. Two directions of research have been borne from relaxing this (strong) assumption: (a) The adversary is virtually omnipotent and can control all the communication channels in the network, (b) Only a partially connected topology of authenticated channels is guaranteed and adversary controls a subset of the communication channels in the network. This work introduces a new setting for (unconditional) secure multiparty computation problem which is an interesting intermediate model with respect to the above well studied models from the literature (by sharing a salient feature from both the above models). We consider the problem of (unconditional) secure multi-party computation when ’some’ of the communication channels connecting the parties can be corrupted passively as well as actively. We model communication channels as entities just like parties and consider a few different types of channels, namely fully secure channels, authenticated but eavesdroppable channels, partially tamperable channels and fully tamperable channels. For this setting, some honest parties may be connected to several other honest parties via corrupted channels and may not be able to authentically/privately communicate with them. Such parties may not be assured the canonical guarantees of correctness or privacy. Honest parties which are not guaranteed correctness or privacy properties are called sacrificed, as is done for the notion of almost everywhere secure computation (above model (b)). We present appropriate definitions of security for this new intermediate model of secure computation for the stand alone setting. We show how to adapt protocols for (unconditional) secure multiparty computation to realize the definitions and also argue the tightness of the results achieved by us. Keyword(s): Secure multiparty computation, Byzantine corruption, Almost everywhere secure multiparty computation, Man-in-the-middle attack, Corruption of channels, Simulation paradigm, Simulation, Input indistinguishability.