Paper 2022/978

Non-Malleable Multi-Party Computation

Abstract

We study a tamper-tolerant implementation security notion for general purpose Multi-Party Computation (MPC) protocols, as an analogue of the leakage-tolerant notion in the MPC literature. An MPC protocol is tamper-tolerant, or more specifically, non-malleable (with respect to a certain type of tampering) if the processing of the protocol under corruption of parties (and tampering of some ideal resource assumed by the protocol) can be simulated by an ideal world adversary who, after the trusted party spit out the output, further decides how the output for honest parties should be tampered with. Intuitively, we relax the correctness of secure computation in a privacy-preserving way, decoupling the two entangled properties that define secure computation. The rationale behind this relaxation is that even the strongest notion of correctness in MPC allows corrupt parties to substitute wrong inputs to the trusted party and the output is incorrect anyway, maybe the importance of insisting on that the adversary does not further tamper with the incorrect output is overrated, at least for some applications. Various weak privacy notions against malicious adversary play an important role in the study of two-party computation, where full security is hard to achieve efficiently. We begin with the honest majority setting, where efficient constructions for general purpose MPC protocols with full security are well understood assuming secure point-to-point channels. We then focus on non-malleability with respect to tampered secure point-to-point channels. (1) We show achievability of non-malleable MPC against the bounded state tampering adversary in the joint tampering model through a naive compiler approach, exploiting a known construction of interactive non-malleable codes. The construction is currently not efficient and should be understood as showing feasibility in a rather strong tampering model. (2) We show efficient constructions of non-malleable MPC protocols against weaker variants of bounded state tampering adversary in the independent tampering model, where the protocol obtained have the same asymptotic communication complexity as best MPC protocols against honest-but-curious adversary. These are all information-theoretic results and are to be contrasted against impossibility of secure MPC when secure point-to-point channels are compromised. Though general non-malleable MPC in no honest majority setting is beyond the scope of this work, we discuss interesting applications of honest majority non-malleable MPC in the celebrated MPC-in-the-head paradigm. Other than an abstract result concerning non-malleability, we also derive, in standard model where there is no tampering, that strong (ideal/real world) privacy against malicious adversary can be achieved in a conceptually very simple way.

Note: This revision contains a tightening of Definition 6 and fixing a few typos.