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Hybrid-Secure MPC: Trading Information-Theoretic Robustness for Computational Privacy

Christoph Lucas and Dominik Raub and Ueli Maurer

Most protocols for distributed, fault-tolerant computation, or multi-party computation (MPC), provide security guarantees in an \textit{all-or-nothing} fashion: If the number of corrupted parties is below a certain threshold, these protocols provide all specified security guarantees. Beyond this threshold, they provide no security guarantees at all. Furthermore, most previous protocols achieve either information-theoretic (IT) security, in which case this threshold is low, or they achieve only computational security, in which case this threshold is high. In contrast, a hybrid-secure protocol provides different security guarantees depending on the set of corrupted parties and the computational power of the adversary, without being aware of the actual adversarial setting. Thus, hybrid-secure MPC protocols allow for graceful degradation of security.

We present a hybrid-secure MPC protocol that provides an optimal trade-off between IT robustness and computational privacy: For any robustness parameter $\rob<\frac{n}{2}$, we obtain one MPC protocol that is simultaneously IT secure with robustness for up to $t\leq\rob$ actively corrupted parties, IT secure with fairness (no robustness) for up to $t<\frac{n}{2}$, and computationally secure with agreement on abort (privacy and correctness only) for up to $t<n-\rob$. Our construction is secure in the universal composability (UC) framework (based on a network of secure channels, a broadcast channel, and a common reference string). It achieves the bound on the trade-off between robustness and privacy shown by Ishai et al. [CRYPTO'06] and Katz [STOC'07], the bound on fairness shown by Cleve [STOC'86], and the bound on IT security shown by Kilian [STOC'00], and is the first protocol that achieves all these bounds simultaneously.

For example, in the special case $\rob=0$ our protocol simultaneously achieves non-robust MPC for up to $t<n$ corrupted parties in the computational setting (like Goldreich et al. [STOC'87]), while providing security with fairness in the IT setting for up to $t<\frac{n}{2}$ corrupted parties (like Rabin and Ben-Or [STOC'89] though without robustness).