Optimally Hybrid-Secure MPC

Most protocols for multi-party computation (MPC) are secure either against information-theoretic (IT) or against computationally bounded adversaries. Hybrid-secure MPC protocols guarantee different levels of security, depending on the power of the adversary. We present a hybrid-secure MPC protocol that provides an optimal trade-off between IT robustness and computational privacy: For any robustness parameter ρ < n 2 we obtain an MPC protocol that is simultaneously IT secure with robustness for up to t ≤ ρ actively corrupted parties, IT secure with fairness (no robustness) for up to t < n 2 and computationally secure with agreement on abort (no fairness) for up to t < n − ρ. Our construction is secure in the universal composability (UC) framework (with broadcast and CRS), and achieves the bounds of Ishai et al. [CRYPTO’06], Katz [STOC’07], and Cleve [STOC’86] on trade-offs between robustness and privacy, and on fairness. For example, in the special case ρ = 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 < n 2 corrupted parties (like Rabin and Ben-Or [STOC’89] though without robustness). A crucial technique in our construction is player emulation, first suggested by Chaum [CRYPTO’89]. In this work we provide a formal and detailed treatment of emulated players in the UC setting.