From Fairness to Full Security in Multiparty Computation

Abstract

In the setting of secure multiparty computation (MPC), a set of mutually distrusting parties wish to jointly compute a function, while guaranteeing the privacy of their inputs and the correctness of the output. An MPC protocol is called fully secure if no adversary can prevent the honest parties from obtaining their outputs. A protocol is called fair if an adversary can prematurely abort the computation, however, only before learning any new information.We present highly efficient transformations from fair computations to fully secure computations, assuming the fraction of honest parties is constant (e.g., 1% of the parties are honest). Compared to previous transformations that require linear invocations (in the number of parties) of the fair computation, our transformations require super-logarithmic, and sometimes even super-constant, such invocations. The main idea is to delegate the computation to chosen random committees that invoke the fair computation. Apart from the benefit of uplifting security, the reduction in the number of parties is also useful, since only committee members are required to work, whereas the remaining parties simply "listen" to the computation over a broadcast channel.One application of these transformations is a new δ-bias coin-flipping protocol, whose round complexity has a super-logarithmic dependency on the number of parties, improving over the protocol of Beimel, Omri, and Orlov (Crypto 2010) that has a linear dependency. A second application is a new fully secure protocol for computing the Boolean OR function, with a superconstant round complexity, improving over the protocol of Gordon and Katz (TCC 2009) whose round complexity is linear in the number of parties.Finally, we show that our positive results are in a sense optimal, by proving that for some functionalities, a super-constant number of (sequential) invocations of the fair computation is necessary for computing the functionality in a fully secure manner.

Tighter Bounds on Multi-Party Coin Flipping via Augmented Weak Martingales and Differentially Private Sampling

“…Awerbuch et al [5] presented an n-party r-round protocol with bias O(n/ √ r) (the two-party case appears also in Cleve [11]). This was improved to (almost) O(1/ √ r) in [6,14], for the case where the fraction of honest parties is constant. Moran, Naor, and Segev [29] resolved the two-party case, presenting a two-party r-round coin-flipping protocol with bias O(1/r).…”

Secure Multiparty Computation and Trusted Hardware: Examining Adoption Challenges and Opportunities

“…Other desirable properties of SMC include agreement on abort (honest parties will agree to abort upon detecting dishonest parties), fairness (either all parties receive the output or none do), graceful degradation (security beyond a threshold), and robustness or guaranteed output delivery (outputs not withheld from honest parties). Some of these properties are precursors to others; for example, Cohen et al [18] show that a fair computation can be transformed into one providing guaranteed output delivery.…”