## Cryptology ePrint Archive: Report 2019/1344

From Fairness to Full Security in Multiparty Computation

Ran Cohen and Iftach Haitner and Eran Omri and Lior Rotem

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 $\delta$-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 super-constant 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.

Category / Keywords: cryptographic protocols / multiparty computation; fairness; guaranteed output delivery; identifiable abort, security reductions

Original Publication (with major differences): SCN 2018
DOI:
10.1007/s00145-016-9245-5