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In this work, we introduce the Gulliver multi-party computation model (GMPC).The GMPC model considers a single highly powerful party, called the server orGulliver, that is connected to $n$ users over a star topology network(alternatively formulated as a full network, where the server can block anymessage). The users are significantly less powerful than the server, and, inparticular, should have both computation and communication complexities thatare polylogarithmic in $n$. Protocols in the GMPC model should be secureagainst malicious adversaries that may corrupt a subset of the users and/or theserver.  Designing protocols in the GMPC model is a delicate task, since users canonly hold information about polylog(n) other users (and, in particular, canonly communicate with polylog(n) other users). In addition, the server canblock any message between any pair of honest parties. Thus, reaching anagreement becomes a challenging task. Nevertheless, we design generic protocolsin the GMPC model, assuming that at most $\alpha<1/6$ fraction of the users maybe corrupted (in addition to the server). Our main contribution is a variant ofFeige's committee election protocol [FOCS 1999] that is secure in the GMPCmodel. Given this tool we show:  1. Assuming fully homomorphic encryption (FHE), any computationally efficientfunction with $O\left(n\cdot polylog(n)\right)$-size output can be securelycomputed in the GMPC model.  2. Any function that can be computed by a circuit of $O(polylog(n))$ depth,$O\left(n\cdot polylog(n)\right)$ size, and bounded fan-in and fan-out can besecurely computed in the GMPC model without assuming FHE.  3. In particular, sorting can be securely computed in the GMPC model withoutassuming FHE. This has important applications for the shuffle model ofdifferential privacy, and resolves an open question of Bell et al. [CCS 2020].

MPC for Tech Giants (GMPC): Enabling Gulliver and the Lilliputians to Cooperate Amicably