In this work, we consider the problem of secure multi-party computation (MPC) with n parties where at most t are under the control of a computationally bounded adversary given the constraint t < n/2. We aim to design a round efficient protocol by minimizing the number of rounds in which the broadcast primitive is involved. In this setting, the previous best protocol can be attributed to Katz-Koo (EUROCRYPT 2007) which is set in the offline-online paradigm (where the parties generate preprocessing data during the offline phase to lighten the computation in the online phase). Their online phase is a constant round protocol with no invocations of broadcast, while the offline phase protocol needs total 29 rounds with a broadcast invocation in one round. Our work improves the round complexity of their offline phase protocol, by running in 4 rounds, with only a single broadcast round. Additionally, we also improve the communication complexity of the offline phase protocol by a factor of Ω(n3). As a technical contribution, we present the first two round computationally-secure verifiable secret-sharing (VSS) scheme that invokes broadcast in only one round.
In this work, we consider the problem of secure multi-party computation (MPC) with n parties where at most t are under the control of a computationally bounded adversary given the constraint t < n/2. We aim to design a round efficient protocol by minimizing the number of rounds in which the broadcast primitive is involved. In this setting, the previous best protocol can be attributed to Katz-Koo (EUROCRYPT 2007) which is set in the offline-online paradigm (where the parties generate preprocessing data during the offline phase to lighten the computation in the online phase). Their online phase is a constant round protocol with no invocations of broadcast, while the offline phase protocol needs total 29 rounds with a broadcast invocation in one round. Our work improves the round complexity of their offline phase protocol, by running in 4 rounds, with only a single broadcast round. Additionally, we also improve the communication complexity of the offline phase protocol by a factor of Ω(n3). As a technical contribution, we present the first two round computationally-secure verifiable secret-sharing (VSS) scheme that invokes broadcast in only one round.
Verifiable secret sharing (VSS) is a fundamental cryptographic primitive, lying at the core of secure multi-party computation (MPC) and, as the distributed analogue of a commitment functionality, used in numerous applications. In this paper we focus on unconditionally secure VSS protocols with honest majority. In this setting it is typically assumed that parties are connected pairwise by authenticated, private channels, and that in addition they have access to a “broadcast ” channel. Because broadcast cannot be simulated on a point-to-point network when a third or more of the parties are corrupt, it is impossible to construct VSS (and more generally, MPC) protocols in this setting without using a broadcast channel (or some equivalent addition to the model). A great deal of research has focused on increasing the efficiency of VSS, primarily in terms of round complexity. In this work we consider a refinement of the round complexity of VSS, by adding a measure we term broadcast complexity. We view the broadcast channel as an expensive resource and seek to minimize the number of rounds in which it is invoked as well. We construct a (linear) VSS protocol which uses the broadcast channel only twice in the sharing phase, while running in an overall constant number of rounds. 1
Broadcast and verifiable secret sharing (VSS) are central building blocks for secure multi-party computation. These protocols are required to be resilient against a Byzantine adversary who controls at most t out of the n parties running the protocol. In this dissertation, we consider the design of fault-tolerant protocols for broadcast and verifiable secret sharing with stronger security guarantees and improved round complexity. Broadcast allows a party to send the same message to all parties, and all parties are assured they have received identical messages. Given a public-key infrastructure (PKI) and digital signatures, it is possible to construct broadcast protocols tolerating any number of corrupted parties. We address two important issues related to broadcast: (1) Almost all existing protocols do not distinguish between corrupted parties (who do not follow the protocol) and honest parties whose secret (signing) keys have been compromised (but who continue to behave honestly); (2) all existing protocols for broadcast are insecure against an adaptive adversary who can choose which parties to corrupt as the protocol progresses. We propose new security models that capture these issues, and present tight feasibility and impossibility results. In the problem of verifiable secret sharing, there is a designated player who shares a secret during an initial sharing phase such that the secret is hidden from an adversary that corrupts at most t parties. In a subsequent reconstruction phase of the protocol, a unique secret, well-defined by the view of honest players in the sharing phase, is reconstructed. The round complexity of VSS protocols is a very important metric of their efficiency. We show two improvements regarding the round complexity of information-theoretic VSS. First, we construct an efficient perfectly secure VSS protocol tolerating t < n/3 corrupted parties that is simultaneously optimal in both the number of rounds and the number of invocations of broadcast. Second, we construct a statistically secure VSS protocol tolerating t < n/2 corrupted parties that has optimal round complexity, and an efficient statistical VSS protocol tolerating t < n/2 corrupted parties that requires one additional round.
We revisit the following question: what is the optimal round complexity of verifiable secret sharing (VSS)? We focus here on the case of perfectly-secure VSS where the number of corrupted parties t satisfies t < n/3, with n being the total number of parties. Work of Gennaro et al. (STOC 2001) and Fitzi et al. (TCC 2006) shows that, assuming a broadcast channel, 3 rounds are necessary and sufficient for efficient VSS. The efficient 3-round protocol of Fitzi et al., however, treats the broadcast channel as being available “for free” and does not attempt to minimize its usage. This approach leads to relatively poor round complexity when protocols are compiled for a point-to-point network. We show here a VSS protocol that is simultaneously optimal in terms of both the number of rounds and the number of invocations of broadcast. Our protocol also has a certain “2-level sharing” property that makes it useful for constructing protocols for general secure computation.
In this work, we study unconditionally-secure multi-party computation (MPC) tolerating t<n/3 corruptions, where n is the total number of parties involved. In this setting, it is well known that if the underlying network is completely asynchronous, then one can achieve only statistical security; moreover it is impossible to ensure input provision and consider inputs of all the honest parties. The best known statistically-secure asynchronous MPC (AMPC) with t<n/3 requires a communication of Ω(n5) field elements per multiplication. We consider a partially synchronous setting, where the parties are assumed to be globally synchronized initially for few rounds and then the network becomes completely asynchronous. In such a setting, we present a MPC protocol, which requires O(n2) communication per multiplication while ensuring input provision. Our MPC protocol relies on a new four round, communication efficient statistical verifiable secret-sharing (VSS) protocol with broadcast communication complexity independent of the number of secret-shared values.
In this dissertation, we consider the design of broadcast and secure multi-party computation (MPC) protocols in the presence of adversarial faults.
Secure multi-party computation is the most generic problem in fault-tolerant distributed computing. In principle, a multi-party computation protocol can be used to solve any distributed cryptographic problem. Informally, the problem of multi-party computation is the following: suppose we have n parties P1, P2,…, Pn where each party Pi has a private input xi. Together, the parties want to compute a function of their inputs (y1, y2,…, yn) = f(x1,x2,…, xn). However, some parties can be corrupted and do not execute a prescribed protocol faithfully. Even worse, they may be controlled by an adversary and attack the protocol in a coordinated manner. Despite the presence of such an adversary, a secure MPC protocol should ensure that each (corrupted) party Pi learn only its output yi but nothing more.
Broadcast in the presence of adversarial faults is one of the simplest special cases of multi-party computation and important component of larger protocols. In short, broadcast allows a party to send the same message to all parties, and all parties to be assured they have received identical messages.
The contribution of this dissertation is twofold. First, we construct broadcast and secure multi-party computation protocols for honest majority in a point-to-point network whose round complexities improve significantly upon prior work. In particular, we give the first expected constant-round authenticated broadcast protocol for honest majority assuming only public-key infrastructure and signatures. Second, we initiate the study of broadcast in radio networks in the presence of adversarial faults. In radio networks, parties communicate through multicasting messages; a message can only be received by the parties within some radius from the sender. Feasibility and impossibility results are given, and our bounds are tight.
Secure Multi-Party Computation (MPC) with small number of parties is an interesting area of research, primarily due to its ability to model most real-life MPC applications and the simplicity and efficiency of the resulting protocols. In this work, we present efficient, constant-round 3-party (3PC) and 4-party (4PC) protocols in the honest-majority setting that achieve strong security notions of fairness (corrupted parties receive their output only if all honest parties receive output) and guaranteed output delivery (corrupted parties cannot prevent honest parties from receiving their output). Being constant-round, our constructions are suitable for Internet-like high-latency networks and are built from garbled circuits (GC). Assuming the minimal model of pairwise-private channels, we present two protocols that involve computation and communication of a single GC-- (a) a 4-round 3PC with fairness, (b) a 5-round 4PC with guaranteed output delivery. Empirically, our protocols are on par with the best known 3PC protocol of Mohassel et al. [CCS 2015] that only achieves security with selective abort, in terms of the computation time, LAN runtime, WAN runtime and communication cost. In fact, our 4PC outperforms the 3PC of Mohassel et al. significantly in terms of per-party computation and communication cost. With an extra GC, we improve the round complexity of our 4PC to four rounds. The only 4PC in our setting, given by Ishai et al. [CRYPTO 2015], involves 12 GCs. Assuming an additional broadcast channel, we present a 5-round 3PC with guaranteed output delivery that involves computation and communication of a single GC. A broadcast channel is inevitable in this setting for achieving guaranteed output delivery, owing to an impossibility result in the literature. The overall broadcast communication of our protocol is nominal and most importantly, is independent of the circuit size. This protocol too induces a nominal overhead compared to the protocol of Mohassel et al.