Abstract Broadcast protocols enable a set of n parties to agree on the input of a designated sender, even facing attacks by malicious parties. In the honest-majority setting, randomization and cryptography were harnessed to achieve low-communication broadcast with sub-quadratic total communication and balanced sub-linear cost per party. However, comparatively little is known in the dishonest-majority setting. Here, the most communication-efficient constructions are based on Dolev and Strong (SICOMP ’83), and sub-quadratic broadcast has not been achieved. On the other hand, the only nontrivial $$\omega (n)$$ ω ( n ) communication lower bounds are restricted to deterministic protocols, or against strong adaptive adversaries that can perform “after the fact” removal of messages. We provide new communication lower bounds in this space, which hold against arbitrary cryptography and setup assumptions, as well as a simple sub-quadratic broadcast protocol showing near tightness of our first bound.
Abstract Broadcast protocols enable a set of n parties to agree on the input of a designated sender, even facing attacks by malicious parties. In the honest-majority setting, randomization and cryptography were harnessed to achieve low-communication broadcast with sub-quadratic total communication and balanced sub-linear cost per party. However, comparatively little is known in the dishonest-majority setting. Here, the most communication-efficient constructions are based on Dolev and Strong (SICOMP ’83), and sub-quadratic broadcast has not been achieved. On the other hand, the only nontrivial ω(n) ω ( n ) communication lower bounds are restricted to deterministic protocols, or against strong adaptive adversaries that can perform “after the fact” removal of messages. We provide new communication lower bounds in this space, which hold against arbitrary cryptography and setup assumptions, as well as a simple sub-quadratic broadcast protocol showing near tightness of our first bound.
Broadcast protocols enable a set of n parties to agree on the input of a designated sender, even facing attacks by malicious parties. In the honest-majority setting, randomization and cryptography were harnessed to achieve low-communication broadcast with sub-quadratic total communication and balanced sub-linear cost per party. However, comparatively little is known in the dishonest-majority setting. Here, the most communication-efficient constructions are based on Dolev and Strong (SICOMP '83), and sub-quadratic broadcast has not been achieved. On the other hand, the only nontrivial ω(n) communication lower bounds are restricted to deterministic protocols, or against strong adaptive adversaries that can perform "after the fact" removal of messages. We provide new communication lower bounds in this space, which hold against arbitrary cryptography and setup assumptions, as well as a simple protocol showing near tightness of our first bound. 1) We demonstrate a tradeoff between resiliency and communication for protocols secure against n−o(n) static corruptions. For example, Ω(n⋅polylog(n)) messages are needed when the number of honest parties is n/polylog(n); Ω(nn) messages are needed for O(n) honest parties; and Ω(n2) messages are needed for O(1) honest parties. Complementarily, we demonstrate broadcast with O(n⋅polylog(n)) total communication facing any constant fraction of static corruptions. 2) Our second bound considers n/2+k corruptions and a weakly adaptive adversary that cannot remove messages "after the fact." We show that any broadcast protocol within this setting can be attacked to force an arbitrary party to send messages to k other parties. This rules out, for example, broadcast facing 51% corruptions in which all non-sender parties have sublinear communication locality.
Abstract. A broadcast protocol allows a sender to distribute a message through a point-to-point network to a set of parties, such that (i) all parties receive the same message, even if the sender is corrupted, and (ii) this is the sender’s message, if he is honest. Broadcast protocols satisfying these properties are known to exist if and only if t < n/3, where n denotes the total number of parties, and t denotes the maximal number of corruptions. When a setup allowing signatures is available to the parties, then such protocols exist even for t < n. Broadcast is the probably most fundamental primitive in distributed cryptography, and is used in almost any cryptographic (multi-party) protocol. However, a broadcast protocol “only ” satisfying the above properties might be insecure when being used in the context of another protocol. In order to be safely usable within other protocols, a broadcast protocol must satisfy a simulation-based security notion, which is secure under composition. In this work, we show that most broadcast protocols in the literature do not satisfy a (natural) simulation-based security notion. We do not know of any broadcast protocol which could be securely invoked in a multi-party computation protocol in the secure-channels model. The problem is that existing protocols for broadcast do not preserve the secrecy of the message while being broadcasted, and in particular allow the adversary to corrupt the sender (and change the message), depending on the message being broadcasted. For example, when every party should broadcast a random bit, the adversary could corrupt those parties that want to broadcast 0, and make them broadcast 1. More concretely, we show that simulatable broadcast in a model with secure channels is possible if and only if t < n/3, respectively t ≤ n/2 when a signature setup is available. The positive results are proven by constructing secure broadcast protocols.
Broadcast among n parties in the presence of t ges n/3 malicious parties is possible only with some additional setup. The most common setup considered is the existence of a PKI and secure, digital signatures, where so-called authenticated broadcast is achievable for any t2) rounds. In particular, we obtain expected constant-round pivtocols for t = n/2 + O(1). ldr On the negative side, we show that even randomized protocols require Omega(2n/(n-t)) rounds. This in particular rules out expected constant-round protocols when the fraction of honest parties is sub-constant.
Broadcast among n parties in the presence of t ges n/3 malicious parties is possible only with some additional setup. The most common setup considered is the existence of a PKI and secure, digital signatures, where so-called authenticated broadcast is achievable for any t2) rounds. In particular, we obtain expected constant-round pivtocols for t = n/2 + O(1). ldr On the negative side, we show that even randomized protocols require Omega(2n/(n-t)) rounds. This in particular rules out expected constant-round protocols when the fraction of honest parties is sub-constant.
We consider the classical problem of synchronous broadcast with dishonest majority, when a public-key infrastructure and digital signatures are available. In a surprising result, Hirt and Zikas (Eurocrypt 2010) recently observed that all existing protocols for this task are insecure against an adaptive adversary who can choose which parties to corrupt as the protocol progresses. Moreover, they prove an impossibility result for adaptively secure broadcast in their setting. We argue that the communication model adopted by Hirt and Zikas is unrealistically pes-simistic. We revisit the problem of adaptively secure broadcast in a more natural synchronous model (with rushing), and show that broadcast is possible in this setting for an arbitrary num-ber of corruptions. Our positive result holds under a strong, simulation-based definition in the universal-composability framework. We also study the impact of adaptive attacks on protocols for secure multi-party computation where broadcast is used as a sub-routine. 1
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.