In the setting of secure multiparty computation, a set of n parties with private inputs wish to jointly compute some functionality of their inputs. One of the most fundamental results of information-theoretically secure computation was presented by Ben-Or, Goldwasser and Wigderson (BGW) in 1988. They demonstrated that any n-party functionality can be computed with perfect security, in the private channels model. When the adversary is semi-honest this holds as long as t < n/2 parties are corrupted, and when the adversary is malicious this holds as long as t < n/3 parties are corrupted. Unfortunately, a full detailed proof of these results was never given. In this paper, we remedy this situation and provide a full proof of security of the BGW protocol. We also derive corollaries for security in the presence of adaptive adversaries and under concurrent general composition (equivalently, universal composability). In addition, we give a full specification of the protocol for the malicious setting. This includes one new step
In the setting of secure multiparty computation, a set of n parties with private inputs wish to jointly compute some functionality of their inputs. One of the most fundamental results of information-theoretically secure computation was presented by Ben-Or, Goldwasser and Wigderson (BGW) in 1988. They demonstrated that any n-party functionality can be computed with perfect security, in the private channels model. When the adversary is semi-honest this holds as long as t < n/2 parties are corrupted, and when the adversary is malicious this holds as long as t < n/3 parties are corrupted. Unfortunately, a full detailed proof of these results was never given. In this paper, we remedy this situation and provide a full proof of security of the BGW protocol. We also derive corollaries for security in the presence of adaptive adversaries and under concurrent general composition (equivalently, universal composability). In addition, we give a full specification of the protocol for the malicious setting. This includes one new step
One of the most fundamental results of secure computation was presented by Ben-Or, Goldwasser and Wigderson (BGW) in 1988. They demonstrated that any n-party functionality can be computed with perfect security, in the private channels model. When the adversary is semi-honest this holds as long as t < n/2 parties are corrupted, and when the adversary is malicious this holds as long as t < n/3 parties are corrupted. In this chapter, we present a full description of the BGW protocol for the semi-honest and malicious settings, along with detailed explanations and intuition regarding the security of the protocols; full proofs can be found in [1].
In the setting of secure multiparty computation, several distrustful parties wish to carry out a distributed computing task on their local private data while satisfying several security properties such as correctness, privacy, independence of inputs and fairness. The aim of secure multiparty computation (MPC) is to enable the parties to carry out the computation in a secure manner, eliminating any attempt of an adversarial entity to harm the execution. The concept of secure computation is very general and fundamental in cryptography, and models any distributed computing task, including simple computations as coin-tossing and broadcast, as well as more complex tasks such as electronic auctions and anonymous transactions. In this thesis, we study two foundational aspects of secure computation: perfect security and fairness. In the first part of this thesis, we study perfect security in secure computation. A protocol that is perfectly secure cannot be broken even when the adversary has unlimited computational power and its security holds unconditionally. One of the most fundamental results of secure computation was presented by Ben-Or, Goldwasser and Wigderson (BGW) in 1988. They demonstrated that any n-party functionality can be computed with perfect security, in the private channels model. When the adversary is semi-honest this holds as long as t < n/2 parties are corrupted, and when the adversary is malicious this holds as long as t < n/3 parties are corrupted. Unfortunately, a full proof of these results was never published. In this thesis, we remedy this situation and provide a full proof of security of the BGW protocol. This also includes a full description of the protocol for the malicious setting. In addition to the above, we observe that by some simple and natural modifications, the BGW protocol can be significantly simplified and one of its expensive (and perhaps most complicated) subprotocols can be saved. We present a new multiplication protocol that is based on the original construction, but is simpler and achieves higher efficiency. In the second part of this thesis, we study fairness in secure two party computation. Informally, the fairness property guarantees that if one party receives its output, then the other party does too. The well-known impossibility result of Cleve (STOC 1986) implies that, in general, it is impossible to securely compute a function with complete fairness without an honest majority. Until recently, the accepted belief has been that nothing non-trivial can be computed with complete fairness in the two party setting. The surprising work of Gordon, Hazay, Katz and Lindell (STOC 2008) shows that this belief is false, and that there exist some non-trivial (deterministic, finite-domain) Boolean functions that can be computed fairly. This raises the fundamental question of characterizing complete fairness in secure two-party computation. We focus on this question and give both positive and negative results. We first characterize
In the setting of secure multiparty computation, a set of parties with private inputs wish to compute some function of their inputs without revealing anything but their output. Over the last decade, the efficiency of secure two-party computation has advanced in leaps and bounds, with speedups of some orders of magnitude, making it fast enough to be of use in practice. In contrast, progress on the case of multiparty computation (with more than two parties) has been much slower, with very little work being done. Currently, the only implemented efficient multiparty protocol has many rounds of communication (linear in the depth of the circuit being computed) and thus is not suited for Internet-like settings where latency is not very low. In this paper, we construct highly efficient constant-round protocols for the setting of multiparty computation for semi-honest adversaries. Our protocols work by constructing a multiparty garbled circuit, as proposed in BMR (Beaver et al., STOC 1990). Our first protocol uses oblivious transfer and constitutes the first concretely-efficient constant-round multiparty protocol for the case of no honest majority. Our second protocol uses BGW, and is significantly more efficient than the FairplayMP protocol (Ben-David et al., CCS 2008) that also uses BGW.
In STOC 1988, Ben-Or, Goldwasser, and Wigderson (BGW) established an important milestone in the fields of cryptography and distributed computing by showing that every functionality can be computed with perfect (information-theoretic and error-free) security at the presence of an active (aka Byzantine) rushing adversary that controls up to n/3 of the parties. We study the round complexity of general secure multiparty computation in the BGW model. Our main result shows that every functionality can be realized in only four rounds of interaction, and that some functionalities cannot be computed in three rounds. This completely settles the round-complexity of perfect actively-secure optimally-resilient MPC, resolving a long line of research. Our lower-bound is based on a novel round-reduction technique that allows us to lift existing three-round lower-bounds for verifiable secret sharing to four-round lower-bounds for general MPC. To prove the upper-bound, we develop new round-efficient protocols for computing degree-2 functionalities over large fields, and establish the completeness of such functionalities. The latter result extends the recent completeness theorem of Applebaum, Brakerski and Tsabary (TCC 2018, Eurocrypt 2019) that was limited to the binary field.
Secure Multiparty Computation (MPC) is an expression encompassing cryptographic techniques that allow mutually distrustful parties to jointly perform computations over private data, ensuring correctness and preserving privacy despite malicious behavior. Guaranteed output is the strongest security goal for MPC: protocols with this property always deliver results. This is in contrast with weaker notions that allow malicious aborts. The seminal works of Ben-Or, Goldwasser, and Wigderson (STOC’88) and Rabin and Ben-Or (STOC’89) showed interactive protocols to compute any function with guaranteed output and perfect security if fewer than one third of parties are corrupted, or with statistical security (with a small error probability) if fewer than half are corrupted. These results hold when the set of participants is fixed throughout the execution. Ostrovsky and Yung’s proactive model (PODC’91) relaxes this assumption by allowing the set of corrupted parties to evolve over time, better capturing the dynamics of long-lived computations, where machines may be periodically compromised and recovered. The recent YOSO (You Only Speak Once) and fluid MPC models (CRYPTO’21) push this ambitious modelling even further by allowing for fully dynamic participation, with parties joining and leaving the computation at will. In this setting, known protocols with guaranteed output fall short of optimal resilience or rely on non-standard communication and adversarial assumptions. Matching the classical BGW and Rabin–Ben-Or bounds in these settings remained an open problem. We resolve these questions within the Layered MPC abstraction of David et al. (CRYPTO’23), in which the interaction pattern of a protocol is restricted to be a layered graph, meaning parties are partitioned into a sequence of disjoint sets (layers) and can send private and broadcast messages to parties in immediately subsequent layers. We match the BGW and Rabin and Ben-Or bounds in this model, fully characterizing the feasibility landscape of Layered MPC with guaranteed output. As a stepping stone towards our statistically secure protocol, we construct a more efficient and conceptually simpler computationally secure protocol relying on linear non-interactive commitments. Our results yield optimally-resilient and maximally-proactive MPC protocols with guaranteed output for both perfect and statistical security.
In the setting of multiparty computation a set of parties with private inputs wish to compute some joint function of their inputs, whilst preserving certain security properties (like privacy and correctness). An adaptively secure protocol is one in which the security properties are preserved even if an adversary can adaptively and dynamically corrupt parties during a computation. This provides a high level of security, that is arguably necessary in today’s world of active computer break-ins. Until now, the work on adaptively secure multiparty computation has focused almost exclusively on the setting of an honest majority, and very few works have considered the honest minority and two-party cases. In addition, significant computational and communication costs are incurred by most protocols that achieve adaptive security. In this work, we consider the two-party setting and assume that honest parties may erase data. We show that in this model it is possible to securely compute any two-party functionality in the presence of adaptive semi-honest adversaries. Furthermore, our protocol remains secure under concurrent general composition (meaning that it remains secure irrespective of the other protocols running together with it). Our protocol is based on Yao’s garbled-circuit construction and, importantly, is as efficient as the analogous protocol for static corruptions. We argue that the model of adaptive corruptions with erasures has been unjustifiably neglected and that it deserves much more attention. 1