On the Round Complexity of Randomized Byzantine Agreement

We prove lower bounds on the round complexity of randomized Byzantine agreement (BA) protocols, bounding the halting probability of such protocols after one and two rounds. In particular, we prove that: 1) BA protocols resilient against n/3 [resp., n/4] corruptions terminate (under attack) at the end of the first round with probability at most o(1) [resp., 1/2+ o(1)]. 2) BA protocols resilient against n/4 corruptions terminate at the end of the second round with probability at most 1-Theta(1). 3) For a large class of protocols (including all BA protocols used in practice) and under a plausible combinatorial conjecture, BA protocols resilient against n/3 [resp., n/4] corruptions terminate at the end of the second round with probability at most o(1) [resp., 1/2 + o(1)]. The above bounds hold even when the parties use a trusted setup phase, e.g., a public-key infrastructure (PKI). The third bound essentially matches the recent protocol of Micali (ITCS\u2717) that tolerates up to n/3 corruptions and terminates at the end of the third round with constant probability

A Framework for Efficient Adaptively Secure Composable Oblivious Transfer in the ROM

Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a number of applications, in particular, as an essential building block for two-party and multi-party computation. We construct a round-optimal (2 rounds) universally composable (UC) protocol for oblivious transfer secure against active adaptive adversaries from any OW-CPA secure public-key encryption scheme with certain properties in the random oracle model (ROM). In terms of computation, our protocol only requires the generation of a public/secret-key pair, two encryption operations and one decryption operation, apart from a few calls to the random oracle. In~terms of communication, our protocol only requires the transfer of one public-key, two ciphertexts, and three binary strings of roughly the same size as the message. Next, we show how to instantiate our construction under the low noise LPN, McEliece, QC-MDPC, LWE, and CDH assumptions. Our instantiations based on the low noise LPN, McEliece, and QC-MDPC assumptions are the first UC-secure OT protocols based on coding assumptions to achieve: 1) adaptive security, 2) optimal round complexity, 3) low communication and computational complexities. Previous results in this setting only achieved static security and used costly cut-and-choose techniques.Our instantiation based on CDH achieves adaptive security at the small cost of communicating only two more group elements as compared to the gap-DH based Simplest OT protocol of Chou and Orlandi (Latincrypt 15), which only achieves static security in the ROM

Multi-party Quantum Computation

We investigate definitions of and protocols for multi-party quantum computing in the scenario where the secret data are quantum systems. We work in the quantum information-theoretic model, where no assumptions are made on the computational power of the adversary. For the slightly weaker task of verifiable quantum secret sharing, we give a protocol which tolerates any t < n/4 cheating parties (out of n). This is shown to be optimal. We use this new tool to establish that any multi-party quantum computation can be securely performed as long as the number of dishonest players is less than n/6.Comment: Masters Thesis. Based on Joint work with Claude Crepeau and Daniel Gottesman. Full version is in preparatio

Separating Two-Round Secure Computation From Oblivious Transfer

We consider the question of minimizing the round complexity of protocols for secure multiparty computation (MPC) with security against an arbitrary number of semi-honest parties. Very recently, Garg and Srinivasan (Eurocrypt 2018) and Benhamouda and Lin (Eurocrypt 2018) constructed such 2-round MPC protocols from minimal assumptions. This was done by showing a round preserving reduction to the task of secure 2-party computation of the oblivious transfer functionality (OT). These constructions made a novel non-black-box use of the underlying OT protocol. The question remained whether this can be done by only making black-box use of 2-round OT. This is of theoretical and potentially also practical value as black-box use of primitives tends to lead to more efficient constructions. Our main result proves that such a black-box construction is impossible, namely that non-black-box use of OT is necessary. As a corollary, a similar separation holds when starting with any 2-party functionality other than OT. As a secondary contribution, we prove several additional results that further clarify the landscape of black-box MPC with minimal interaction. In particular, we complement the separation from 2-party functionalities by presenting a complete 4-party functionality, give evidence for the difficulty of ruling out a complete 3-party functionality and for the difficulty of ruling out black-box constructions of 3-round MPC from 2-round OT, and separate a relaxed "non-compact" variant of 2-party homomorphic secret sharing from 2-round OT

Combining behavioural types with security analysis

Today's software systems are highly distributed and interconnected, and they increasingly rely on communication to achieve their goals; due to their societal importance, security and trustworthiness are crucial aspects for the correctness of these systems. Behavioural types, which extend data types by describing also the structured behaviour of programs, are a widely studied approach to the enforcement of correctness properties in communicating systems. This paper offers a unified overview of proposals based on behavioural types which are aimed at the analysis of security properties

The Bottleneck Complexity of Secure Multiparty Computation

In this work, we initiate the study of bottleneck complexity as a new communication efficiency measure for secure multiparty computation (MPC). Roughly, the bottleneck complexity of an MPC protocol is defined as the maximum communication complexity required by any party within the protocol execution. We observe that even without security, bottleneck communication complexity is an interesting measure of communication complexity for (distributed) functions and propose it as a fundamental area to explore. While achieving O(n) bottleneck complexity (where n is the number of parties) is straightforward, we show that: (1) achieving sublinear bottleneck complexity is not always possible, even when no security is required. (2) On the other hand, several useful classes of functions do have o(n) bottleneck complexity, when no security is required. Our main positive result is a compiler that transforms any (possibly insecure) efficient protocol with fixed communication-pattern for computing any functionality into a secure MPC protocol while preserving the bottleneck complexity of the underlying protocol (up to security parameter overhead). Given our compiler, an efficient protocol for any function f with sublinear bottleneck complexity can be transformed into an MPC protocol for f with the same bottleneck complexity. Along the way, we build cryptographic primitives - incremental fully-homomorphic encryption, succinct non-interactive arguments of knowledge with ID-based simulation-extractability property and verifiable protocol execution - that may be of independent interest

Output privacy in secure multiparty computation

Abstract. In secure multiparty computation, a set of mutually mistrusting players engage in a protocol to compute an arbitrary, publicly known polynomial-sized function of the party’s private inputs, in a way that does not reveal (to an adversary controlling some of the players) any knowledge about the remaining inputs, beyond what can be deduced from the obtained output(s). Since its introduction by Yao [39], and Goldreich, Micali and Wigderson [29], this powerful paradigm has received a lot of attention. All throughout, however, very little attention has been given to the privacy of the players ’ outputs. Yet, disclosure of (part of) the output(s) may have serious consequences for the overall security of the application e.g., when the computed output is a secret key; or when the evaluation of the function is part of a larger computation, so that the function’s output(s) will be used as input(s) in the next phase. In this work, we define the notion of private-output multiparty computation. This newly revised notion encompasses (as a particular case) the classical definition and allows a set of players to jointly compute the output of a common function in such a way that the execution of the protocol reveals no information (to an adversary controlling some of the players) about (some part of) the outputs (other than what follows from the description of the function itself). Next, we formall

Rational Multiparty Computation

The field of rational cryptography considers the design of cryptographic protocols in the presence of rational agents seeking to maximize local utility functions. This departs from the standard secure multiparty computation setting, where players are assumed to be either honest or malicious. ^ We detail the construction of both a two-party and a multiparty game theoretic framework for constructing rational cryptographic protocols. Our framework specifies the utility function assumptions necessary to realize the privacy, correctness, and fairness guarantees for protocols. We demonstrate that our framework correctly models cryptographic protocols, such as rational secret sharing, where existing work considers equilibrium concepts that yield unreasonable equilibria. Similarly, we demonstrate that cryptography may be applied to the game theoretic domain, constructing an auction market not realizable in the original formulation. Additionally, we demonstrate that modeling players as rational agents allows us to design a protocol that destabilizes coalitions. Thus, we establish a mutual benefit from combining the two fields, while demonstrating the applicability of our framework to real-world market environments.^ We also give an application of game theory to adversarial interactions where cryptography is not necessary. Specifically, we consider adversarial machine learning, where the adversary is rational and reacts to the presence of a data miner. We give a general extension to classification algorithms that returns greater expected utility for the data miner than existing classification methods