We consider the problem of distributing a computation between two parties, such that any bounded-communication leakage function applied to the local views of the two parties reveals essentially nothing about the input. This problem can be motivated by the goal of outsourcing computations on sensitive data to two servers in the cloud, where both servers can be simultaneously corrupted by viruses that have a limited communication bandwidth. We present a simple and efficient reduction of the above problem to that of constructing parity-resilient circuits, namely circuits that map an encoded input to an encoded output so that the parity of any subset of the wires is essentially independent of the input. We then construct parity-resilient circuits from circuits that are resilient to local leakage, which can in turn be obtained from protocols for secure multiparty computation. Our main reduction builds on a novel generalization of the ε-biased masking lemma that applies to interactive protocols. Applying the above, we obtain two-party protocols with resilience to bounded-communication leakage either in the information-theoretic setting, relying on random oblivious transfer correlations, or in the computational setting, relying on non-committing encryption which can be based on a variety of standard cryptographic assumptions.
We consider the problem of distributing a computation between two parties, such that any bounded-communication leakage function applied to the local views of the two parties reveals essentially nothing about the input. This problem can be motivated by the goal of outsourcing computations on sensitive data to two servers in the cloud, where both servers can be simultaneously corrupted by viruses that have a limited communication bandwidth. We present a simple and efficient reduction of the above problem to that of constructing parity-resilient circuits, namely circuits that map an encoded input to an encoded output so that the parity of any subset of the wires is essentially independent of the input. We then construct parity-resilient circuits from circuits that are resilient to local leakage, which can in turn be obtained from protocols for secure multiparty computation. Our main reduction builds on a novel generalization of the ε-biased masking lemma that applies to interactive protocols. Applying the above, we obtain two-party protocols with resilience to bounded-communication leakage either in the information-theoretic setting, relying on random oblivious transfer correlations, or in the computational setting, relying on non-committing encryption which can be based on a variety of standard cryptographic assumptions.
We consider the question of protecting a general computation device, modeled by a stateful Boolean circuit, against leakage of partial information about its internal wires. Goyal et al. (FOCS 2016) obtained a solution for the case of bounded-communication leakage, where the wires are partitioned into two parts and the leakage can be any function computed using t bits of communication between the parts. However, this solution suffers from two major limitations: (1) it only applies to a one-shot (stateless) computation, mapping an encoded input to an encoded output, and (2) the leakage-resilient circuit consumes fresh random bits, whose number scales linearly with the circuit complexity of the computed function. In this work, we eliminate the first limitation and make progress on the second. Concretely: - We present the first construction of stateful circuits that offer information-theoretic protection against continuous bounded-communication leakage. As an application, we extend a two-party “malware-resilient” protocol of Goyal et al. to the continuous-leakage case. - For simple types of bounded-communication leakage, which leak t parities or t disjunctions of circuit wires or their negations, we obtain a deterministic variant that does not require any fresh randomness beyond the randomness in the initial state. Here we get computational security based on a subexponentially secure one-way function. This is the first deterministic leakage-resilient circuit construction for any nontrivial class of global leakage.
We construct a multiparty computation (MPC) protocol that is secure even if a malicious adversary, in addition to corrupting 1-ε fraction of all parties for an arbitrarily small constant ε >0, can leak information about the secret state of each honest party. This leakage can be continuous for an unbounded number of executions of the MPC protocol, computing different functions on the same or different set of inputs. We assume a (necessary) "leak-free" preprocessing stage. We emphasize that we achieve leakage resilience without weakening the security guarantee of classical MPC. Namely, an adversary who is given leakage on honest parties' states, is guaranteed to learn nothing beyond the input and output values of corrupted parties. This is in contrast with previous works on leakage in the multi-party protocol setting, which weaken the security notion, and only guarantee that a protocol which leaks l bits about the parties' secret states, yields at most l bits of leakage on the parties' private inputs. For some functions, such as voting, such leakage can be detrimental.
Current secure multiparty protocols have the following deficiency. The public transcript of the communication can be used as an involuntary commitment of the parties to their inputs and outputs. Thus parties can be later coerced by some authority to reveal their private data. Previous work that has pointed this interesting problem out contained only partial treatment. In this work we present the first general treatment of the coercion problem in secure computation. First we present a general definition of protocols that provide resilience to coercion. Our definition constitutes a natural extension of the general paradigm used for defining secure multiparty protocols. Next we show that if trapdoor permutations exist then any function can be incoercibly computed (i.e., computed by a protocol that provides resilience to coercion) in the presence of computationally bounded adversaries and only public communication channels. This holds as long as less than half the parties are coerced (or corrupted). In particular, ours are the first incoercible protocols without physical security assumptions. Also, our protocols constitute an alternative solution to the recently solved adaptive security problem. Our techniques are quite surprising and include non-standard use of deniable encryptions.
The notion of secure computation is central to cryptography. Introduced in the seminal works of Yao [FOCS'82, FOCS'86] and Goldreich, Micali and Wigderson [STOC'87], secure multiparty computation allows a group of (mutually) distrustful parties to jointly compute any functionality over their individual private inputs in such a manner that the honest parties obtain the correct outputs and no group of malicious parties learn anything beyond their inputs and the prescribed outputs. General feasibility results for secure computation were given by Yao [FOCS'86] and Goldreich et al. [STOC'87] more than two decades ago. Subsequent to these works, designing secure computation protocols that can tolerate more powerful adversaries and satisfy stronger notions of security has been a very active area of research. In this dissertation, we study two such new frontiers in the area of secure computation.
In the first part of this dissertation, we initiate a study of designing leakage-resilient interactive protocols. Specifically, we consider the scenario where an adversary, in addition to corrupting a subset of parties, can leak (potentially via physical attacks) arbitrary information from the secret state of any honest party. This is in contrast to the standard notion of secure computation where it is assumed that the adversary only has black-box'' access to the honest parties. In particular, we formalize a meaningful definition of leakage-resilient zero knowledge proof systems and provide constructions that satisfy our notion. We also discuss various applications of our results.
The second part of this dissertation concerns with the general question of whether it is possible to securely run cryptographic protocols over an insecure network environment such as the Internet. It is well-known that the standard notion of secure computation is only relevant to the stand-alone setting where a single protocol is being executed in isolation; as such it does not guarantee security when multiple protocol sessions may be executed concurrently under the control of an adversary who is present across all sessions. We consider the open problem of constructing secure password-based authenticated key exchange protocols in such a setting in the plain model (i.e., without assuming any trusted infrastructure or random oracles). We give the first construction of such a protocol based on standard cryptographic assumptions. Our results are in fact much more general, and extend to other functionalities w.r.t. a (necessarily) weakened notion of concurrently secure computation.
The results presented in this dissertation stem from two papers which are joint works with Sanjam Garg and Amit Sahai, and with Vipul Goyal and Rafail Ostrovsky, respectively.
We consider the problem of securely generating useful instances of two-party correlations, such as many independent copies of a random oblivious transfer (OT) correlation, using a small amount of communication. This problem is motivated by the goal of secure computation with silent preprocessing, where a low-communication input-independent setup, followed by local ("silent") computation, enables a lightweight "non-cryptographic" online phase once the inputs are known. Recent works of Boyle et al. (CCS 2018, Crypto 2019) achieve this goal with good concrete efficiency for useful kinds of two-party correlations, including OT correlations, under different variants of the Learning Parity with Noise (LPN) assumption, and using a small number of "base'' oblivious transfers. The protocols of Boyle et al. have several limitations. First, they require a large number of communication rounds. Second, they are only secure against semi-honest parties. Finally, their concrete efficiency estimates are not backed by an actual implementation. In this work we address these limitations, making three main contributions: Eliminating interaction. Under the same assumption, we obtain the first concretely efficient 2-round protocols for generating useful correlations, including OT correlations, in the semi-honest security model. This implies the first efficient 2-round OT extension protocol of any kind and, more generally, protocols for non-interactive secure computation (NISC) that are concretely efficient and have the silent preprocessing feature. Malicious security. We provide security against malicious parties without additional interaction and with only a modest overhead; prior to our work, no similar protocols were known with any number of rounds. Implementation. Finally, we implemented, optimized, and benchmarked our 2-round OT extension protocol, demonstrating that it offers a more attractive alternative to the OT extension protocol of Ishai et al. (Crypto 2003) in many realistic settings.
In [AGP14] Ananth et al. showed that continual leakage-resilient non-transferable interactive proofs exist when a leak-free input-encoding phase is allowed and a common reference string is available. They left open the problem of removing the need of a common reference string. In [BGJK12] Boyle et al. showed that for some interesting functionalities continual leakage-resilient secure computation is possible when leak-free interactive preprocessing and input-encoding phases are allowed. They left open the problem of removing the interactive pre-processing. In this work we study the above questions. Our main contribution shows that leakage-resilient black-box zero-knowledge is impossible when relying on a leak-free input-encoding phase only (i.e., without CRS/preprocessing). Additionally, we also show that leakage-resilient multi-party computation for all functionalities is impossible (regardless of the number of players assuming just one corrupted player) when relying only on a leak-free input-encoding phase (i.e., without CRS/preprocessing). Our results are achieved by extending a technique of [NVZ13] to prove lower bounds for leakage-resilient security. Indeed as in [NVZ13] we use leakage queries to run an execution of a communication-efficient protocol in the head of the adversary. Moreover, to defeat the black-box simulator we connect the above technique for leakage resilience to security against reset attacks.