Fast Two-Party Secure Computation with Minimal Assumptions

All recent implementations of two-party secure computation protocols require specific complexity assumptions for their correctness and/or efficiency (e.g., DDH, homomorphic encryption, Sigma protocols for specific languages). We propose and implement a Yao-based protocol for secure two-party computation against malicious adver- saries that enjoys the following benefits: (1) it assumes the minimal hardness assumption, that is, oblivious transfers; (2) it has constant round complexity; (3) its overhead is O(k) times of the Yao protocol’s, which is the best one could hope for by using the circuit-level cut-and-choose technique to achieve malicious security; and (4) it is embarrassingly parallelizable in that its depth complexity is roughly the same as the honest-but-curious Yao protocol. To achieve these properties, we use the cut-and-choose paradigm, but solve the main three problems for achiev- ing malicious security (input consistency, selective failure, and output authentication) in a novel and efficient manner. In particular, we propose an efficient witness-indistinguishable proof for output authentication; we suggest the use of an auxiliary 2-universal circuit to ensure the generator’s input consistency; and we advance the performance of the state-of-the-art approach defending the selective failure attack. Not only does our protocol require weaker complexity assumptions, but our implementation of this protocol also demonstrates a several factor improvement over the best prior two-party secure computation protocol which rely on specific number theoretic assumptions

Reuse It Or Lose It: More Efficient Secure Computation Through Reuse of Encrypted Values

Two-party secure function evaluation (SFE) has become significantly more feasible, even on resource-constrained devices, because of advances in server-aided computation systems. However, there are still bottlenecks, particularly in the input validation stage of a computation. Moreover, SFE research has not yet devoted sufficient attention to the important problem of retaining state after a computation has been performed so that expensive processing does not have to be repeated if a similar computation is done again. This paper presents PartialGC, an SFE system that allows the reuse of encrypted values generated during a garbled-circuit computation. We show that using PartialGC can reduce computation time by as much as 96% and bandwidth by as much as 98% in comparison with previous outsourcing schemes for secure computation. We demonstrate the feasibility of our approach with two sets of experiments, one in which the garbled circuit is evaluated on a mobile device and one in which it is evaluated on a server. We also use PartialGC to build a privacy-preserving "friend finder" application for Android. The reuse of previous inputs to allow stateful evaluation represents a new way of looking at SFE and further reduces computational barriers.Comment: 20 pages, shorter conference version published in Proceedings of the 2014 ACM SIGSAC Conference on Computer and Communications Security, Pages 582-596, ACM New York, NY, US

On Garbling Schemes with and without Privacy

Garbling schemes allow to construct two-party function evaluation with security against cheating parties (SFE). To achieve this goal, one party (the Garbler) sends multiple encodings of a circuit (called Garbled Circuits) to the other party (the Evaluator) and opens a subset of these encodings, showing that they were generated honestly. For the remaining garbled circuits, the garbler sends encodings of the inputs. This allows the evaluator to compute the result of function, while the encoding ensures that no other information beyond the output is revealed. To achieve active security against a malicious adversary, the garbler in current protocols has to send O(s) circuits (where s is the statistical security parameter). In this work we show that, for a certain class of circuits, one can reduce this overhead. We consider circuits where sub-circuits depend only on one party\u27s input. Intuitively, one can evaluate these sub-circuits using only one circuit and privacy-free garbling. This has applications to e.g. input validation in SFE and allows to construct more efficient SFE protocols in such cases. We additionally show how to integrate our solution with the SFE protocol of Frederiksen et al. (FJN14), thus reducing the overhead even further

Non-Interactive Secure Computation Based on Cut-and-Choose

In recent years, secure two-party computation (2PC) has been demonstrated to be feasible in practice. However, all efficient general-computation 2PC protocols require multiple rounds of interaction between the two players. This property restricts 2PC to be only relevant to scenarios where both players can be simultaneously online, and where communication latency is not an issue. This work considers the model of 2PC with a single round of interaction, called Non-Interactive Secure Computation (NISC). In addition to the non-interaction property, we also consider a flavor of NISC that allows reusing the first message for many different 2PC invocations, possibly with different players acting as the player who sends the second message, similar to a public-key encryption where a single public-key can be used to encrypt many different messages. We present a NISC protocol that is based on the cut-and-choose paradigm of Lindell and Pinkas (Eurocrypt 2007). This protocol achieves concrete efficiency similar to that of best multi-round 2PC protocols based on the cut-and-choose paradigm. The protocol requires only $t$ garbled circuits for achieving cheating probability of $2^{-t}$, similar to the recent result of Lindell (Crypto 2013), but only needs a single round of interaction. To validate the efficiency of our protocol, we provide a prototype implementation of it and show experiments that confirm its competitiveness with that of the best multi-round 2PC protocols. This is the first prototype implementation of an efficient NISC protocol. In addition to our NISC protocol, we introduce a new encoding technique that significantly reduces communication in the NISC setting. We further show how our NISC protocol can be improved in the multi-round setting, resulting in a highly efficient constant-round 2PC that is also suitable for pipelined implementation

Enforcing Input Correctness via Certification in Garbled Circuit Evaluation

Secure multi-party computation allows a number of participants to securely evaluate a function on their private inputs and has a growing number of applications. Two standard adversarial models that treat the participants as semi-honest or malicious, respectively, are normally considered for showing security of constructions in this framework. In this work, we go beyond the standard security model in the presence of malicious participants and treat the problem of enforcing correct inputs to be entered into the computation. We achieve this by having a certification authority certify user’s information, which is consequently used in secure two-party computation based on garbled circuit evaluation. The focus of this work on enforcing correctness of garbler’s inputs via certification, as prior work already allows one to achieve this goal for circuit evaluator’s input. Thus, in this work, we put forward a novel approach for certifying user’s input and tying certification to garbler’s input used during secure function evaluation based on garbled circuits. Our construction achieves notable performance of adding only one (standard) signature verification and O(nρ) symmetric key/hash operations to the cost of garbled circuit evaluation in the malicious model via cut-and-choose, in which ρ circuits are garbled and n is the length of the garbler’s input in bits. Security of our construction is rigorously proved in the standard model

Accumulating Automata and Cascaded Equations Automata for Communicationless Information Theoretically Secure Multi-Party Computation

Information theoretically secure multi-party computation implies severe communication overhead among the computing participants, as there is a need to reduce the polynomial degree after each multiplication. In particular, when the input is (practically) unbounded, the number of multiplications and therefore the communication bandwidth among the participants may be practically unbounded. In some scenarios the communication among the participants should better be avoided altogether, avoiding linkage among the secret share holders. For example, when processes in clouds operate over streaming secret shares without communicating with each other, they can actually hide their linkage and activity in the crowd. An adversary that is able to compromise processes in the cloud may need to capture and analyze a very large number of possible shares. Consider a dealer that wants to repeatedly compute functions on a long file with the assistance of $m$ servers. The dealer does not wish to leak either the input file or the result of the computation to any of the servers. We investigate this setting given two constraints. The dealer is allowed to share each symbol of the input file among the servers and is allowed to halt the computation at any point. However, the dealer is otherwise stateless. Furthermore, each server is not allowed any communication beyond the shares of the inputs that it receives and the information it provides to the dealer during reconstruction. We present a protocol in this setting for generalized string matching, including wildcards. We also present solutions for identifying other regular languages, as well as particular context free and context sensitive languages. The results can be described by a newly defined {\em accumulating automata} and {\em cascaded equations automata} which may be of an independent interest. As an application of {\em accumulating automata} and {\em cascaded equations automata}, secure and private repeated computations on a secret shared file among communicationless clouds are presented