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ACM SIGSAC Conference on Computer and Communications Security (CCS)

Fast two-party secure computation with minimal assumptions

Abhi A. Shelat, Chih-Hao Shen

Published Jan 1, 2013• 87 citations
Publisher

Abstract

Almost all existing protocols for secure two-party computation require a specific hardness assumption, such as DDH, discrete logarithm, or a random oracle, even after assuming oracle access to the oblivious transfer functionality for their correctness and/or efficiency. We propose and implement a Yao-based protocol that is secure against malicious adversaries and enjoys the following benefits:

DOI
10.1145/2508859.2516698

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Abstract. 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 adversaries 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 linear times (in terms of security parameter) 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 Yao protocol. To achieve these properties, we use the cut-and-choose paradigm, but solve the main three problems for achieving 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.

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Almost all existing protocols for secure two-party computation require a specific hardness assumption, such as DDH, discrete logarithm, or a random oracle, even after assuming oracle access to the oblivious transfer functionality for their correctness and/or efficiency. We propose and implement a Yao-based protocol that is secure against malicious adversaries and enjoys the following benefits:
Abstract. 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 adversaries 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 linear times (in terms of security parameter) 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 Yao protocol. To achieve these properties, we use the cut-and-choose paradigm, but solve the main three problems for achieving 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.
Protocols for secure two-party computation enable a pair of parties to compute a function of their inputs while preserving security properties such as privacy, correctness and independence of inputs. Recently, a number of protocols have been proposed for the efficient construction of two-party computation secure in the presence of malicious adversaries (where security is proven under the standard simulation-based ideal/real model paradigm for defining security). In this paper, we present a protocol for this task that follows the methodology of using cut-and-choose to boost Yao’s protocol to be secure in the presence of malicious adversaries. Relying on specific assumptions (DDH), we construct a protocol that is significantly more efficient and far simpler than the protocol of Lindell and Pinkas (Eurocrypt 2007) that follows the same methodology. We provide an exact, concrete analysis of the efficiency of our scheme and demonstrate that (at least for not very small circuits) our protocol is more efficient than any other known today. secure two-party computation, malicious adversaries, cut-and-choose, concrete effi-Keywords: ciency An extended abstract of this work appeared at TCC 2011.
Abstract. We show an efficient secure two-party protocol, based on Yao’s construction, which provides security against malicious adversaries. Yao’s original protocol is only secure in the presence of semi-honest adversaries. Security against malicious adversaries can be obtained by applying the compiler of Goldreich, Micali and Wigderson (the “GMW compiler”). However, this approach does not seem to be very practical as it requires using generic zero-knowledge proofs. Our construction is based on applying cut-and-choose techniques to the original circuit and inputs. Security is proved according to the ideal/real simulation paradigm, and the proof is in the standard model (with no random oracle model or common reference string assumptions). The resulting protocol is computationally efficient: the only usage of asymmetric cryptography is for running O(1) oblivious transfers for each input bit (or for each bit of a statistical security parameter, whichever is larger). Our protocol combines techniques from folklore (like cut-and-choose) along with new techniques for efficiently proving consistency of inputs. We remark that a naive implementation of the cut-and-choose technique with Yao’s protocol does not yield a secure protocol. This is the first paper to show how to properly implement these techniques, and to provide a full proof of security. Our protocol can also be interpreted as a constant-round black-box reduction of secure two-party com-putation to oblivious transfer and perfectly-hiding commitments, or a black-box reduction of secure two-party computation to oblivious transfer alone, with a number of rounds which is linear in a sta-tistical security parameter. These two reductions are comparable to Kilian’s reduction, which uses OT alone but incurs a number of rounds which is linear in the depth of the circuit [18]. 1
We propose a new approach to practical two-party computation secure against an active adversary. All prior practical protocols were based on Yao's garbled circuits. We use an OT-based approach and get efficiency via OT extension in the random oracle model. To get a practical protocol we introduce a number of novel techniques for relating the outputs and inputs of OTs in a larger construction. We also report on an implementation of this approach, that shows that our protocol is more efficient than any previous one: For big enough circuits, we can evaluate more than 20000 Boolean gates per second. As an example, evaluating one oblivious AES encryption (~34000 gates) takes 64 seconds, but when repeating the task 27 times it only takes less than 3 seconds per instance.