Garbled circuits is a cryptographic technique, which has been used among other things for the construction of two and threeparty secure computation, private function evaluation and secure outsourcing. Garbling schemes is a primitive which formalizes the syntax and security properties of garbled circuits. We define a generalization of garbling schemes called reactive garbling schemes. We consider functions and garbled functions taking multiple inputs and giving multiple outputs. Two garbled functions can be linked together: an encoded output of one garbled function can be transformed into an encoded input of the other garbled function without communication between the parties. Reactive garbling schemes also allow partial evaluation of garbled functions even when only some of the encoded inputs are provided. It is possible to further evaluate the linked garbled functions when more garbled inputs become available. It is also possible to later garble more functions and link them to the ongoing garbled evaluation. We provide rigorous definitions for reactive garbling schemes. We define a new notion of security for reactive garbling schemes called confidentiality. We provide both simulation based and indistinguishability based notions of security. We also show that the simulation based notion of security implies the indistinguishability based notion of security. We present an instantiation of reactive garbling schemes. We present an application of reactive garbling schemes to reactive two-party computation secure against a malicious, static adversary. We demonstrate how garbling schemes can be used to give abstract black-box descriptions and proof of several advanced applications of garbled circuits in the literature, including Minilego and Lindell’s forge-and-lose technique.
Garbled circuits is a cryptographic technique, which has been used among other things for the construction of two and threeparty secure computation, private function evaluation and secure outsourcing. Garbling schemes is a primitive which formalizes the syntax and security properties of garbled circuits. We define a generalization of garbling schemes called reactive garbling schemes. We consider functions and garbled functions taking multiple inputs and giving multiple outputs. Two garbled functions can be linked together: an encoded output of one garbled function can be transformed into an encoded input of the other garbled function without communication between the parties. Reactive garbling schemes also allow partial evaluation of garbled functions even when only some of the encoded inputs are provided. It is possible to further evaluate the linked garbled functions when more garbled inputs become available. It is also possible to later garble more functions and link them to the ongoing garbled evaluation. We provide rigorous definitions for reactive garbling schemes. We define a new notion of security for reactive garbling schemes called confidentiality. We provide both simulation based and indistinguishability based notions of security. We also show that the simulation based notion of security implies the indistinguishability based notion of security. We present an instantiation of reactive garbling schemes. We present an application of reactive garbling schemes to reactive two-party computation secure against a malicious, static adversary. We demonstrate how garbling schemes can be used to give abstract black-box descriptions and proof of several advanced applications of garbled circuits in the literature, including Minilego and Lindell’s forge-and-lose technique.
Abstract. Garbled circuits is a cryptographic technique, which has been used among other things for the con-struction of two and three-party secure computation, private function evaluation and secure outsourcing. Garbling schemes is a primitive which formalizes the syntax and security properties of garbled circuits. We dene a gener-alization of garbling schemes called reactive garbling schemes. We consider functions and garbled functions taking multiple inputs and giving multiple outputs. Two garbled functions can be linked together: an encoded output of one garbled function can be transformed into an encoded input of the other garbled function without commu-nication between the parties. Reactive garbling schemes also allow partial evaluation of garbled functions even when only some of the encoded inputs are provided. It is possible to further evaluate the linked garbled functions when more garbled inputs become available. It is also possible to later garble more functions and link them to the ongoing garbled evaluation. We provide rigorous denitions for reactive garbling schemes. We dene a new notion of security for reactive garbling schemes called condentiality. We provide both simulation based and in-distinguishability based notions of security. We also show that the simulation based notion of security implies the indistinguishability based notion of security. We present an instantiation of reactive garbling schemes. We present an application of reactive garbling schemes to reactive two-party computation secure against a malicious adversary. We demonstrate how garbling schemes can be used to give abstract black-box descriptions and proof of several advanced applications of garbled circuits in the literature, including Minilego and Lindell’s forge-and-loose technique. 1
This paper reports on a number of conceptual and technical contributions to the currently very lively field of two-party computation (2PC) based on garbled circuits. Our main contributions are as follows: 1. We propose the notion of an interactive garbling scheme, where the garbled circuit is generated through an interactive protocol between the garbler and the evaluator. The garbled circuit is correct and privacy preserving even if one of the two parties was acting maliciously during garbling. The security notion is game based. 2. We show that an interactive garbling scheme combined with a Universally Composable (UC) secure oblivious transfer protocol can be used in a black-box manner to implement two-party computation (2PC) UC securely against any probabilistic polynomial time static and malicious adversary. The protocol abstracts many recent protocols for implementing 2PC from garbled circuits and will allow future designers of interactive garbling schemes to prove security with the simple game based definitions, as opposed to directly proving UC security for each new scheme. 3. We propose an instantiation of interactive garbling by designing a new protocol in the LEGO family of protocols for efficient garbling against a malicious adversary. The new protocol is based on several new technical contributions and optimizations, for example making it possible to get distinct output to both parties with minimal overhead. The scheme makes black-box usage of a XOR-homomorphic commitment scheme, an authentic, private and oblivious garbling scheme and a 2-correlation-robust and collision-resistant hash function. When comparing our resulting 2PC protocol to previous works in the same setting we see a noticeable reduction in the communication that directly depends on the size of the circuit (e.g. 33% for circuits larger than 501,271 AND gates).
Secure two-party computation problem is about two parties that want to compute some function of their private inputs in a way that other party won’t learn it. We describe a general way to perform secure two-party computation of a function specified as a boolean circuit, which was proposed by A.A. Yao in 1982. This method is named Yao garbled circuit evaluation and is secure against semi-honest adversaries. We present a new efficient protocol for secure two-party computation Circus, that is secure against malicious adversary in consistency model. Consistency model implies that either both parties will receive correct output and persist privacy of their inputs or a honest party will know, that is was cheated and that adversary potentially have learnt 1 bit of other party’s input value. We specify all necessary sub-protocols and their security requirements and prove security of Circus in malicious environment.
Abstract. We consider secure two-party computation in a multiple-execution setting, where two parties wish to securely evaluate the same circuit multiple times. We design efficient garbled-circuit-based two-party protocols secure against malicious adversaries. Recent works by Lindell (Crypto 2013) and Huang-Katz-Evans (Crypto 2013) have obtained op-timal complexity for cut-and-choose performed over garbled circuits in the single execution setting. We show that it is possible to obtain much lower amortized overhead for cut-and-choose in the multiple-execution setting. Our efficiency improvements result from a novel way to combine a recent technique of Lindell (Crypto 2013) with LEGO-based cut-and-choose techniques (TCC 2009, Eurocrypt 2013). In concrete terms, for 40-bit statistical security we obtain a 2 × improvement (per execution) in com-munication and computation for as few as 7 executions, and require only 8 garbled circuits (i.e., a 5 × improvement) per execution for as low as 3500 executions. Our results suggest the exciting possibility that secure two-party computation in the malicious setting can be less than an order of magnitude more expensive than in the semi-honest setting. 1
In this thesis we design and implement three approaches to provide efficient Secure Two- Party Computation (2PC) protocols that are secure in presence of malicious adversaries. The field of secure two-party computation enables two mutually distrusting parties, each with their own private input, to run a computation of an arbitrary program. At the end of the computation, nothing about their private input is leaked except for what can be learned from the output of the computation. The seminal work of Yao in 1986 provided the first proof that such a computation is feasible using the so called garbled circuits and given an Oblivious Transfer protocol. In this thesis, we follow Yao’s garbled circuit approach and focus on efficient protocols that are secure against malicious adversaries. We examine three different categories of optimization. In each category, we present a 2PC protocol, prove its security, and implement it as a proof of concept to demonstrate its running time in practice. Non-interactive Secure Computation: In this category, we offer the first implementation of a malicious 2PC protocol that reduces the required rounds of interaction between the two parties to only two rounds (i.e., each party sends only one message to the other party). Mixed Secure Two-Party Computation: In the second category we target big and complex programs and break them into subprograms. Then, we compute each subprogram using the most efficient 2PC protocol that is suitable for it. Finally, we securely connect these subprograms together. The goal is to reduce the overhead of the garbled circuits significantly, which results in a more efficient overall 2PC protocol for programs with specific properties. Secure Computation for Random Access Machine Programs: In the third category, we target programs that require random access to the memory (as opposed to a sequential access). We present the first efficient maliciously-secure protocol for computing such programs.
Abstract. We propose a new two-party computation protocol using Yao’s garbled circuits, which is secure in the case of malicious behavior. To illustrate the need for the new protocol, we first discuss security issues of three existing protocols for secure two-party computation using garbled circuits, in the case of malicious behavior. The first is a protocol by Pinkas (Eurocrypt 2003), and the other two are the committed-input scheme and the k-leaked model, both presented by Mohassel and Franklin (PKC 2006). We address security flaws in all schemes, which allow leaking of information on the private inputs. In the k-leaked model leaking of some information is permitted if a participant is cheating, but then the honest participant should be aware of it. We show that this is not the case. After discussing these security issues of the known schemes, we describe our new protocol. It is based on the protocol by Pinkas, and the correction of the flaw of the scheme by Pinkas makes our protocol not only more secure, but also more efficient. We provide a detailed informal security analysis of our new protocol. Keywords: Secure two-party computation, Yao’s garbled circuit, active adversary 1