Protocols for secure computation enable mutually distrustful parties to jointly compute on their private inputs without revealing anything but the result. Over recent years, secure computation has become practical and considerable effort has been made to make it more and more efficient. A highly important tool in the design of two-party protocols is Yao's garbled circuit construction (Yao 1986), and multiple optimizations on this primitive have led to performance improvements of orders of magnitude over the last years. However, many of these improvements come at the price of making very strong assumptions on the underlying cryptographic primitives being used (e.g., that AES is secure for related keys, that it is circular secure, and even that it behaves like a random permutation when keyed with a public fixed key). The justification behind making these strong assumptions has been that otherwise it is not possible to achieve fast garbling and thus fast secure computation. In this paper, we take a step back and examine whether it is really the case that such strong assumptions are needed. We provide new methods for garbling that are secure solely under the assumption that the primitive used (e.g., AES) is a pseudorandom function. Our results show that in many cases, the penalty incurred is not significant, and so a more conservative approach to the assumptions being used can be adopted.
Protocols for secure computation enable mutually distrustful parties to jointly compute on their private inputs without revealing anything but the result. Over recent years, secure computation has become practical and considerable effort has been made to make it more and more efficient. A highly important tool in the design of two-party protocols is Yao's garbled circuit construction (Yao 1986), and multiple optimizations on this primitive have led to performance improvements of orders of magnitude over the last years. However, many of these improvements come at the price of making very strong assumptions on the underlying cryptographic primitives being used (e.g., that AES is secure for related keys, that it is circular secure, and even that it behaves like a random permutation when keyed with a public fixed key). The justification behind making these strong assumptions has been that otherwise it is not possible to achieve fast garbling and thus fast secure computation. In this paper, we take a step back and examine whether it is really the case that such strong assumptions are needed. We provide new methods for garbling that are secure solely under the assumption that the primitive used (e.g., AES) is a pseudorandom function. Our results show that in many cases, the penalty incurred is not significant, and so a more conservative approach to the assumptions being used can be adopted.
Protocols for secure computation enable mutually distrustful parties to jointly compute on their private inputs without revealing anything but the result. Over recent years, secure com-putation has become practical and considerable effort has been made to make it more and more efficient. A highly important tool in the design of two-party protocols is Yao’s garbled circuit construction (Yao 1986), and multiple optimizations on this primitive have led to performance improvements of orders of magnitude over the last years. However, many of these improvements come at the price of making very strong assumptions on the underlying cryptographic primitives being used (e.g., that AES is secure for related keys, that it is circular secure, and even that it behaves like a random permutation when keyed with a public fixed key). The justification behind making these strong assumptions has been that otherwise it is not possible to achieve fast garbling and thus fast secure computation. In this paper, we take a step back and examine whether it is really the case that such strong assumptions are needed. We provide new methods for garbling that are secure solely under the assumption that the primitive used (e.g., AES) is a pseudorandom function. Our results show that in many cases, the penalty incurred is not significant, and so a more conservative approach to the assumptions being used can be adopted.
Secure two-party computation enables two parties to evaluate a function cooperatively without revealing to either party anything beyond the function's output. The garbled-circuit technique, a generic approach to secure two-party computation for semi-honest participants, was developed by Yao in the 1980s, but has been viewed as being of limited practical significance due to its inefficiency. We demonstrate several techniques for improving the running time and memory requirements of the garbled-circuit technique, resulting in an implementation of generic secure two-party computation that is significantly faster than any previously reported while also scaling to arbitrarily large circuits. We validate our approach by demonstrating secure computation of circuits with over 109 gates at a rate of roughly 10 microseconds per garbled gate, and showing order-of-magnitude improvements over the best previous privacy-preserving protocols for computing Hamming distance, Levenshtein distance, Smith-Waterman genome alignment, and AES.
In the setting of secure two-party computation, two parties wish to securely compute a joint function of their private inputs, while revealing only the output. One of the primary techniques for achieving efficient secure two-party computation is that of Yao’s garbled circuits (FOCS 1986). In the semi-honest model, where just one garbled circuit is constructed and evaluated, Yao’s protocol has proven itself to be very efficient. However, a malicious adversary who constructs the garbled circuit may construct a garbling of a different circuit computing a different function, and this cannot be detected (due to the garbling). In order to solve this problem, many circuits are sent and some of them are opened to check that they are correct while the others are evaluated. This methodology, called cut-and-choose, introduces significant overhead, both in computation and in communication, and is mainly due to the number of circuits that must be used in order to prevent cheating. In this paper, we present a cut-and-choose protocol for secure computation based on garbled circuits, with security in the presence of malicious adversaries, that vastly improves on all previous protocols of this type. Concretely, for a cheating probability of at most 2−40, the best previous works send between 125 and 128 circuits. In contrast, in our protocol 40 circuits alone suffice (with some additional overhead). Asymptotically, we achieve a cheating probability of 2−s where s is the number of garbled circuits, in contrast to the previous best of 2−0.32s. We achieve this by introducing a new cut-and-choose methodology with the property that in order to cheat, all of the evaluated circuits must be incorrect, and not just the majority as in previous works. The security of our protocol relies on the Decisional Diffie-Hellman assumption.
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. Secure multi-party computation has been considered by the cryptographic community for a number of years. Until recently it has been a purely theoretical area, with few implementations with which to test various ideas. This has led to a number of optimisations being proposed which are quite restricted in their application. In this paper we describe an implementation of the two-party case, using Yao’s garbled circuits, and present various algorithmic protocol improvements. These optimisations are analysed both theoretically and empirically, using experiments of various adversarial situations. Our experimental data is provided for reasonably large circuits, including one which performs an AES encryption, a problem which we discuss in the context of various possible applications. 1
Consider several parties that do not trust each other, yet they wish to correctly compute some common function of their local inputs while keeping these inputs private. This problem is known as "Secure Multi-Party Computation", and was introduced by Andrew Yao in 1982. Secure multi-party computations have some real world examples like electronic auctions, electronic voting or fingerprinting. In this thesis we consider the case where there are only two parties involved. This is known as "Secure Two-Party Computation". If there is a trusted third party called Carol, then the problem is pretty straightforward. The participating parties could hand their inputs in Carol who can compute the common function correctly and could return the outputs to the corresponding parties. The goal is to achieve (almost) the same result when there is no trusted third party. Cryptographic protocols are designed in order to solve these kinds of problems. These protocols are analyzed within an appropriate model in which the behavior of parties is structured. The basic level is called the Semi-Honest Model where parties are assumed to follow the protocol specification, but later can derive additional information based on the messages which have been received so far. A more realistic model is the so-called Malicious Model. The common approach is to first analyze a protocol in the semi-honest model and then later extend it into the malicious model. Any cryptographic protocol for secure two-party computation must satisfy the following security requirements: correctness, privacy and fairness. It must guarantee the correctness of the result while preserving the privacy of the parties’ inputs, even if one of the parties is malicious and behaves arbitrarily throughout the protocol. It must also guarantee fairness. This roughly means that whenever a party aborts the protocol prematurely, he or she should not have any advantage over the other party in discovering the output. The main question for researchers is to construct new protocols that achieve the above mentioned goals for secure multi-party computation. Of course, such protocols must be secure in a given model, as well as be as efficient as possible. In 1986, Yao presented the first general protocol for secure two-party computation which was applicable only to the semi-honest model. He uses a tool called "Garbled Circuit". Yao’s protocol uses the underlying primitives ("Pseudorandom Generator" and "Oblivious Transfer") as blackboxes which lead to efficient results. After Yao’s work many variants and improvements have been proposed for the malicious model. In this thesis, we design several new protocols for secure two-party computation based on Yao’s garbled circuit. Before we present the details of our new designs, we first show several weaknesses, security flaws or problems with the existing protocols in the literature. We first work in the semi-honest model and then extend it into the malicious model by presenting new protocols. Finally we add fairness to our protocol. Oblivious transfer (OT) is a fundamental primitive in modern cryptography which is useful for implementing protocols for secure multi-party computation. We study several variants of oblivious transfer in this thesis. We present a new protocol for the so-called "Committed OT". This protocol is very efficient in the sense that it is quite good in comparison to the most efficient committed OT protocols in the literature. The abovementioned flaw with the use of OT can be fixed with our committed oblivious transfer protocol. Furthermore, it is more general than all previous protocols, and, therefore, it is of independent interest. We also deal with fairness in this thesis. For protocols based on garbled circuit, so far only Benny Pinkas has presented a protocol in the literature for achieving fairness. We show a subtle problem with this protocol where the privacy of the inputs of one party can be compromised. We also describe this problem in detail which is in fact related to the fairness, and finally propose a more efficient scheme that does achieve fairness.