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SIAM Journal on Computing

Equivocating Yao: Constant-Round Adaptively Secure Multiparty Computation in the Plain Model

Ran Canetti, Oxana Poburinnaya, Muthuramakrishnan Venkitasubramaniam

Published Jan 13, 2022• 2 citations
Publisher

Abstract

Yao's circuit garbling scheme is one of the basic building blocks of cryptographic protocol design. Originally designed to enable two-message, two-party secure computation, the scheme has been extended in many ways and has innumerable applications. Still, a basic question has remained open throughout the years: Can the scheme be extended to guarantee security in the face of an adversary that corrupts both parties, adaptively, as the computation proceeds? We answer this question in the affirmative. We define a new type of symmetric encryption, called functionally equivocal encryption (FEE), and show that when Yao's scheme is implemented with FEE as the underlying encryption mechanism, it becomes secure against such adaptive adversaries. We then show how to implement FEE from any one-way function. Combining our scheme with noncommitting encryption, we obtain the first two-message, two-party computation protocol, and the first constant-round multiparty computation protocol, in the plain model, that are secure against semihonest adversaries who can adaptively corrupt all parties. Using standard techniques, this protocol can be made standalone secure against malicious corruptions in the plain model and universal composability secure in the common random string model. Additional applications include the first fully leakage-tolerant general multiparty computation protocol (with preprocessing), as well as a public-key version of FEE which can serve as a replacement for noncommitting encryption with better efficiency than what is possible for the latter.

DOI
10.1137/17m1151602

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Yao's circuit garbling scheme is one of the basic building blocks of cryptographic protocol design. Originally designed to enable two-message, two-party secure computation, the scheme has been extended in many ways and has innumerable applications. Still, a basic question has remained open throughout the years: Can the scheme be extended to guarantee security in the face of an adversary that corrupts both parties, adaptively, as the computation proceeds?

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IEEE Asia-Pacific Services Computing Conference (APSCC)•Dec 1, 2012•5 citations
Yao's circuit garbling scheme is one of the basic building blocks of cryptographic protocol design. Originally designed to enable two-message, two-party secure computation, the scheme has been extended in many ways and has innumerable applications. Still, a basic question has remained open throughout the years: Can the scheme be extended to guarantee security in the face of an adversary that corrupts both parties, adaptively, as the computation proceeds? We answer this question in the affirmative. We define a new type of symmetric encryption, called functionally equivocal encryption (FEE), and show that when Yao's scheme is implemented with FEE as the underlying encryption mechanism, it becomes secure against such adaptive adversaries. We then show how to implement FEE from any one-way function. Combining our scheme with noncommitting encryption, we obtain the first two-message, two-party computation protocol, and the first constant-round multiparty computation protocol, in the plain model, that are secure against semihonest adversaries who can adaptively corrupt all parties. Using standard techniques, this protocol can be made standalone secure against malicious corruptions in the plain model and universal composability secure in the common random string model. Additional applications include the first fully leakage-tolerant general multiparty computation protocol (with preprocessing), as well as a public-key version of FEE which can serve as a replacement for noncommitting encryption with better efficiency than what is possible for the latter.
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.
Cryptographic protocols with adaptive security ensure that security holds against an adver-sary who can dynamically determine which parties to corrupt as the protocol progresses—or even after the protocol is finished. In the setting where all parties may potentially be corrupted, and secure erasure is not assumed, it has been a long-standing open question to design secure-computation protocols with adaptive security running in constant rounds. Here, we show a constant-round, universally composable protocol for computing any functionality, tolerating a malicious, adaptive adversary corrupting any number of parties. Interest-ingly, our protocol can compute all functionalities, not just adaptively well-formed ones.
Adaptive security is a strong security notion that captures additional security threats that are not addressed by static corruptions. For instance, it captures real-world scenarios where “hackers ” actively break into computers, possibly while they are executing secure protocols. Studying this setting is interesting from both theoretical and practical points of view. A primary building block in designing adaptively secure protocols is a non-committing encryption (NCE) that implements secure communication channels in the presence of adaptive corruptions. Current constructions require a number of public key operations that grows linearly with the length of the message. Furthermore, general two-party protocols require a number of NCE calls that is dependent both on the circuit size and the security parameter. In this paper we study the two-party setting in which at most one of the parties is adaptively corrupted, which we believe is the right security notion in the two-party setting. We study the feasibility of (1) NCE with constant number of public key operations for large message spaces. (2) Oblivious transfer with constant number of public key operations for large sender’s input spaces, and (3) constant round secure computation protocols with an overall number of public key operations that is linear in the circuit size. Our study demonstrates that such primitives indeed exist in the presence of single corruptions, while this is not known for fully adaptive security (where both parties may get corrupted).
In the setting of multiparty computation a set of parties with private inputs wish to compute some joint function of their inputs, whilst preserving certain security properties (like privacy and correctness). An adaptively secure protocol is one in which the security properties are preserved even if an adversary can adaptively and dynamically corrupt parties during a computation. This provides a high level of security, that is arguably necessary in today’s world of active computer break-ins. Until now, the work on adaptively secure multiparty computation has focused almost exclusively on the setting of an honest majority, and very few works have considered the honest minority and two-party cases. In addition, significant computational and communication costs are incurred by most protocols that achieve adaptive security. In this work, we consider the two-party setting and assume that honest parties may erase data. We show that in this model it is possible to securely compute any two-party functionality in the presence of adaptive semi-honest adversaries. Furthermore, our protocol remains secure under concurrent general composition (meaning that it remains secure irrespective of the other protocols running together with it). Our protocol is based on Yao’s garbled-circuit construction and, importantly, is as efficient as the analogous protocol for static corruptions. We argue that the model of adaptive corruptions with erasures has been unjustifiably neglected and that it deserves much more attention. 1
Yao first introduced a constant-round protocol for secure two-party computation (2PC) withstanding semi-honest adversaries by using a tool called "garbled circuit". Later, many protocols based on garbled circuit approach have been presented, most of which discussed malicious adversaries and efficiency about 2PC. However, there only have a few protocols dealing with the fundamental property of fairness for Yao's garbled circuit approach, in which one involved a trusted third party and the others are very expensive. In the paper, we propose' an efficient Yao's garbled circuit protocol for fair secure 2PC based on ElGamal encryption, Pedersen commitment, Cachin et al.'s verifiable oblivious transfer and Ou-Ruan et al.'s gradual release homomorphic timed commitment. The protocol achieves two advantages: it doesn't need the third party and it is more efficient than other fair secure Yao's protocols.