We present the first two-round, two-party general function evaluation protocol that is secure against honest-but-curious adaptive corruption of both parties. In addition, the protocol is incoercible for one of the parties, and fully leakage tolerant. It requires a global (non-programmable) reference string and is based on one way functions and general-purpose indistinguishability obfuscation with sub-exponential security, as well as augmented non-committing encryption. A Byzantine version of the protocol, obtained by applying the Canetti et al. [STOC 02] compiler, achieves UC security with comparable efficiency parameters, but is no longer incoercible.
We present the first two-round, two-party general function evaluation protocol that is secure against honest-but-curious adaptive corruption of both parties. In addition, the protocol is incoercible for one of the parties, and fully leakage tolerant. It requires a global (non-programmable) reference string and is based on one way functions and general-purpose indistinguishability obfuscation with sub-exponential security, as well as augmented non-committing encryption. A Byzantine version of the protocol, obtained by applying the Canetti et al. [STOC 02] compiler, achieves UC security with comparable efficiency parameters, but is no longer incoercible.
Secure multi-party computation (MPC) enables distrustful parties to jointly perform computations while guaranteeing both the privacy of their inputs and the correctness of the computation.
This thesis explores two aspects of secure multi-party computation: adaptive security and round efficiency. Adaptive security is concerned with an adversary that adaptively determines who and when to corrupt during the course of the computation. Even though this is a very natural and realistic assumption about the adversary, most of the MPC literature addresses security only against a static adversary — an adversary that chooses (and fixes) which parties to corrupt before the protocol starts executing. A protocol is called round-efficient if it runs in a small number of rounds. Constructing such protocols is important since efficiency of a protocol is greatly influenced by its round complexity.
The security in this thesis is formulated in the universal composability (UC) framework introduced by Canetti [Can01]. Protocols secure in the UC framework remain secure even when executed concurrently with other arbitrary protocols running in some larger network, and can be used as subroutines of larger protocols in a modular fashion. This property is important considering that nowadays many protocols are executed concurrently with others in the Internet.
With the focus on adaptive security and round efficiency, we obtain the following results:
(1) We show that with access to an ideal commitment functionality, there exists a protocol that UC realizes any well-formed multi-party functionality against a malicious, adaptive adversary that may corrupt any number of parties, with black-box access to any protocol that UC realizes oblivious transfer against a semi-honest, adaptive adversary.
(2) We show that there exists a protocol that UC realizes oblivious transfer against a semi-honest, adaptive adversary, with black-box access to a cryptographic primitive called a trapdoor simulatable cryptosystem, which is a natural relaxation of a simulatable cryptosystem introduced by Damgard and Nielsen [3N00].
We also show that the primitive can be constructed based on hardness of factoring.
(3) We present a single-message protocol that UC realizes two-party computing with encrypted data (a variant of secure two-party computation), based on the DDH assumption and non- interactive zero-knowledge arguments. The protocol achieves security against a malicious, static adversary.
(4) We present two round-efficient protocols that UC realize multi-party computing with encrypted data (a variant of secure multi-party computation), based on the DDH assumption and non-interactive zero-knowledge arguments. The first (resp. second) protocol requires one round (resp. two rounds) with appropriate preprocessing, which is independent of the exact circuit and actual inputs of the specific instance problem to solve — only the bound on the circuit size is known. Although the first protocol is more round-efficient, the preprocessing of the second is sometimes better under some efficiency considerations. Both protocols achieve security against a malicious, static adversary that may corrupt up to all but one parties.
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).
Current secure multiparty protocols have the following deficiency. The public transcript of the communication can be used as an involuntary commitment of the parties to their inputs and outputs. Thus parties can be later coerced by some authority to reveal their private data. Previous work that has pointed this interesting problem out contained only partial treatment. In this work we present the first general treatment of the coercion problem in secure computation. First we present a general definition of protocols that provide resilience to coercion. Our definition constitutes a natural extension of the general paradigm used for defining secure multiparty protocols. Next we show that if trapdoor permutations exist then any function can be incoercibly computed (i.e., computed by a protocol that provides resilience to coercion) in the presence of computationally bounded adversaries and only public communication channels. This holds as long as less than half the parties are coerced (or corrupted). In particular, ours are the first incoercible protocols without physical security assumptions. Also, our protocols constitute an alternative solution to the recently solved adaptive security problem. Our techniques are quite surprising and include non-standard use of deniable encryptions.
Abstract. The recently proposed universally composable (UC) security framework, for analyzing security of cryptographic protocols, provides very strong security guarantees. In particular, a protocol proven secure in this framework is guaranteed to maintain its security even when deployed in arbitrary multi-party, multi-protocol, multi-execution environments. Protocols for securely carrying out essentially any cryptographic task in a universally composable way exist, both in the case of an honest majority (in the plain model, i.e., without set-up assumptions) and in the case of no honest majority (in the common reference string model). However, in the plain model, little was known for the case of no honest majority and, in particular, for the important special case of two-party protocols. We study the feasibility of universally composable two-party function evaluation in the plain model. Our results show that very few functions can be computed in this model so as to provide the UC security guarantees. Specifically, for the case of deterministic functions, we provide a full characterization of the functions computable in this model. (Essentially, these are the functions that depend on at most one of the parties’ inputs, and furthermore are “efficiently invertible ” in a sense defined within.) For the case of probabilistic functions, we show that the only functions computable in this model are those where one of the parties can essentially uniquely determine the joint output. 1
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.
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