Abstract. We consider the round complexity of multi-party computation in the presence of a static adversary who controls a majority of the parties. Here, n players wish to securely compute some functionality and up to n − 1 of these players may be arbitrarily malicious. Previous protocols for this setting (when a broadcast channel is available) require O(n) rounds. We present two protocols with improved round complexity: The first assumes only the existence of trapdoor permutations and dense cryptosystems, and achieves round complexity O(log n) based on a proof scheduling technique of Chor and Rabin [13]; the second requires a stronger hardness assumption (along with the non-black-box techniques of Barak [2]) and achieves O(1) round complexity. 1
Abstract. We consider the round complexity of multi-party computation in the presence of a static adversary who controls a majority of the parties. Here, n players wish to securely compute some functionality and up to n − 1 of these players may be arbitrarily malicious. Previous protocols for this setting (when a broadcast channel is available) require O(n) rounds. We present two protocols with improved round complexity: The first assumes only the existence of trapdoor permutations and dense cryptosystems, and achieves round complexity O(log n) based on a proof scheduling technique of Chor and Rabin [13]; the second requires a stronger hardness assumption (along with the non-black-box techniques of Barak [2]) and achieves O(1) round complexity. 1
We present round-efficient protocols for secure multi-party computation with a dishonest majority that rely on black-box access to the underlying primitives. Our main contributions are as follows: · a O(log* n)-round protocol that relies on black-box access to dense cryptosystems, homomorphic encryption schemes, or lossy encryption schemes. This improves upon the recent O(1)log* n-round protocol of Lin, Pass and Venkitasubramaniam (STOC 2009) that relies on non-black-box access to a smaller class of primitives. · a O(1)-round protocol requiring in addition, black-box access to a one-way function with sub-exponential hardness, improving upon the recent work of Pass and Wee (Eurocrypt 2010). These are the first black-box constructions for secure computation with sublinear round complexity. Our constructions build on and improve upon the work of Lin and Pass (STOC 2009) on nonmalleability amplification, as well as that of Ishai et al. (STOC 2006) on black-box secure computation. In addition to the results on secure computation, we also obtain a simple construction of a 0(log* n)-round non-malleable commitment scheme based on one-way functions, improving upon the recent O(1)log* n-round protocol of Lin and Pass (STOC 2009). Our construction uses a novel transformation for handling arbitrary man-in-the-middle scheduling strategies which improves upon a previous construction of Barak (FOCS 2002).
We show how to securely realize any multi-party functionality in a way that preserves security under an a-priori bounded number of concurrent executions, regardless of the number of corrupted parties. Previous protocols for the above task either rely on set-up assumptions such as a Common Reference String, or require an honest majority. Our constructions are in the plain model and rely on standard intractability assumptions (enhanced trapdoor permutations and collision resistant hash functions). Even though our main focus is on feasibility of concurrent multi-party computation we actually obtain a protocol using only a constant number of communication rounds. As a consequence our protocol yields the first construction of constant-round phstand-alone secure multi-party computation with a dishonest majority, proven secure under standard (polynomial-time) hardness assumptions; previous solutions to this task either require logarithmic round-complexity, or subexponential hardness assumptions. The core of our protocol is a novel construction of (concurrently) simulation-sound zero-knowledge protocols, which might be of independent interest. Finally, we extend the framework constructed to give a protocol for secure multi-party (and thus two-party) computation for any number of corrupted parties, which remains secure even when arbitrary subsets of parties concurrently execute the protocol, possibly with interchangeable roles. As far as we know, for the case of two-party or multi-party protocols with a dishonest majority, this is the first positive result for any non-trivial functionality which achieves this property in the plain model.
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.
In STOC’05, von Ahn, Hopper and Langford introduced the notion of covert computation. In covert computation, a party runs a secure computation protocol over a covert (or steganographic) channel without knowing if the other parties are participating as well or not. At the end of the protocol, if all parties participated in the protocol and if the function output is “favorable ” to all parties, then the output is revealed (along with the fact that everyone participated). All covert computation protocols known so far require a large polynomial number of rounds. In this work, we first study the question of the round complexity of covert computation and obtain the following results: • There does not exist a constant round covert computation protocol with respect to black box simulation even for the case of two parties. (In comparison, such protocols are known even for the multi-party case if there is no covertness requirement.) • By relying on the two slot non-black-box simulation technique of Pass (STOC’04) and techniques from cryptography in NC 0 (Applebaum et al, FOCS’04), we obtain a construction of a constant round covert multi-party computation protocol. Put together, the above adds one more example to the growing list of tasks for which non-black-box simulation techniques (introduced in the work of Barak in FOCS’01) are necessary. Finally, we study the problem of covert multi-party computation in the setting where the parties only have point to point (covert) communication channels. We observe that our covert computation protocol for the broadcast channel inherits, from the protocol of Pass, the property of secure composition in the bounded concurrent setting. Then, as an application of this protocol, somewhat surprisingly we show the existence of covert multi-party computation with point to point channels (assuming that the number of parties is a constant). 0 1
We present a round-efficient black-box construction of a general multi-party computation (MPC) protocol that satisfies composability in the plain model. The security of our protocol is proven in the angel-based UC framework [Prabhakaran and Sahai, STOC’04] under the minimal assumption of the existence of semi-honest oblivious transfer protocols. The round complexity of our protocol is max(O(log2n),O(ROT))
when the round complexity of the underlying oblivious transfer protocol is ROT
. Since constant-round semi-honest oblivious transfer protocols can be constructed under standard assumptions (such as the existence of enhanced trapdoor permutations), our result gives a O(log2n)
-round protocol under these assumptions. Previously, only an O(max(nϵ,ROT))
-round protocol was shown, where ϵ>0
is an arbitrary constant. We obtain our MPC protocol by constructing a O(log2n)
-round CCA-secure commitment scheme in a black-box way under the assumption of the existence of one-way functions.
In this work, we consider the problem of secure multi-party computation (MPC) with n parties where at most t are under the control of a computationally bounded adversary given the constraint t < n/2. We aim to design a round efficient protocol by minimizing the number of rounds in which the broadcast primitive is involved. In this setting, the previous best protocol can be attributed to Katz-Koo (EUROCRYPT 2007) which is set in the offline-online paradigm (where the parties generate preprocessing data during the offline phase to lighten the computation in the online phase). Their online phase is a constant round protocol with no invocations of broadcast, while the offline phase protocol needs total 29 rounds with a broadcast invocation in one round. Our work improves the round complexity of their offline phase protocol, by running in 4 rounds, with only a single broadcast round. Additionally, we also improve the communication complexity of the offline phase protocol by a factor of Ω(n3). As a technical contribution, we present the first two round computationally-secure verifiable secret-sharing (VSS) scheme that invokes broadcast in only one round.