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 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 propose the first black-box construction of non-malleable commitments according to the standard notion of non-malleability with respect to commitment. Our construction additionally only requires a constant number of rounds and is based only on (black-box use of) one-way functions. Prior to our work, no black-box construction of non-malleable commitments was known (except for relaxed notions of security) in any (polynomial) number of rounds based on any cryptographic assumption. This closes the wide gap existent between black-box and non-black-box constructions for the problem of non-malleable commitments. Our construction relies on (and can be seen as a generalization of) the recent non-malleable commitment scheme of Goyal (STOC 2011). We also show how to get black-box constructions for a host of other cryptographic primitives. We extend our construction to get constant-round concurrent non-malleable commitments, constant-round multi-party coin tossing, and non-malleable statistically hiding commitments (satisfying the notion of non-malleability with respect to opening). All of the mentioned results make only a black-box use of one-way functions. Our primary technical contribution is a novel way of implementing the proof of consistency typically required in the constructions of non-malleable commitments (and other related primitives). We do this by relying on ideas from the ``zero-knowledge from secure multi-party computation" paradigm of Ishai, Kushilevitz, Ostrovsky, and Sahai (STOC 2007). We extend in a novel way this ``computation in the head" paradigm (which can be though of as bringing powerful error-correcting codes into purely computational setting). To construct a non-malleable commitment scheme, we apply our computation in the head techniques to the recent (constant-round) construction of Goyal. Along the way, we also present a simplification of the construction of Goyal where a part of the protocol is implemented in an information theoretic manner. Such a simplification is crucial for getting a black-box construction. This is done by making use of pair wise-independent hash functions and strong randomness extractors. We show that our techniques have multiple applications, as elaborated in the paper. Hence, we believe our techniques might be useful in other settings in future.
We provide the first constant round constructions of non-malleable commitment and zero-knowledge protocols based only on one-way functions. This improves upon several previous (incomparable) works which required either: (a) super-constant number of rounds, or, (b) non-standard or sub-exponential hardness assumptions, or, (c) non-black-box simulation and collision resistant hash functions. These constructions also allow us to obtain the first constant round multi-party computation protocol relying only on the existence of constant round oblivious transfer protocols. Our primary technique can be seen as a means of implementing the previous “two-slot simulation ” idea in the area of non-malleability with only black-box simulation. A simple modification of our commitment scheme gives a construction which makes use of the underlying one-way function in a black-box way. The modified construction satisfies the notion of what we call nonmalleability w.r.t. replacement. Non-malleability w.r.t. replacement is a slightly weaker yet natural notion of non-malleability which we believe suffices for many application of non-malleable commitments. We show that a commitment scheme which is non-malleable only w.r.t. replacement is sufficient to obtain a (fully) black-box multi-party computation protocol. This allows us to obtain a constant round multi-party computation protocol making only a black-box use of the standard cryptographic primitives with polynomial-time hardness thus directly improving upon the recent work of Wee (FOCS’10). 0 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 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.
Non-malleable commitment is one of the most fundamental cryptographic primitives in that it is often used as a basic building block in modern cryptography. Briefly, a commitment scheme allows a sender to commit to a value while keeping the value secret from the receiver. In addition, when the commitment is opened in a later stage, the scheme guarantees that the sender can reveal only the unique value being committed to in the previous stage. A commitment scheme is said to be non-malleable if no adversary can succeed in committing to a related massage m', after seeing a commitment of a message m. In this dissertation, we study the construction of non-malleable commitments and some of their applications.A black-box construction of non-malleable commitment is presented in the first part of this dissertation. Our protocol requires only a constant number of rounds and satisfies the standard notion of non-malleability w.r.t. commitment. Our technique is based on ideas from the ``zero-knowledge from secure multi-party computation'' paradigm by Ishai, Kushilevitz, Ostrovsky, and Sahai (STOC 2007). Furthermore, our construction only uses one-way functions as a black-box and thus does not depend on the actual implementation details of the functions. Prior to our result, under the standard notion of security, no black-box construction of constant-round non-malleable commitment was known. Hence, our main result closes the gap between black-box and non-black-box constructions for the problem of non-malleable commitment.In the second part of this dissertation, we show that our technique can be applied to multiple applications. Specifically, we extend our work to obtain a constant-round concurrent non-malleable commitment, a constant-round multi-party parallel coin tossing, and a non-malleable statistically hiding commitment (according to the notion of non-malleability w.r.t. opening.) Additionally, all results mentioned above are based only on a black-box use of one-way functions.
It is well known that the secure computation of non-trivial functionalities in the setting of no honest majority requires computational assumptions. We study the way such computational assumptions are used. Specifically, we ask whether the secure protocol can use the underlying primitive (e.g., one-way trapdoor permutation) in a black-box way, or must it be nonblack-box (by referring to the code that computes this primitive)? Despite the fact that many general constructions of cryptographic schemes (e.g., CPA-secure encryption) refer to the underlying primitive in a black-box way only, there are some constructions that are inherently nonblack-box. Indeed, all known constructions of protocols for general secure computation that are secure in the presence of a malicious adversary and without an honest majority use the underlying primitive in a nonblack-box way (requiring to prove in zero-knowledge statements that relate to the primitive).In this paper, we study whether such nonblack-box use is essential. We present protocols that use only black-box access to a family of (enhanced) trapdoor permutations or to a homomorphic public-key encryption scheme. The result is a protocol whose communication complexity is independent of the computational complexity of the underlying primitive (e.g., a trapdoor permutation) and whose computational complexity grows only linearly with that of the underlying primitive. This is the first protocol to exhibit these properties.