International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Muthuramakrishnan Venkitasubramaniam

Affiliation: University of Rochester, USA

Publications

Year
Venue
Title
2020
JOFC
On the Power of Secure Two-Party Computation
Carmit Hazay Muthuramakrishnan Venkitasubramaniam
Ishai, Kushilevitz, Ostrovsky and Sahai (STOC 2007 ; SIAM J Comput 39(3):1121–1152, 2009 ) introduced the powerful “MPC-in-the-head” technique that provided a general transformation of information-theoretic MPC protocols secure against passive adversaries to a ZK proof in a “black-box” way. In this work, we extend this technique and provide a generic transformation of any semi-honest secure two-party computation (2PC) protocol (with mild adaptive security guarantees) in the so-called oblivious-transfer hybrid model to an adaptive ZK proof for any $$\textsf {NP}$$ NP language, in a “black-box” way assuming only one-way functions. Our basic construction based on Goldreich–Micali–Wigderson’s 2PC protocol yields an adaptive ZK proof with communication complexity proportional to quadratic in the size of the circuit implementing the $$\textsf {NP}$$ NP relation. Previously such proofs relied on an expensive Karp reduction of the $$\textsf {NP}$$ NP language to Graph Hamiltonicity [Lindell and Zarosim (TCC 2009 ; J Cryptol 24(4):761–799, 2011 )]. As an application of our techniques, we show how to obtain a ZK proof with an “input-delayed” property for any $$\textsf {NP}$$ NP language without relying on expensive Karp reductions that is black box in the underlying one-way function. Namely, the input-delayed property allows the honest prover’s algorithm to receive the actual statement to be proved only in the final round. We further generalize this to obtain a “commit-and-prove” protocol with the same property where the prover commits to a witness w in the second message and proves a statement x regarding the witness w in zero-knowledge where the statement is determined only in the last round. This improves a previous construction of Lapidot and Shamir (Crypto 1990 ) that was designed specifically for the Graph Hamiltonicity problem and relied on the underlying primitives in a non-black-box way. Additionally, we provide a general transformation to construct a randomized encoding of a function f from any 2PC protocol that securely computes a related functionality (in a black-box way) from one-way functions. We show that if the 2PC protocol has mild adaptive security guarantees (which are satisfied by both the Yao’s and GMW’s protocol), then the resulting randomized encoding can be decomposed to an offline/online encoding.
2020
EUROCRYPT
Which Languages Have 4-Round Fully Black-Box Zero-Knowledge Arguments from One-Way Functions? 📺
Carmit Hazay Rafael Pass Muthuramakrishnan Venkitasubramaniam
We prove that if a language $\cL$ has a 4-round fully black-box zero-knowledge argument with negligible soundness based on one-way functions, then $\overline{\cL} \in \MA$. Since $\coNP \subseteq \MA$ implies that the polynomial hierarchy collapses, our result implies that $\NP$-complete languages are unlikely to have 4-round fully black-box zero-knowledge arguments based on one-way functions. In TCC 2018, Hazay and Venkitasubramaniam, and Khurana, Ostrovsky, and Srinivasan demonstrated 4-round fully black-box zero-knowledge arguments for all languages in $\NP$ based on injective one-way functions. Their results also imply a 5-round protocol based on one-way functions. In essence, our result resolves the round complexity of fully black-box zero-knowledge arguments based on one-way functions.
2020
EUROCRYPT
The Price of Active Security in Cryptographic Protocols 📺
Carmit Hazay Muthuramakrishnan Venkitasubramaniam Mor Weiss
We construct the first actively-secure Multi-Party Computation (MPC) protocols with an \emph{arbitrary} number of parties in the dishonest majority setting, for an \emph{arbitrary} field $\FF$ with \emph{constant communication overhead} over the ``passive-GMW'' protocol (Goldreich, Micali and Wigderson, STOC `87). Our protocols rely on passive implementations of Oblivious Transfer (OT) in the boolean setting and Oblivious Linear function Evaluation (OLE) in the arithmetic setting. Previously, such protocols were only known over sufficiently large fields (Genkin et al. STOC `14) or a constant number of parties (Ishai et al. CRYPTO `08). Conceptually, our protocols are obtained via a new compiler from a passively-secure protocol for a distributed multiplication functionality $\cF_\mult$, to an actively-secure protocol for general functionalities. Roughly, $\cF_\mult$ is parameterized by a linear-secret sharing scheme $\cS$, where it takes $\cS$-shares of two secrets and returns $\cS$-shares of their product. We show that our compilation is concretely efficient for sufficiently large fields, resulting in an overhead of 2 when securely computing natural circuits. Our compiler has two additional benefits: (1) it can rely on \emph{any} passive implementation of $\cF_\mult$, which, besides the standard implementation based on OT (for boolean) and OLE (for arithmetic) allows us to rely on implementations based on threshold cryptosystems (Cramer et al. Eurocrypt `01); and (2) it can rely on weaker-than-passive (i.e., imperfect/leaky) implementations, which in some parameter regimes yield actively-secure protocols with overhead less than 2. Instantiating this compiler with an ``honest-majority'' implementations of $\cF_\mult$, we obtain the first honest-majority protocol with optimal corruption threshold for boolean circuits with constant communication overhead over the best passive protocol (Damg{\aa}rd and Nielsen, CRYPTO `07).
2020
PKC
Going Beyond Dual Execution: MPC for Functions with Efficient Verification 📺
Carmit Hazay Abhi Shelat Muthuramakrishnan Venkitasubramaniam
The dual execution paradigm of Mohassel and Franklin (PKC’06) and Huang, Katz and Evans (IEEE ’12) shows how to achieve the notion of 1-bit leakage security at roughly twice the cost of semi-honest security for the special case of two-party secure computation . To date, there are no multi-party computation (MPC) protocols that offer such a strong trade-off between security and semi-honest performance. Our main result is to address this shortcoming by designing 1-bit leakage protocols for the multi-party setting, albeit for a special class of functions. We say that function f ( x ,  y ) is efficiently verifiable by g if the running time of g is always smaller than f and $$g(x,y,z)=1$$ if and only if $$f(x,y)=z$$ . In the two-party setting, we first improve dual execution by observing that the “second execution” can be an evaluation of g instead of f , and that by definition, the evaluation of g is asymptotically more efficient. Our main MPC result is to construct a 1-bit leakage protocol for such functions from any passive protocol for f that is secure up to additive errors and any active protocol for g . An important result by Genkin et al. (STOC ’14) shows how the classic protocols by Goldreich et al. (STOC ’87) and Ben-Or et al. (STOC ’88) naturally support this property, which allows to instantiate our compiler with two-party and multi-party protocols. A key technical result we prove is that the passive protocol for distributed garbling due to Beaver et al. (STOC ’90) is in fact secure up to additive errors against malicious adversaries, thereby, yielding another powerful instantiation of our paradigm in the constant-round multi-party setting. As another concrete example of instantiating our approach, we present a novel protocol for computing perfect matching that is secure in the 1-bit leakage model and whose communication complexity is less than the honest-but-curious implementations of textbook algorithms for perfect matching.
2019
JOFC
On Black-Box Complexity of Universally Composable Security in the CRS Model
Carmit Hazay Muthuramakrishnan Venkitasubramaniam
In this work, we study the intrinsic complexity of black-box Universally Composable (UC) secure computation based on general assumptions. We present a thorough study in various corruption modelings while focusing on achieving security in the common reference string (CRS) model. Our results involve the following:Static UC secure computation. Designing the first static UC oblivious transfer protocol based on public-key encryption and stand-alone semi-honest oblivious transfer. As a corollary, we obtain the first black-box constructions of UC secure computation assuming only two-round semi-honest oblivious transfer.One-sided UC secure computation. Designing adaptive UC two-party computation with single corruptions assuming public-key encryption with oblivious ciphertext generation.Adaptive UC secure computation. Designing adaptively secure UC commitment scheme assuming only public-key encryption with oblivious ciphertext generation. As a corollary, we obtain the first black-box constructions of adaptive UC secure computation assuming only (trapdoor) simulatable public-key encryption (as well as a variety of concrete assumptions).We remark that such a result was not known even under non-black-box constructions.
2019
JOFC
What Security Can We Achieve Within 4 Rounds?
Carmit Hazay Muthuramakrishnan Venkitasubramaniam
Katz and Ostrovsky (Crypto 2004) proved that five rounds are necessary for stand-alone general black-box constructions of secure two-party protocols and at least four rounds are necessary if only one party needs to receive the output. Recently, Ostrovsky, Richelson and Scafuro (Crypto 2015) proved optimality of this result by showing how to realize stand-alone, secure two-party computation under general assumptions (with black-box proof of security) in four rounds where only one party receives the output, and an extension to five rounds where both parties receive the output. In this paper, we study the question of what security is achievable for stand-alone two-party protocols within four rounds and show the following results: 1. A 4-round two-party protocol for coin-tossing that achieves 1 /  p - security (i.e., simulation fails with probability at most $$1/p+{\mathsf {negl}}$$ 1 / p + negl ), in the presence of malicious corruptions. 2. A 4-round two-party protocol for general functionalities where both parties receive the output, that achieves 1 /  p -security and privacy in the presence of malicious adversaries corrupting one of the parties, and full security in the presence of non-aborting malicious adversaries corrupting the other party. 3. A 3-round oblivious-transfer protocol that achieves 1 /  p -security against arbitrary malicious senders, while simultaneously guaranteeing a meaningful notion of privacy against malicious corruptions of either party. 4. Finally, we show that the simulation-based security guarantees for our 3-round protocols are optimal by proving that 1 /  p -simulation security is impossible to achieve against both parties in three rounds or less when requiring some minimal guarantees on the privacy of their inputs.
2018
CRYPTO
Round-Optimal Secure Multi-Party Computation 📺
Shai Halevi Carmit Hazay Antigoni Polychroniadou Muthuramakrishnan Venkitasubramaniam
Secure multi-party computation (MPC) is a central cryptographic task that allows a set of mutually distrustful parties to jointly compute some function of their private inputs where security should hold in the presence of a malicious adversary that can corrupt any number of parties. Despite extensive research, the precise round complexity of this “standard-bearer” cryptographic primitive is unknown. Recently, Garg, Mukherjee, Pandey and Polychroniadou, in EUROCRYPT 2016 demonstrated that the round complexity of any MPC protocol relying on black-box proofs of security in the plain model must be at least four. Following this work, independently Ananth, Choudhuri and Jain, CRYPTO 2017 and Brakerski, Halevi, and Polychroniadou, TCC 2017 made progress towards solving this question and constructed four-round protocols based on non-polynomial time assumptions. More recently, Ciampi, Ostrovsky, Siniscalchi and Visconti in TCC 2017 closed the gap for two-party protocols by constructing a four-round protocol from polynomial-time assumptions. In another work, Ciampi, Ostrovsky, Siniscalchi and Visconti TCC 2017 showed how to design a four-round multi-party protocol for the specific case of multi-party coin-tossing.In this work, we resolve this question by designing a four-round actively secure multi-party (two or more parties) protocol for general functionalities under standard polynomial-time hardness assumptions with a black-box proof of security.
2018
TCC
Round-Optimal Fully Black-Box Zero-Knowledge Arguments from One-Way Permutations
Carmit Hazay Muthuramakrishnan Venkitasubramaniam
In this paper, we revisit the round complexity of designing zero-knowledge (ZK) arguments via a black-box construction from minimal assumptions. Our main result implements a 4-round ZK argument for any language in $$\textsf {NP}$$ NP, based on injective one-way functions, that makes black-box use of the underlying function. As a corollary, we also obtain the first 4-round perfect zero-knowledge argument for $$\textsf {NP}$$ NP based on claw-free permutations via a black-box construction and 4-round input-delayed commit-and-prove zero-knowledge argument based on injective one-way functions.
2018
TCC
Two-Round Adaptively Secure Multiparty Computation from Standard Assumptions
Fabrice Benhamouda Huijia Lin Antigoni Polychroniadou Muthuramakrishnan Venkitasubramaniam
We present the first two-round multiparty computation (MPC) protocols secure against malicious adaptive corruption in the common reference string (CRS) model, based on DDH, LWE, or QR. Prior two-round adaptively secure protocols were known only in the two-party setting against semi-honest adversaries, or in the general multiparty setting assuming the existence of indistinguishability obfuscation (iO).Our protocols are constructed in two steps. First, we construct two-round oblivious transfer (OT) protocols secure against malicious adaptive corruption in the CRS model based on DDH, LWE, or QR. We achieve this by generically transforming any two-round OT that is only secure against static corruption but has certain oblivious sampleability properties, into a two-round adaptively secure OT. Prior constructions were only secure against semi-honest adversaries or based on iO.Second, building upon recent constructions of two-round MPC from two-round OT in the weaker static corruption setting [Garg and Srinivasan, Benhamouda and Lin, Eurocrypt’18] and using equivocal garbled circuits from [Canetti, Poburinnaya and Venkitasubramaniam, STOC’17], we show how to construct two-round adaptively secure MPC from two-round adaptively secure OT and constant-round adaptively secure MPC, with respect to both malicious and semi-honest adversaries. As a corollary, we also obtain the first 2-round MPC secure against semi-honest adaptive corruption in the plain model based on augmented non-committing encryption (NCE), which can be based on a variety of assumptions, CDH, RSA, DDH, LWE, or factoring Blum integers. Finally, we mention that our OT and MPC protocols in the CRS model are, in fact, adaptively secure in the Universal Composability framework.
2017
PKC
2017
PKC
2017
PKC
Scalable Multi-party Private Set-Intersection
Carmit Hazay Muthuramakrishnan Venkitasubramaniam
2017
TCC
2017
TCC
2016
CRYPTO
On the Power of Secure Two-Party Computation 📺
Carmit Hazay Muthuramakrishnan Venkitasubramaniam
2016
TCC
2016
TCC
2015
EPRINT
2015
EPRINT
What Security can we Achieve in 4-Rounds?
Carmit Hazay Muthuramakrishnan Venkitasubramaniam
2015
EPRINT
2015
TCC
2015
ASIACRYPT
2015
ASIACRYPT
Secure Computation from Millionaire
Abhi Shelat Muthuramakrishnan Venkitasubramaniam
2014
TCC
2014
EPRINT
2014
JOFC
2013
ASIACRYPT
2012
ASIACRYPT
2012
ASIACRYPT
A Unified Framework for UC from Only OT
Rafael Pass Huijia Lin Muthuramakrishnan Venkitasubramaniam
2011
TCC
2010
TCC
2010
TCC
2010
CRYPTO
2008
TCC
2008
TCC
On Constant-Round Concurrent Zero-Knowledge
Rafael Pass Muthuramakrishnan Venkitasubramaniam
2008
EUROCRYPT
2007
EPRINT
Precise Concurrent Zero Knowledge
Omkant Pandey Rafael Pass Amit Sahai Wei-Lung Dustin Tseng Muthuramakrishnan Venkitasubramaniam
\emph{Precise zero knowledge} introduced by Micali and Pass (STOC'06) guarantees that the view of any verifier $V$ can be simulated in time closely related to the \emph{actual} (as opposed to worst-case) time spent by $V$ in the generated view. We provide the first constructions of precise concurrent zero-knowledge protocols. Our constructions have essentially optimal precision; consequently this improves also upon the previously tightest non-precise concurrent zero-knowledge protocols by Kilian and Petrank (STOC'01) and Prabhakaran, Rosen and Sahai (FOCS'02) whose simulators have a quadratic worst-case overhead. Additionally, we achieve a statistically-precise concurrent zero-knowledge property---which requires simulation of unbounded verifiers participating in an unbounded number of concurrent executions; as such we obtain the first (even non-precise) concurrent zero-knowledge protocols which handle verifiers participating in a super-polynomial number of concurrent executions.

Program Committees

Eurocrypt 2020
TCC 2019
Eurocrypt 2018
Crypto 2014
PKC 2011