Committed MPC

Frederiksen, Tore Kasper; Pinkas, Benny; Yanai, Avishay

doi:10.1007/978-3-319-76578-5_20

Cited by 15 publications

(40 citation statements)

References 38 publications

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“…On the other hand, a large relative dimension, or rate, of C will reduce the communication cost, so it is desirable to optimize both parameters. A very similar phenomenon occurs in recent work about commitment schemes, which are a building block of many multiparty computation protocols; in fact, when these schemes have a number of additional homomorphic properties and in addition can be composed securely, we can base the entire secure computation protocol on them [14]. Efficient commitment schemes with such properties were constructed in [5] based on binary linear codes, where multiplicative homomorphic properties require again to have a relatively large d(C * 2 ) (see [5, section 4]) and the rate of the code is also desired to be large to reduce the communication overhead.…”

Section: Introductionsupporting

confidence: 53%

Squares of matrix-product codes

Cascudo

Gundersen²,

Ruano

2020

Finite Fields and Their Applications

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The component-wise or Schur product C * C ′ of two linear error-correcting codes C and C ′ over certain finite field is the linear code spanned by all component-wise products of a codeword in C with a codeword in C ′ . When C = C ′ , we call the product the square of C and denote it C * 2 . Motivated by several applications of squares of linear codes in the area of cryptography, in this paper we study squares of so-called matrixproduct codes, a general construction that allows to obtain new longer codes from several "constituent" codes. We show that in many cases we can relate the square of a matrix-product code to the squares and products of their constituent codes, which allow us to give bounds or even determine its minimum distance. We consider the well-known (u, u+v)-construction, or Plotkin sum (which is a special case of a matrix-product code) and determine which parameters we can obtain when the constituent codes are certain cyclic codes. In addition, we use the same techniques to study the squares of other matrix-product codes, for example when the defining matrix is Vandermonde (where the minimum distance is in a certain sense maximal with respect to matrix-product codes).

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Section: Introductionsupporting

confidence: 53%

Squares of matrix-product codes

Cascudo

Gundersen²,

Ruano

2020

Finite Fields and Their Applications

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“…No. of bits Ours (MB) SHA3-256 (MB) Improvement 2 14 2.51 19.93 8× 2 18 10.90 300.34 28× 2 22 141.25 4805.39 34× 2 26 2169.02 76900* 35× 2 30 34022.77 1230200* 36× A PROOFS FROM SECTION 4…”

Section: Discussionmentioning

confidence: 99%

“…In Table 5, we show the number of indices |I| for the commitment that needs to be computed alongside the size of the entire commitment that a committer needs to prepare in order to commit its input. In these experiments 𝑝 = 3/8 Improvement over LowMCHash-256 2 14 6.14 × 10 5 2.32 × 10 5 5.17 × 10 4 12× 4× 2 18 9.29 × 10 6 3.65 × 10 6 1.90 × 10 5 49× 19× 2 22 1.48 × 10 8 5.84 × 10 7 2.29 × 10 6 65× 25× 2 26 2.37 × 10 9 9.34 × 10 8 3.42 × 10 7 69× 27× 2 30 3.79 × 10 10 1.49 × 10 10 5.39 × 10 8 70× 28× No. of bits Ours (s) SHA3-256 (s) Improvement 2 14 0.07 0.57 8× 2 18 0.22 8.16 36× 2 22 2.67 133.23 50× 2 26 39.14 2200* 56× 2 30 590.70 35500* 60× ).…”

Section: Experimental Performancementioning

confidence: 99%

“…In these experiments 𝑝 = 3/8 Improvement over LowMCHash-256 2 14 6.14 × 10 5 2.32 × 10 5 5.17 × 10 4 12× 4× 2 18 9.29 × 10 6 3.65 × 10 6 1.90 × 10 5 49× 19× 2 22 1.48 × 10 8 5.84 × 10 7 2.29 × 10 6 65× 25× 2 26 2.37 × 10 9 9.34 × 10 8 3.42 × 10 7 69× 27× 2 30 3.79 × 10 10 1.49 × 10 10 5.39 × 10 8 70× 28× No. of bits Ours (s) SHA3-256 (s) Improvement 2 14 0.07 0.57 8× 2 18 0.22 8.16 36× 2 22 2.67 133.23 50× 2 26 39.14 2200* 56× 2 30 590.70 35500* 60× ). The size of the commitment results in a very limited communication and space requirement.…”

Section: Experimental Performancementioning

confidence: 99%

“…Secure multi-party computation (MPC) methods have undergone impressive improvements in the last decade. Advances in the scalability of garbled circuit protocols [10,47,48], commitment schemes [18], and oblivious transfer [6,36] have transformed the range of applications for MPC [30]. In particular, a significant amount of research efforts have been recently devoted to finding efficient MPC protocols for training and evaluation of widely-deployed machine learning (ML) models [1,19,21,33,34,37,43,45].…”

Section: Introductionmentioning

confidence: 99%

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MPC-Friendly Commitments for Publicly Verifiable Covert Security

Agrawal¹,

Bell²,

Gascón³

et al. 2021

Preprint

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We address the problem of efficiently verifying a commitment in a two-party computation. This addresses the scenario where a party P1 commits to a value 𝑥 to be used in a subsequent secure computation with another party P2 that wants to receive assurance that P1 did not cheat, i.e. that 𝑥 was indeed the value inputted into the secure computation. Our constructions operate in the publicly verifiable covert (PVC) security model, which is a relaxation of the malicious model of MPC appropriate in settings where P1 faces a reputational harm if caught cheating.We introduce the notion of PVC commitment scheme and indexed hash functions to build commitments schemes tailored to the PVC framework, and propose constructions for both arithmetic and Boolean circuits that result in very efficient circuits. From a practical standpoint, our constructions for Boolean circuits are 60× faster to evaluate securely, and use 36× less communication than baseline methods based on hashing. Moreover, we show that our constructions are tight in terms of required non-linear operations, by proving lower bounds on the nonlinear gate count of commitment verification circuits. Finally, we present a technique to amplify the security properties our constructions that allows to efficiently recover malicious guarantees with statistical security.

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Efficient UC Commitment Extension with Homomorphism for Free (and Applications)

Cascudo

Damgård

David

et al. 2019

Lecture Notes in Computer Science

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Homomorphic universally composable (UC) commitments allow for the sender to reveal the result of additions and multiplications of values contained in commitments without revealing the values themselves while assuring the receiver of the correctness of such computation on committed values. In this work, we construct essentially optimal additively homomorphic UC commitments from any (not necessarily UC or homomorphic) extractable commitment. We obtain amortized linear computational complexity in the length of the input messages and rate 1. Next, we show how to extend our scheme to also obtain multiplicative homomorphism at the cost of asymptotic optimality but retaining low concrete complexity for practical parameters. While the previously best constructions use UC oblivious transfer as the main building block, our constructions only require extractable commitments and PRGs, achieving better concrete efficiency and offering new insights into the sufficient conditions for obtaining homomorphic UC commitments. Moreover, our techniques yield public coin protocols, which are compatible with the Fiat-Shamir heuristic. These results come at the cost of realizing a restricted version of the homomorphic commitment functionality where the sender is allowed to perform any number of commitments and operations on committed messages but is only allowed to perform a single batch opening of a number of commitments. Although this functionality seems restrictive, we show that it can be used as a building block for more efficient instantiations of recent protocols for secure multiparty computation and zero knowledge non-interactive arguments of knowledge.

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Committed MPC

Cited by 15 publications

References 38 publications

Squares of matrix-product codes

Squares of matrix-product codes

MPC-Friendly Commitments for Publicly Verifiable Covert Security

Efficient UC Commitment Extension with Homomorphism for Free (and Applications)

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