Secure Computation Based on Leaky Correlations: High Resilience Setting

Block, Alexander R.; Maji, Hemanta K.; Nguyen, Huy Hung

doi:10.1007/978-3-319-63715-0_1

Cited by 11 publications

(4 citation statements)

References 62 publications

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“…The former work is in the context of information-theoretically secure protocols, while the latter studied 2-party protocols over small fields where the assumed resource is OLE over an extension field. This is partially based on a previous work also by Block et al,[4] where (asymptotically less efficient) constructions of RMFEs were implicitly used.…”

Section: Related Workmentioning

confidence: 99%

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A Secret-Sharing Based MPC Protocol for Boolean Circuits with Good Amortized Complexity

Cascudo

Gundersen

2020

Lecture Notes in Computer Science

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We present a new secure multiparty computation protocol in the preprocessing model that allows for the evaluation of a number of instances of a boolean circuit in parallel, with a small online communication complexity per instance of 10 bits per party and multiplication gate. Our protocol is secure against an active dishonest majority, and can also be transformed, via existing techniques, into a protocol for the evaluation of a single "well-formed" boolean circuit with the same complexity per multiplication gate at the cost of some overhead that depends on the topology of the circuit. Our protocol uses an approach introduced recently in the setting of honest majority and information-theoretical security which, using an algebraic notion called reverse multiplication friendly embeddings, essentially transforms a batch of evaluations of an arithmetic circuit over a small field into one evaluation of another arithmetic circuit over a larger field. To obtain security against a dishonest majority we combine this approach with the well-known SPDZ protocol that operates over a large field. Structurally our protocol is most similar to MiniMAC, a protocol which bases its security on the use of error-correcting codes, but our protocol has a communication complexity which is half of that of MiniMAC when the best available binary codes are used. With respect to certain variant of MiniMAC that utilizes codes over larger fields, our communication complexity is slightly worse; however, that variant of MiniMAC needs a much larger preprocessing than ours. We also show that our protocol also has smaller amortized communication complexity than Committed MPC, a protocol for general fields based on homomorphic commitments, if we use the best available constructions for those commitments. Finally, we construct a preprocessing phase from oblivious transfer based on ideas from MASCOT and Committed MPC.

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Section: Related Workmentioning

confidence: 99%

“…Our ideas can be extended to arithmetic circuits over other small fields 4. Here we assume that broadcasting messages of M bits requires to send M bits to every other player, which one can achieve with small overhead that vanishes for large messages[13, full version] …”

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confidence: 99%

A Secret-Sharing Based MPC Protocol for Boolean Circuits with Good Amortized Complexity

Cascudo

Gundersen

2020

Lecture Notes in Computer Science

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“…While this notion has not been explicitely defined 3 in the literature to the best of our knowledge, a construction for RMFEs was introduced in another work on secure multiparty computation, more precisely on the problem of correlation extraction [BMN17], where it is used to embed a number of instances of oblivious linear evaluation over a small field into one instance of OLE over the extension field. They obtain, for every prime power q and every integer ≥ 1, a (2 , 3 ) q .…”

Section: Main Ideasmentioning

confidence: 99%

Amortized Complexity of Information-Theoretically Secure MPC Revisited

Cascudo

Cramer

Xing

et al. 2018

Lecture Notes in Computer Science

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A fundamental and widely-applied paradigm due to Franklin and Yung (STOC 1992) on Shamir-secret-sharing based general n-player MPC shows how one may trade the adversary threshold t against amortized communication complexity, by using a so-called packed version of Shamir's scheme. For e.g. the BGW-protocol (with active security), this trade-off means that if t + 2k − 2 < n/3, then k parallel evaluations of the same arithmetic circuit on different inputs can be performed at the overall cost corresponding to a single BGW-execution. In this paper we propose a novel paradigm for amortized MPC that offers a different trade-off, namely with the size of the field of the circuit which is securely computed, instead of the adversary threshold. Thus, unlike the Franklin-Yung paradigm, this leaves the adversary threshold unchanged. Therefore, for instance, this paradigm may yield constructions enjoying the maximal adversary threshold (n−1)/3 in the BGWmodel (secure channels, perfect security, active adversary, synchronous communication). Our idea is to compile an MPC for a circuit over an extension field to a parallel MPC of the same circuit but with inputs defined over its base field and with the same adversary threshold. Key technical handles are our notion of reverse multiplication-friendly embeddings (RMFE) and our proof, by algebraic-geometric means, that these are constant-rate, as well as efficient auxiliary protocols for creating "subspace-randomness" with good amortized complexity. In the BGW-model, we show that the latter can be constructed by combining our tensored-up linear secret sharing with protocols based on hyper-invertible matricesá la Beerliova-Hirt (or variations thereof). Along the way, we suggest alternatives for hyper-invertible matrices with the same functionality but which can be defined over a large enough constant size field, which we believe is of independent interest. As a demonstration of the merits of the novel paradigm, we show that, in the BGW-model and with an optimal adversary threshold (n − 1)/3 ,

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“…Reverse Multiplication Friendly Embeddings (RMFEs), as introduced in [CCXY18, CRX19] (and recap in Section 2.4) , can also be seen as a SIMD encoding. On a technical level, the combinatorial problem behind our SIMD construction has been previously applied in the context of packing for homomorphic encryption [OSV20] and leakage-resilient MPC [BMN17].…”

Section: Simd Encodingsmentioning

confidence: 99%

Securely computing threshold variants of signature schemes (and more!)

Lee

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It is thanks to the love, support, and guidance of many people in my life that this work is possible.Thank you to my PhD advisor, abhi shelat, for the guidance through the years. I am incredibly fortunate to have been advised by a great researcher who cares so much for his students. I don't take for granted your support and advice.I would like to thank my thesis committee: Daniel Wichs, Jon Ullman, and Muthuramakrishnan Venkitasubramaniam. Thank you Jon and Daniel for creating such a nice atmosphere and group here. I'll miss running into you two at the coffee machine and talking about anything and everything. Muthu, it's such a treat to have you at the beginning and end of my PhD. Thank you for being part of this! A special thank you to Brent Waters, who introduced me to cryptography back when I was an undergraduate at UT Austin. Even after I graduated and left Texas, Brent has always been so nice to me.My time at Northeastern was way more fun than I ever expected, thanks in particular to my grad school besties Yash Kondi, Jack Doerner, Willy Quach, Ariel Hamlin, and Matthew Jagielski. PhD is stressful but having you all around made my time here such a joy. Plus, you guys are such good researchers! The bar was set high. I am forever grateful for your friendship and all you've taught me. I'm also pretty grateful to everyone at 6th floor ISEC who gave me food (Changming Liu and Giorgio Severi in particular were the most generous).Throughout these past years, I've had the fortune of meeting and working with so many amazing groups, from everyone who's passed through Northeastern

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Secure Computation Based on Leaky Correlations: High Resilience Setting

Cited by 11 publications

References 62 publications

A Secret-Sharing Based MPC Protocol for Boolean Circuits with Good Amortized Complexity

A Secret-Sharing Based MPC Protocol for Boolean Circuits with Good Amortized Complexity

Amortized Complexity of Information-Theoretically Secure MPC Revisited

Securely computing threshold variants of signature schemes (and more!)

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