40 Search Results for "Chung, Kai-Min"

Volume

LIPIcs, Volume 267

4th Conference on Information-Theoretic Cryptography (ITC 2023)

ITC 2023, June 6-8, 2023, Aarhus University, Aarhus, Denmark

Editors: Kai-Min Chung

Document
Complete Volume
DOI: 10.4230/LIPIcs.ITC.2023
LIPIcs, Volume 267, ITC 2023, Complete Volume

Authors: Kai-Min Chung

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
LIPIcs, Volume 267, ITC 2023, Complete Volume
Cite as

4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 1-358, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Proceedings{chung:LIPIcs.ITC.2023,
  title =	{{LIPIcs, Volume 267, ITC 2023, Complete Volume}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{1--358},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023},
  URN =		{urn:nbn:de:0030-drops-183272},
  doi =		{10.4230/LIPIcs.ITC.2023},
  annote =	{Keywords: LIPIcs, Volume 267, ITC 2023, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.ITC.2023.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Kai-Min Chung

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chung:LIPIcs.ITC.2023.0,
  author =	{Chung, Kai-Min},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{0:i--0:xii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.0},
  URN =		{urn:nbn:de:0030-drops-183280},
  doi =		{10.4230/LIPIcs.ITC.2023.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.ITC.2023.1
Two-Round Perfectly Secure Message Transmission with Optimal Transmission Rate

Authors: Nicolas Resch and Chen Yuan

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
In the model of Perfectly Secure Message Transmission (PSMT), a sender Alice is connected to a receiver Bob via n parallel two-way channels, and Alice holds an 𝓁 symbol secret that she wishes to communicate to Bob. There is an unbounded adversary Eve that controls t of the channels, where n = 2t+1. Eve is able to corrupt any symbol sent through the channels she controls, and furthermore may attempt to infer Alice’s secret by observing the symbols sent through the channels she controls. The transmission is required to be (a) reliable, i.e., Bob must always be able to recover Alice’s secret, regardless of Eve’s corruptions; and (b) private, i.e., Eve may not learn anything about Alice’s secret. We focus on the two-round model, where Bob is permitted to first transmit to Alice, and then Alice responds to Bob. In this work we provide upper and lower bounds for the PSMT model when the length of the communicated secret 𝓁 is asymptotically large. Specifically, we first construct a protocol that allows Alice to communicate an 𝓁 symbol secret to Bob by transmitting at most 2(1+o_{𝓁→∞}(1))n𝓁 symbols. Under a reasonable assumption (which is satisfied by all known efficient two-round PSMT protocols), we complement this with a lower bound showing that 2n𝓁 symbols are necessary for Alice to privately and reliably communicate her secret. This provides strong evidence that our construction is optimal (even up to the leading constant).
Cite as

Nicolas Resch and Chen Yuan. Two-Round Perfectly Secure Message Transmission with Optimal Transmission Rate. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{resch_et_al:LIPIcs.ITC.2023.1,
  author =	{Resch, Nicolas and Yuan, Chen},
  title =	{{Two-Round Perfectly Secure Message Transmission with Optimal Transmission Rate}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.1},
  URN =		{urn:nbn:de:0030-drops-183297},
  doi =		{10.4230/LIPIcs.ITC.2023.1},
  annote =	{Keywords: Secure transmission, Information theoretical secure, MDS codes}
}
Document
DOI: 10.4230/LIPIcs.ITC.2023.2
A Lower Bound on the Share Size in Evolving Secret Sharing

Authors: Noam Mazor

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
Secret sharing schemes allow sharing a secret between a set of parties in a way that ensures that only authorized subsets of the parties learn the secret. Evolving secret sharing schemes (Komargodski, Naor, and Yogev [TCC '16]) allow achieving this end in a scenario where the parties arrive in an online fashion, and there is no a-priory bound on the number of parties. An important complexity measure of a secret sharing scheme is the share size, which is the maximum number of bits that a party may receive as a share. While there has been a significant progress in recent years, the best constructions for both secret sharing and evolving secret sharing schemes have a share size that is exponential in the number of parties. On the other hand, the best lower bound, by Csirmaz [Eurocrypt '95], is sub-linear. In this work, we give a tight lower bound on the share size of evolving secret sharing schemes. Specifically, we show that the sub-linear lower bound of Csirmaz implies an exponential lower bound on evolving secret sharing.
Cite as

Noam Mazor. A Lower Bound on the Share Size in Evolving Secret Sharing. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 2:1-2:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{mazor:LIPIcs.ITC.2023.2,
  author =	{Mazor, Noam},
  title =	{{A Lower Bound on the Share Size in Evolving Secret Sharing}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{2:1--2:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.2},
  URN =		{urn:nbn:de:0030-drops-183300},
  doi =		{10.4230/LIPIcs.ITC.2023.2},
  annote =	{Keywords: Secret sharing, Evolving secret sharing}
}
Document
DOI: 10.4230/LIPIcs.ITC.2023.3
Csirmaz’s Duality Conjecture and Threshold Secret Sharing

Authors: Andrej Bogdanov

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
We conjecture that the smallest possible share size for binary secrets for the t-out-of-n and (n-t+1)-out-of-n access structures is the same for all 1 ≤ t ≤ n. This is a strenghtening of a recent conjecture by Csirmaz (J. Math. Cryptol., 2020). We prove the conjecture for t = 2 and all n. Our proof gives a new (n-1)-out-of-n secret sharing scheme for binary secrets with share alphabet size n.
Cite as

Andrej Bogdanov. Csirmaz’s Duality Conjecture and Threshold Secret Sharing. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 3:1-3:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bogdanov:LIPIcs.ITC.2023.3,
  author =	{Bogdanov, Andrej},
  title =	{{Csirmaz’s Duality Conjecture and Threshold Secret Sharing}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{3:1--3:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.3},
  URN =		{urn:nbn:de:0030-drops-183317},
  doi =		{10.4230/LIPIcs.ITC.2023.3},
  annote =	{Keywords: Threshold secret sharing, Fourier analysis}
}
Document
DOI: 10.4230/LIPIcs.ITC.2023.4
The Cost of Statistical Security in Proofs for Repeated Squaring

Authors: Cody Freitag and Ilan Komargodski

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
In recent years, the number of applications of the repeated squaring assumption has been growing rapidly. The assumption states that, given a group element x, an integer T, and an RSA modulus N, it is hard to compute x^2^T mod N - or even decide whether y?=x^2^T mod N - in parallel time less than the trivial approach of simply computing T squares. This rise has been driven by efficient proof systems for repeated squaring, opening the door to more efficient constructions of verifiable delay functions, various secure computation primitives, and proof systems for more general languages. In this work, we study the complexity of statistically sound proofs for the repeated squaring relation. Technically, we consider proofs where the prover sends at most k ≥ 0 elements and the (probabilistic) verifier performs generic group operations over the group ℤ_N^⋆. As our main contribution, we show that for any (one-round) proof with a randomized verifier (i.e., an MA proof) the verifier either runs in parallel time Ω(T/(k+1)) with high probability, or is able to factor N given the proof provided by the prover. This shows that either the prover essentially sends p,q such that N = p⋅ q (which is infeasible or undesirable in most applications), or a variant of Pietrzak’s proof of repeated squaring (ITCS 2019) has optimal verifier complexity O(T/(k+1)). In particular, it is impossible to obtain a statistically sound one-round proof of repeated squaring with efficiency on par with the computationally-sound protocol of Wesolowski (EUROCRYPT 2019), with a generic group verifier. We further extend our one-round lower bound to a natural class of recursive interactive proofs for repeated squaring. For r-round recursive proofs where the prover is allowed to send k group elements per round, we show that the verifier either runs in parallel time Ω(T/(k+1)^r) with high probability, or is able to factor N given the proof transcript.
Cite as

Cody Freitag and Ilan Komargodski. The Cost of Statistical Security in Proofs for Repeated Squaring. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{freitag_et_al:LIPIcs.ITC.2023.4,
  author =	{Freitag, Cody and Komargodski, Ilan},
  title =	{{The Cost of Statistical Security in Proofs for Repeated Squaring}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{4:1--4:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.4},
  URN =		{urn:nbn:de:0030-drops-183326},
  doi =		{10.4230/LIPIcs.ITC.2023.4},
  annote =	{Keywords: Cryptographic Proofs, Repeated Squaring, Lower Bounds}
}
Document
DOI: 10.4230/LIPIcs.ITC.2023.5
Interactive Non-Malleable Codes Against Desynchronizing Attacks in the Multi-Party Setting

Authors: Nils Fleischhacker, Suparno Ghoshal, and Mark Simkin

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
Interactive Non-Malleable Codes were introduced by Fleischhacker et al. (TCC 2019) in the two party setting with synchronous tampering. The idea of this type of non-malleable code is that it "encodes" an interactive protocol in such a way that, even if the messages are tampered with according to some class F of tampering functions, the result of the execution will either be correct, or completely unrelated to the inputs of the participating parties. In the synchronous setting the adversary is able to modify the messages being exchanged but cannot drop messages nor desynchronize the two parties by first running the protocol with the first party and then with the second party. In this work, we define interactive non-malleable codes in the non-synchronous multi-party setting and construct such interactive non-malleable codes for the class F^s_bounded of bounded-state tampering functions.
Cite as

Nils Fleischhacker, Suparno Ghoshal, and Mark Simkin. Interactive Non-Malleable Codes Against Desynchronizing Attacks in the Multi-Party Setting. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 5:1-5:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fleischhacker_et_al:LIPIcs.ITC.2023.5,
  author =	{Fleischhacker, Nils and Ghoshal, Suparno and Simkin, Mark},
  title =	{{Interactive Non-Malleable Codes Against Desynchronizing Attacks in the Multi-Party Setting}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{5:1--5:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.5},
  URN =		{urn:nbn:de:0030-drops-183331},
  doi =		{10.4230/LIPIcs.ITC.2023.5},
  annote =	{Keywords: non-malleability, multi-party protocols}
}
Document
DOI: 10.4230/LIPIcs.ITC.2023.6
Asymmetric Multi-Party Computation

Authors: Vipul Goyal, Chen-Da Liu-Zhang, and Rafail Ostrovsky

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
Current protocols for Multi-Party Computation (MPC) consider the setting where all parties have access to similar resources. For example, all parties have access to channels bounded by the same worst-case delay upper bound Δ, and all channels have the same cost of communication. As a consequence, the overall protocol performance (resp. the communication cost) may be heavily affected by the slowest (resp. the most expensive) channel, even when most channels are fast (resp. cheap). Given the state of affairs, we initiate a systematic study of asymmetric MPC. In asymmetric MPC, the parties are divided into two categories: fast and slow parties, depending on whether they have access to high-end or low-end resources. We investigate two different models. In the first, we consider asymmetric communication delays: Fast parties are connected via channels with small delay δ among themselves, while channels connected to (at least) one slow party have a large delay Δ ≫ δ. In the second model, we consider asymmetric communication costs: Fast parties benefit from channels with cheap communication, while channels connected to a slow party have an expensive communication. We provide a wide range of positive and negative results exploring the trade-offs between the achievable number of tolerated corruptions t and slow parties s, versus the round complexity and communication cost in each of the models. Among others, we achieve the following results. In the model with asymmetric communication delays, focusing on the information-theoretic (i-t) setting: - An i-t asymmetric MPC protocol with security with abort as long as t+s < n and t < n/2, in a constant number of slow rounds. - We show that achieving an i-t asymmetric MPC protocol for t+s = n and with number of slow rounds independent of the circuit size implies an i-t synchronous MPC protocol with round complexity independent of the circuit size, which is a major problem in the field of round-complexity of MPC. - We identify a new primitive, asymmetric broadcast, that allows to consistently distribute a value among the fast parties, and at a later time the same value to slow parties. We completely characterize the feasibility of asymmetric broadcast by showing that it is possible if and only if 2t + s < n. - An i-t asymmetric MPC protocol with guaranteed output delivery as long as t+s < n and t < n/2, in a number of slow rounds independent of the circuit size. In the model with asymmetric communication cost, we achieve an asymmetric MPC protocol for security with abort for t+s < n and t < n/2, based on one-way functions (OWF). The protocol communicates a number of bits over expensive channels that is independent of the circuit size. We conjecture that assuming OWF is needed and further provide a partial result in this direction.
Cite as

Vipul Goyal, Chen-Da Liu-Zhang, and Rafail Ostrovsky. Asymmetric Multi-Party Computation. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 6:1-6:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{goyal_et_al:LIPIcs.ITC.2023.6,
  author =	{Goyal, Vipul and Liu-Zhang, Chen-Da and Ostrovsky, Rafail},
  title =	{{Asymmetric Multi-Party Computation}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{6:1--6:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.6},
  URN =		{urn:nbn:de:0030-drops-183342},
  doi =		{10.4230/LIPIcs.ITC.2023.6},
  annote =	{Keywords: multiparty computation, asymmetric, delays, communication}
}
Document
DOI: 10.4230/LIPIcs.ITC.2023.7
Phoenix: Secure Computation in an Unstable Network with Dropouts and Comebacks

Authors: Ivan Damgård, Daniel Escudero, and Antigoni Polychroniadou

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
We consider the task of designing secure computation protocols in an unstable network where honest parties can drop out at any time, according to a schedule provided by the adversary. This type of setting, where even honest parties are prone to failures, is more realistic than traditional models, and has therefore gained a lot of attention recently. Our model, Phoenix, enables a new approach to secure multiparty computation with dropouts, allowing parties to drop out and re-enter the computation on an adversarially-chosen schedule and without assuming that these parties receive the messages that were sent to them while being offline - features that are not available in the existing models of Sleepy MPC (Guo et al., CRYPTO '19), Fluid MPC (Choudhuri et al., CRYPTO '21 ) and YOSO (Gentry et al. CRYPTO '21). Phoenix does assume an upper bound on the number of rounds that an honest party can be off-line - otherwise protocols in this setting cannot guarantee termination within a bounded number of rounds; however, if one settles for a weaker notion, namely guaranteed output delivery only for honest parties who stay on-line long enough, this requirement is not necessary. In this work, we study the settings of perfect, statistical and computational security and design MPC protocols in each of these scenarios. We assume that the intersection of online-and-honest parties from one round to the next is at least 2t+1, t+1 and 1 respectively, where t is the number of (actively) corrupt parties. We show the intersection requirements to be optimal. Our (positive) results are obtained in a way that may be of independent interest: we implement a traditional stable network on top of the unstable one, which allows us to plug in any MPC protocol on top. This approach adds a necessary overhead to the round count of the protocols, which is related to the maximal number of rounds an honest party can be offline. We also present a novel, perfectly secure MPC protocol in the preprocessing model that avoids this overhead by following a more "direct" approach rather than first building a stable network and then using existing protocols. We introduce our network model in the UC-framework, show that the composition theorem still holds, and prove the security of our protocols within this setting.
Cite as

Ivan Damgård, Daniel Escudero, and Antigoni Polychroniadou. Phoenix: Secure Computation in an Unstable Network with Dropouts and Comebacks. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 7:1-7:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{damgard_et_al:LIPIcs.ITC.2023.7,
  author =	{Damg\r{a}rd, Ivan and Escudero, Daniel and Polychroniadou, Antigoni},
  title =	{{Phoenix: Secure Computation in an Unstable Network with Dropouts and Comebacks}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{7:1--7:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.7},
  URN =		{urn:nbn:de:0030-drops-183355},
  doi =		{10.4230/LIPIcs.ITC.2023.7},
  annote =	{Keywords: Secure Multiparty Computation, Unstable Networks}
}
Document
DOI: 10.4230/LIPIcs.ITC.2023.8
Weighted Secret Sharing from Wiretap Channels

Authors: Fabrice Benhamouda, Shai Halevi, and Lev Stambler

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
Secret-sharing allows splitting a piece of secret information among a group of shareholders, so that it takes a large enough subset of them to recover it. In weighted secret-sharing, each shareholder has an integer weight, and it takes a subset of large-enough weight to recover the secret. Schemes in the literature for weighted threshold secret sharing either have share sizes that grow linearly with the total weight, or ones that depend on huge public information (essentially a garbled circuit) of size (quasi)polynomial in the number of parties. To do better, we investigate a relaxation, (α, β)-ramp weighted secret sharing, where subsets of weight β W can recover the secret (with W the total weight), but subsets of weight α W or less cannot learn anything about it. These can be constructed from standard secret-sharing schemes, but known constructions require long shares even for short secrets, achieving share sizes of max(W,|secret|/ε), where ε = β-α. In this note we first observe that simple rounding let us replace the total weight W by N/ε, where N is the number of parties. Combined with known constructions, this yields share sizes of O(max(N,|secret|)/ε). Our main contribution is a novel connection between weighted secret sharing and wiretap channels, that improves or even eliminates the dependence on N, at a price of increased dependence on 1/ε. We observe that for certain additive-noise (ℛ,𝒜) wiretap channels, any semantically secure scheme can be naturally transformed into an (α,β)-ramp weighted secret-sharing, where α,β are essentially the respective capacities of the channels 𝒜,ℛ. We present two instantiations of this type of construction, one using Binary Symmetric wiretap Channels, and the other using additive Gaussian Wiretap Channels. Depending on the parameters of the underlying wiretap channels, this gives rise to (α, β)-ramp schemes with share sizes |secret|⋅log N/poly(ε) or even just |secret|/poly(ε).
Cite as

Fabrice Benhamouda, Shai Halevi, and Lev Stambler. Weighted Secret Sharing from Wiretap Channels. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{benhamouda_et_al:LIPIcs.ITC.2023.8,
  author =	{Benhamouda, Fabrice and Halevi, Shai and Stambler, Lev},
  title =	{{Weighted Secret Sharing from Wiretap Channels}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.8},
  URN =		{urn:nbn:de:0030-drops-183365},
  doi =		{10.4230/LIPIcs.ITC.2023.8},
  annote =	{Keywords: Secret sharing, ramp weighted secret sharing, wiretap channel}
}
Document
DOI: 10.4230/LIPIcs.ITC.2023.9
Quantum Security of Subset Cover Problems

Authors: Samuel Bouaziz-Ermann, Alex B. Grilo, and Damien Vergnaud

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
The subset cover problem for k ≥ 1 hash functions, which can be seen as an extension of the collision problem, was introduced in 2002 by Reyzin and Reyzin to analyse the security of their hash-function based signature scheme HORS. The security of many hash-based signature schemes relies on this problem or a variant of this problem (e.g. HORS, SPHINCS, SPHINCS+, ...). Recently, Yuan, Tibouchi and Abe (2022) introduced a variant to the subset cover problem, called restricted subset cover, and proposed a quantum algorithm for this problem. In this work, we prove that any quantum algorithm needs to make Ω((k+1)^{-(2^k)/(2^{k+1}-1})⋅ N^{(2^{k}-1})/(2^{k+1}-1)}) queries to the underlying hash functions with codomain size N to solve the restricted subset cover problem, which essentially matches the query complexity of the algorithm proposed by Yuan, Tibouchi and Abe. We also analyze the security of the general (r,k)-subset cover problem, which is the underlying problem that implies the unforgeability of HORS under a r-chosen message attack (for r ≥ 1). We prove that a generic quantum algorithm needs to make Ω(N^{k/5}) queries to the underlying hash functions to find a (1,k)-subset cover. We also propose a quantum algorithm that finds a (r,k)-subset cover making O (N^{k/(2+2r)}) queries to the k hash functions.
Cite as

Samuel Bouaziz-Ermann, Alex B. Grilo, and Damien Vergnaud. Quantum Security of Subset Cover Problems. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{bouazizermann_et_al:LIPIcs.ITC.2023.9,
  author =	{Bouaziz-Ermann, Samuel and Grilo, Alex B. and Vergnaud, Damien},
  title =	{{Quantum Security of Subset Cover Problems}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.9},
  URN =		{urn:nbn:de:0030-drops-183378},
  doi =		{10.4230/LIPIcs.ITC.2023.9},
  annote =	{Keywords: Cryptography, Random oracle model, Quantum information}
}
Document
DOI: 10.4230/LIPIcs.ITC.2023.10
Distributed Shuffling in Adversarial Environments

Authors: Kasper Green Larsen, Maciej Obremski, and Mark Simkin

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
We study mix-nets in the context of cryptocurrencies. Here we have many computationally weak shufflers that speak one after another and want to joinlty shuffle a list of ciphertexts (c₁, … , c_n). Each shuffler can only permute k << n ciphertexts at a time. An adversary A can track some of the ciphertexts and adaptively corrupt some of the shufflers. We present a simple protocol for shuffling the list of ciphertexts efficiently. The main technical contribution of this work is to prove that our simple shuffling strategy does indeed provide good anonymity guarantees and at the same time terminates quickly. Our shuffling algorithm provides a strict improvement over the current shuffling strategy in Ethereum’s block proposer elections. Our algorithm is secure against a stronger adversary, provides provable security guarantees, and is comparably in efficiency to the current approach.
Cite as

Kasper Green Larsen, Maciej Obremski, and Mark Simkin. Distributed Shuffling in Adversarial Environments. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{larsen_et_al:LIPIcs.ITC.2023.10,
  author =	{Larsen, Kasper Green and Obremski, Maciej and Simkin, Mark},
  title =	{{Distributed Shuffling in Adversarial Environments}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{10:1--10:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.10},
  URN =		{urn:nbn:de:0030-drops-183385},
  doi =		{10.4230/LIPIcs.ITC.2023.10},
  annote =	{Keywords: Distributed Computing, Shuffling}
}
Document
DOI: 10.4230/LIPIcs.ITC.2023.11
MPC with Low Bottleneck-Complexity: Information-Theoretic Security and More

Authors: Hannah Keller, Claudio Orlandi, Anat Paskin-Cherniavsky, and Divya Ravi

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
The bottleneck-complexity (BC) of secure multiparty computation (MPC) protocols is a measure of the maximum number of bits which are sent and received by any party in protocol. As the name suggests, the goal of studying BC-efficient protocols is to increase overall efficiency by making sure that the workload in the protocol is somehow "amortized" by the protocol participants. Orlandi et al. [Orlandi et al., 2022] initiated the study of BC-efficient protocols from simple assumptions in the correlated randomness model and for semi-honest adversaries. In this work, we extend the study of [Orlandi et al., 2022] in two primary directions: (a) to a larger and more general class of functions and (b) to the information-theoretic setting. In particular, we offer semi-honest secure protocols for the useful function classes of abelian programs, "read-k" non-abelian programs, and "read-k" generalized formulas. Our constructions use a novel abstraction, called incremental function secret-sharing (IFSS), that can be instantiated with unconditional security or from one-way functions (with different efficiency trade-offs).
Cite as

Hannah Keller, Claudio Orlandi, Anat Paskin-Cherniavsky, and Divya Ravi. MPC with Low Bottleneck-Complexity: Information-Theoretic Security and More. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{keller_et_al:LIPIcs.ITC.2023.11,
  author =	{Keller, Hannah and Orlandi, Claudio and Paskin-Cherniavsky, Anat and Ravi, Divya},
  title =	{{MPC with Low Bottleneck-Complexity: Information-Theoretic Security and More}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{11:1--11:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.11},
  URN =		{urn:nbn:de:0030-drops-183391},
  doi =		{10.4230/LIPIcs.ITC.2023.11},
  annote =	{Keywords: Secure Multiparty Computation, Bottleneck Complexity, Information-theoretic}
}
Document
DOI: 10.4230/LIPIcs.ITC.2023.12
Randomness Recoverable Secret Sharing Schemes

Authors: Mohammad Hajiabadi, Shahram Khazaei, and Behzad Vahdani

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract
It is well-known that randomness is essential for secure cryptography. The randomness used in cryptographic primitives is not necessarily recoverable even by the party who can, e.g., decrypt or recover the underlying secret/message. Several cryptographic primitives that support randomness recovery have turned out useful in various applications. In this paper, we study randomness recoverable secret sharing schemes (RR-SSS), in both information-theoretic and computational settings and provide two results. First, we show that while every access structure admits a perfect RR-SSS, there are very simple access structures (e.g., in monotone AC⁰) that do not admit efficient perfect (or even statistical) RR-SSS. Second, we show that the existence of efficient computational RR-SSS for certain access structures in monotone AC⁰ implies the existence of one-way functions. This stands in sharp contrast to (non-RR) SSS schemes for which no such results are known. RR-SSS plays a key role in making advanced attributed-based encryption schemes randomness recoverable, which in turn have applications in the context of designated-verifier non-interactive zero knowledge.
Cite as

Mohammad Hajiabadi, Shahram Khazaei, and Behzad Vahdani. Randomness Recoverable Secret Sharing Schemes. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 12:1-12:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hajiabadi_et_al:LIPIcs.ITC.2023.12,
  author =	{Hajiabadi, Mohammad and Khazaei, Shahram and Vahdani, Behzad},
  title =	{{Randomness Recoverable Secret Sharing Schemes}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{12:1--12:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.12},
  URN =		{urn:nbn:de:0030-drops-183404},
  doi =		{10.4230/LIPIcs.ITC.2023.12},
  annote =	{Keywords: Secret sharing, Randomness recovery}
}
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