Volume
LIPIcs, Volume 199
2nd Conference on Information-Theoretic Cryptography (ITC 2021)
-
Part of:
Series:
Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Conference on Information-Theoretic Cryptography (ITC)
Event
ITC 2021, July 23-26, 2021, Virtual ConferenceEditor
Publication Details
- published at: 2021-07-19
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-197-9
- DBLP: db/conf/icits/itc2021
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Complete Volume
LIPIcs, Volume 199, ITC 2021, Complete Volume
Abstract
LIPIcs, Volume 199, ITC 2021, Complete Volume
Cite as
2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 1-590, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@Proceedings{tessaro:LIPIcs.ITC.2021,
title = {{LIPIcs, Volume 199, ITC 2021, Complete Volume}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {1--590},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021},
URN = {urn:nbn:de:0030-drops-143187},
doi = {10.4230/LIPIcs.ITC.2021},
annote = {Keywords: LIPIcs, Volume 199, ITC 2021, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{tessaro:LIPIcs.ITC.2021.0,
author = {Tessaro, Stefano},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {0:i--0:xii},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.0},
URN = {urn:nbn:de:0030-drops-143195},
doi = {10.4230/LIPIcs.ITC.2021.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Group Structure in Correlations and Its Applications in Cryptography
Abstract
Correlated random variables are a key tool in cryptographic applications like secure multi-party computation. We investigate the power of a class of correlations that we term group correlations: A group correlation is a uniform distribution over pairs (x,y) ∈ G² such that x+y ∈ S, where G is a (possibly non-abelian) group and S is a subset of G. We also introduce bi-affine correlation{s}, and show how they relate to group correlations. We present several structural results, new protocols and applications of these correlations. The new applications include a completeness result for black box group computation, perfectly secure protocols for evaluating a broad class of black box "mixed-groups" circuits with bi-affine homomorphisms, and new information-theoretic results. Finally, we uncover a striking structure underlying OLE: In particular, we show that OLE over 𝔽_{2ⁿ}, is isomorphic to a group correlation over ℤ_4^n.
Cite as
Guru-Vamsi Policharla, Manoj Prabhakaran, Rajeev Raghunath, and Parjanya Vyas. Group Structure in Correlations and Its Applications in Cryptography. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 1:1-1:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{policharla_et_al:LIPIcs.ITC.2021.1,
author = {Policharla, Guru-Vamsi and Prabhakaran, Manoj and Raghunath, Rajeev and Vyas, Parjanya},
title = {{Group Structure in Correlations and Its Applications in Cryptography}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {1:1--1:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.1},
URN = {urn:nbn:de:0030-drops-143208},
doi = {10.4230/LIPIcs.ITC.2021.1},
annote = {Keywords: Group correlations, bi-affine correlations, secure computation}
}
Document
More Communication Lower Bounds for Information-Theoretic MPC
Abstract
We prove two classes of lower bounds on the communication complexity of information-theoretically secure multiparty computation. The first lower bound applies to perfect passive secure multiparty computation in the standard model with n = 2t+1 parties of which t are corrupted. We show a lower bound that applies to secure evaluation of any function, assuming that each party can choose to learn or not learn the output. Specifically, we show that there is a function H^* such that for any protocol that evaluates y_i = b_i ⋅ f(x₁,...,x_n) with perfect passive security (where b_i is a private boolean input), the total communication must be at least 1/2 ∑_{i = 1}ⁿ H_f^*(x_i) bits of information.
The second lower bound applies to the perfect maliciously secure setting with n = 3t+1 parties. We show that for any n and all large enough S, there exists a reactive functionality F_S taking an S-bit string as input (and with short output) such that any protocol implementing F_S with perfect malicious security must communicate Ω(nS) bits. Since the functionalities we study can be implemented with linear size circuits, the result can equivalently be stated as follows: for any n and all large enough g ∈ ℕ there exists a reactive functionality F_C doing computation specified by a Boolean circuit C with g gates, where any perfectly secure protocol implementing F_C must communicate Ω(n g) bits. The results easily extends to constructing similar functionalities defined over any fixed finite field. Using known techniques, we also show an upper bound that matches the lower bound up to a constant factor (existing upper bounds are a factor lg n off for Boolean circuits).
Both results also extend to the case where the threshold t is suboptimal. Namely if n = kt+s the bound is weakened by a factor O(s), which corresponds to known optimizations via packed secret-sharing.
Cite as
Ivan Bjerre Damgård, Boyang Li, and Nikolaj Ignatieff Schwartzbach. More Communication Lower Bounds for Information-Theoretic MPC. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{damgard_et_al:LIPIcs.ITC.2021.2,
author = {Damg\r{a}rd, Ivan Bjerre and Li, Boyang and Schwartzbach, Nikolaj Ignatieff},
title = {{More Communication Lower Bounds for Information-Theoretic MPC}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {2:1--2:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.2},
URN = {urn:nbn:de:0030-drops-143211},
doi = {10.4230/LIPIcs.ITC.2021.2},
annote = {Keywords: Multiparty Computation, Lower bounds}
}
Document
On Prover-Efficient Public-Coin Emulation of Interactive Proofs
Abstract
A central question in the study of interactive proofs is the relationship between private-coin proofs, where the verifier is allowed to hide its randomness from the prover, and public-coin proofs, where the verifier’s random coins are sent to the prover. The seminal work of Goldwasser and Sipser [STOC 1986] showed how to transform private-coin proofs into public-coin ones. However, their transformation incurs a super-polynomial blowup in the running time of the honest prover.
In this work, we study transformations from private-coin proofs to public-coin proofs that preserve (up to polynomial factors) the running time of the prover. We re-consider this question in light of the emergence of doubly-efficient interactive proofs, where the honest prover is required to run in polynomial time and the verifier should run in near-linear time. Can every private-coin doubly-efficient interactive proof be transformed into a public-coin doubly-efficient proof? Adapting a result of Vadhan [STOC 2000], we show that, assuming one-way functions exist, there is no general-purpose black-box private-coin to public-coin transformation for doubly-efficient interactive proofs.
Our main result is a loose converse: if (auxiliary-input infinitely-often) one-way functions do not exist, then there exists a general-purpose efficiency-preserving transformation. To prove this result, we show a general condition that suffices for transforming a doubly-efficient private coin protocol: every such protocol induces an efficiently computable function, such that if this function is efficiently invertible (in the sense of one-way functions), then the proof can be efficiently transformed into a public-coin proof system with a polynomial-time honest prover.
This result motivates a study of other general conditions that allow for efficiency-preserving private to public coin transformations. We identify an additional (incomparable) condition to that used in our main result. This condition allows for transforming any private coin interactive proof where (roughly) it is possible to efficiently approximate the number of verifier coins consistent with a partial transcript. This allows for transforming any constant-round interactive proof that has this property (even if it is not doubly-efficient). We demonstrate the applicability of this final result by using it to transform a private-coin protocol of Rothblum, Vadhan and Wigderson [STOC 2013], obtaining a doubly-efficient public-coin protocol for verifying that a given graph is close to bipartite in a setting for which such a protocol was not previously known.
Cite as
Gal Arnon and Guy N. Rothblum. On Prover-Efficient Public-Coin Emulation of Interactive Proofs. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{arnon_et_al:LIPIcs.ITC.2021.3,
author = {Arnon, Gal and Rothblum, Guy N.},
title = {{On Prover-Efficient Public-Coin Emulation of Interactive Proofs}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {3:1--3:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.3},
URN = {urn:nbn:de:0030-drops-143226},
doi = {10.4230/LIPIcs.ITC.2021.3},
annote = {Keywords: Interactive Proofs, Computational complexity, Cryptography}
}
Document
On the Randomness Complexity of Interactive Proofs and Statistical Zero-Knowledge Proofs
Abstract
We study the randomness complexity of interactive proofs and zero-knowledge proofs. In particular, we ask whether it is possible to reduce the randomness complexity, R, of the verifier to be comparable with the number of bits, C_V, that the verifier sends during the interaction. We show that such randomness sparsification is possible in several settings. Specifically, unconditional sparsification can be obtained in the non-uniform setting (where the verifier is modelled as a circuit), and in the uniform setting where the parties have access to a (reusable) common-random-string (CRS). We further show that constant-round uniform protocols can be sparsified without a CRS under a plausible worst-case complexity-theoretic assumption that was used previously in the context of derandomization.
All the above sparsification results preserve statistical-zero knowledge provided that this property holds against a cheating verifier. We further show that randomness sparsification can be applied to honest-verifier statistical zero-knowledge (HVSZK) proofs at the expense of increasing the communication from the prover by R-F bits, or, in the case of honest-verifier perfect zero-knowledge (HVPZK) by slowing down the simulation by a factor of 2^{R-F}. Here F is a new measure of accessible bit complexity of an HVZK proof system that ranges from 0 to R, where a maximal grade of R is achieved when zero-knowledge holds against a "semi-malicious" verifier that maliciously selects its random tape and then plays honestly. Consequently, we show that some classical HVSZK proof systems, like the one for the complete Statistical-Distance problem (Sahai and Vadhan, JACM 2003) admit randomness sparsification with no penalty.
Along the way we introduce new notions of pseudorandomness against interactive proof systems, and study their relations to existing notions of pseudorandomness.
Cite as
Benny Applebaum and Eyal Golombek. On the Randomness Complexity of Interactive Proofs and Statistical Zero-Knowledge Proofs. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{applebaum_et_al:LIPIcs.ITC.2021.4,
author = {Applebaum, Benny and Golombek, Eyal},
title = {{On the Randomness Complexity of Interactive Proofs and Statistical Zero-Knowledge Proofs}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {4:1--4:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.4},
URN = {urn:nbn:de:0030-drops-143238},
doi = {10.4230/LIPIcs.ITC.2021.4},
annote = {Keywords: Interactive proofs, Zero-knowledge proofs, Pseudorandomness}
}
Document
Line-Point Zero Knowledge and Its Applications
Abstract
We introduce and study a simple kind of proof system called line-point zero knowledge (LPZK). In an LPZK proof, the prover encodes the witness as an affine line 𝐯(t) : = at + 𝐛 in a vector space 𝔽ⁿ, and the verifier queries the line at a single random point t = α. LPZK is motivated by recent practical protocols for vector oblivious linear evaluation (VOLE), which can be used to compile LPZK proof systems into lightweight designated-verifier NIZK protocols.
We construct LPZK systems for proving satisfiability of arithmetic circuits with attractive efficiency features. These give rise to designated-verifier NIZK protocols that require only 2-5 times the computation of evaluating the circuit in the clear (following an input-independent preprocessing phase), and where the prover communicates roughly 2 field elements per multiplication gate, or roughly 1 element in the random oracle model with a modestly higher computation cost. On the theoretical side, our LPZK systems give rise to the first linear interactive proofs (Bitansky et al., TCC 2013) that are zero knowledge against a malicious verifier.
We then apply LPZK towards simplifying and improving recent constructions of reusable non-interactive secure computation (NISC) from VOLE (Chase et al., Crypto 2019). As an application, we give concretely efficient and reusable NISC protocols over VOLE for bounded inner product, where the sender’s input vector should have a bounded L₂-norm.
Cite as
Samuel Dittmer, Yuval Ishai, and Rafail Ostrovsky. Line-Point Zero Knowledge and Its Applications. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{dittmer_et_al:LIPIcs.ITC.2021.5,
author = {Dittmer, Samuel and Ishai, Yuval and Ostrovsky, Rafail},
title = {{Line-Point Zero Knowledge and Its Applications}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {5:1--5:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.5},
URN = {urn:nbn:de:0030-drops-143249},
doi = {10.4230/LIPIcs.ITC.2021.5},
annote = {Keywords: Zero-knowledge proofs, NIZK, correlated randomness, vector oblivious linear evaluation, non-interactive secure computation}
}
Document
ZK-PCPs from Leakage-Resilient Secret Sharing
Abstract
Zero-Knowledge PCPs (ZK-PCPs; Kilian, Petrank, and Tardos, STOC `97) are PCPs with the additional zero-knowledge guarantee that the view of any (possibly malicious) verifier making a bounded number of queries to the proof can be efficiently simulated up to a small statistical distance. Similarly, ZK-PCPs of Proximity (ZK-PCPPs; Ishai and Weiss, TCC `14) are PCPPs in which the view of an adversarial verifier can be efficiently simulated with few queries to the input.
Previous ZK-PCP constructions obtained an exponential gap between the query complexity q of the honest verifier, and the bound q^* on the queries of a malicious verifier (i.e., q = poly log (q^*)), but required either exponential-time simulation, or adaptive honest verification. This should be contrasted with standard PCPs, that can be verified non-adaptively (i.e., with a single round of queries to the proof). The problem of constructing such ZK-PCPs, even when q^* = q, has remained open since they were first introduced more than 2 decades ago. This question is also open for ZK-PCPPs, for which no construction with non-adaptive honest verification is known (not even with exponential-time simulation).
We resolve this question by constructing the first ZK-PCPs and ZK-PCPPs which simultaneously achieve efficient zero-knowledge simulation and non-adaptive honest verification. Our schemes have a square-root query gap, namely q^*/q = O(√n) where n is the input length.
Our constructions combine the "MPC-in-the-head" technique (Ishai et al., STOC `07) with leakage-resilient secret sharing. Specifically, we use the MPC-in-the-head technique to construct a ZK-PCP variant over a large alphabet, then employ leakage-resilient secret sharing to design a new alphabet reduction for ZK-PCPs which preserves zero-knowledge.
Cite as
Carmit Hazay, Muthuramakrishnan Venkitasubramaniam, and Mor Weiss. ZK-PCPs from Leakage-Resilient Secret Sharing. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{hazay_et_al:LIPIcs.ITC.2021.6,
author = {Hazay, Carmit and Venkitasubramaniam, Muthuramakrishnan and Weiss, Mor},
title = {{ZK-PCPs from Leakage-Resilient Secret Sharing}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {6:1--6:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.6},
URN = {urn:nbn:de:0030-drops-143250},
doi = {10.4230/LIPIcs.ITC.2021.6},
annote = {Keywords: Zero Knowledge, Probabilisitically Checkable Proofs, PCPs of Proximity, Leakage Resilience, Secret Sharing}
}
Document
Secure Merge with O(n log log n) Secure Operations
Abstract
Data-oblivious algorithms are a key component of many secure computation protocols.
In this work, we show that advances in secure multiparty shuffling algorithms can be used to increase the efficiency of several key cryptographic tools.
The key observation is that many secure computation protocols rely heavily on secure shuffles. The best data-oblivious shuffling algorithms require O(n log n), operations, but in the two-party or multiparty setting, secure shuffling can be achieved with only O(n) communication.
Leveraging the efficiency of secure multiparty shuffling, we give novel, information-theoretic algorithms that improve the efficiency of securely sorting sparse lists, secure stable compaction, and securely merging two sorted lists.
Securely sorting private lists is a key component of many larger secure computation protocols. The best data-oblivious sorting algorithms for sorting a list of n elements require O(n log n) comparisons. Using black-box access to a linear-communication secure shuffle, we give a secure algorithm for sorting a list of length n with t ≪ n nonzero elements with communication O(t log² n + n), which beats the best oblivious algorithms when the number of nonzero elements, t, satisfies t < n/log² n.
Secure compaction is the problem of removing dummy elements from a list, and is essentially equivalent to sorting on 1-bit keys. The best oblivious compaction algorithms run in O(n)-time, but they are unstable, i.e., the order of the remaining elements is not preserved. Using black-box access to a linear-communication secure shuffle, we give an information-theoretic stable compaction algorithm with only O(n) communication.
Our main result is a novel secure merge protocol. The best previous algorithms for securely merging two sorted lists into a sorted whole required O(n log n) secure operations. Using black-box access to an O(n)-communication secure shuffle, we give the first multi-party secure merge algorithm that requires only O(n log log n) communication. Our algorithm takes as input n secret-shared values, and outputs a secret-sharing of the sorted list.
All our algorithms are generic, i.e., they can be implemented using generic secure computations techniques and make black-box access to a secure shuffle. Our techniques extend naturally to the multiparty situation (with a constant number of parties) as well as to handle malicious adversaries without changing the asymptotic efficiency.
These algorithm have applications to securely computing database joins and order statistics on private data as well as multiparty Oblivious RAM protocols.
Cite as
Brett Hemenway Falk and Rafail Ostrovsky. Secure Merge with O(n log log n) Secure Operations. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 7:1-7:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{falk_et_al:LIPIcs.ITC.2021.7,
author = {Falk, Brett Hemenway and Ostrovsky, Rafail},
title = {{Secure Merge with O(n log log n) Secure Operations}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {7:1--7:29},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.7},
URN = {urn:nbn:de:0030-drops-143265},
doi = {10.4230/LIPIcs.ITC.2021.7},
annote = {Keywords: Secure computation, Data-oblivious algorithms, Sorting, Merging, Shuffling, Compaction}
}
Document
Perfectly Oblivious (Parallel) RAM Revisited, and Improved Constructions
Abstract
Oblivious RAM (ORAM) is a technique for compiling any RAM program to an oblivious counterpart, i.e., one whose access patterns do not leak information about the secret inputs. Similarly, Oblivious Parallel RAM (OPRAM) compiles a parallel RAM program to an oblivious counterpart. In this paper, we care about ORAM/OPRAM with perfect security, i.e., the access patterns must be identically distributed no matter what the program’s memory request sequence is. In the past, two types of perfect ORAMs/OPRAMs have been considered: constructions whose performance bounds hold in expectation (but may occasionally run more slowly); and constructions whose performance bounds hold deterministically (even though the algorithms themselves are randomized).
In this paper, we revisit the performance metrics for perfect ORAM/OPRAM, and show novel constructions that achieve asymptotical improvements for all performance metrics. Our first result is a new perfectly secure OPRAM scheme with O(log³ N/log log N) expected overhead. In comparison, prior literature has been stuck at O(log³ N) for more than a decade.
Next, we show how to construct a perfect ORAM with O(log³ N/log log N) deterministic simulation overhead. We further show how to make the scheme parallel, resulting in an perfect OPRAM with O(log⁴ N/log log N) deterministic simulation overhead. For perfect ORAMs/OPRAMs with deterministic performance bounds, our results achieve subexponential improvement over the state-of-the-art. Specifically, the best known prior scheme incurs more than √N deterministic simulation overhead (Raskin and Simkin, Asiacrypt'19); moreover, their scheme works only for the sequential setting and is not amenable to parallelization.
Finally, we additionally consider perfect ORAMs/OPRAMs whose performance bounds hold with high probability. For this new performance metric, we show new constructions whose simulation overhead is upper bounded by O(log³ /log log N) except with negligible in N probability, i.e., we prove high-probability performance bounds that match the expected bounds mentioned earlier.
Cite as
T-H. Hubert Chan, Elaine Shi, Wei-Kai Lin, and Kartik Nayak. Perfectly Oblivious (Parallel) RAM Revisited, and Improved Constructions. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 8:1-8:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{chan_et_al:LIPIcs.ITC.2021.8,
author = {Chan, T-H. Hubert and Shi, Elaine and Lin, Wei-Kai and Nayak, Kartik},
title = {{Perfectly Oblivious (Parallel) RAM Revisited, and Improved Constructions}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {8:1--8:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.8},
URN = {urn:nbn:de:0030-drops-143271},
doi = {10.4230/LIPIcs.ITC.2021.8},
annote = {Keywords: perfect oblivious RAM, oblivious PRAM}
}
Document
On the Complexity of Anonymous Communication Through Public Networks
Abstract
Onion routing is the most widely used approach to anonymous communication online. The idea is that Alice wraps her message to Bob in layers of encryption to form an "onion" and routes it through a series of intermediaries. Each intermediary’s job is to decrypt ("peel") the onion it receives to obtain instructions for where to send it next. The intuition is that, by the time it gets to Bob, the onion will have mixed with so many other onions that its origin will be hard to trace even for an adversary that observes the entire network and controls a fraction of the participants, possibly including Bob. Despite its widespread use in practice, until now no onion routing protocol was known that simultaneously achieved, in the presence of an active adversary that observes all network traffic and controls a constant fraction of the participants, (a) anonymity; (b) fault-tolerance, where even if a few of the onions are dropped, the protocol still delivers the rest; and (c) reasonable communication and computational complexity as a function of the security parameter and the number of participants.
In this paper, we give the first onion routing protocol that meets these goals: our protocol (a) achieves anonymity; (b) tolerates a polylogarithmic (in the security parameter) number of dropped onions and still delivers the rest; and (c) requires a polylogarithmic number of rounds and a polylogarithmic number of onions sent per participant per round. We also show that to achieve anonymity in a fault-tolerant fashion via onion routing, this number of onions and rounds is necessary. Of independent interest, our analysis introduces two new security properties of onion routing - mixing and equalizing - and we show that together they imply anonymity.
Cite as
Megumi Ando, Anna Lysyanskaya, and Eli Upfal. On the Complexity of Anonymous Communication Through Public Networks. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 9:1-9:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{ando_et_al:LIPIcs.ITC.2021.9,
author = {Ando, Megumi and Lysyanskaya, Anna and Upfal, Eli},
title = {{On the Complexity of Anonymous Communication Through Public Networks}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {9:1--9:25},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.9},
URN = {urn:nbn:de:0030-drops-143282},
doi = {10.4230/LIPIcs.ITC.2021.9},
annote = {Keywords: Anonymity, privacy, onion routing}
}
Document
Broadcast Secret-Sharing, Bounds and Applications
Abstract
Consider a sender 𝒮 and a group of n recipients. 𝒮 holds a secret message 𝗆 of length l bits and the goal is to allow 𝒮 to create a secret sharing of 𝗆 with privacy threshold t among the recipients, by broadcasting a single message 𝖼 to the recipients. Our goal is to do this with information theoretic security in a model with a simple form of correlated randomness. Namely, for each subset 𝒜 of recipients of size q, 𝒮 may share a random key with all recipients in 𝒜. (The keys shared with different subsets 𝒜 must be independent.) We call this Broadcast Secret-Sharing (BSS) with parameters l, n, t and q.
Our main question is: how large must 𝖼 be, as a function of the parameters? We show that (n-t)/q l is a lower bound, and we show an upper bound of ((n(t+1)/(q+t)) -t)l, matching the lower bound whenever t = 0, or when q = 1 or n-t.
When q = n-t, the size of 𝖼 is exactly l which is clearly minimal. The protocol demonstrating the upper bound in this case requires 𝒮 to share a key with every subset of size n-t. We show that this overhead cannot be avoided when 𝖼 has minimal size.
We also show that if access is additionally given to an idealized PRG, the lower bound on ciphertext size becomes (n-t)/q λ + l - negl(λ) (where λ is the length of the input to the PRG). The upper bound becomes ((n(t+1))/(q+t) -t)λ + l.
BSS can be applied directly to secret-key threshold encryption. We can also consider a setting where the correlated randomness is generated using computationally secure and non-interactive key exchange, where we assume that each recipient has an (independently generated) public key for this purpose. In this model, any protocol for non-interactive secret sharing becomes an ad hoc threshold encryption (ATE) scheme, which is a threshold encryption scheme with no trusted setup beyond a PKI. Our upper bounds imply new ATE schemes, and our lower bound becomes a lower bound on the ciphertext size in any ATE scheme that uses a key exchange functionality and no other cryptographic primitives.
Cite as
Ivan Bjerre Damgård, Kasper Green Larsen, and Sophia Yakoubov. Broadcast Secret-Sharing, Bounds and Applications. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{damgard_et_al:LIPIcs.ITC.2021.10,
author = {Damg\r{a}rd, Ivan Bjerre and Larsen, Kasper Green and Yakoubov, Sophia},
title = {{Broadcast Secret-Sharing, Bounds and Applications}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {10:1--10:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.10},
URN = {urn:nbn:de:0030-drops-143299},
doi = {10.4230/LIPIcs.ITC.2021.10},
annote = {Keywords: Secret-Sharing, Ad-hoc Threshold Encryption}
}
Document
Locally Reconstructable Non-Malleable Secret Sharing
Abstract
Non-malleable secret sharing (NMSS) schemes, introduced by Goyal and Kumar (STOC 2018), ensure that a secret m can be distributed into shares m₁,⋯,m_n (for some n), such that any t (a parameter ≤ n) shares can be reconstructed to recover the secret m, any t-1 shares doesn't leak information about m and even if the shares that are used for reconstruction are tampered, it is guaranteed that the reconstruction of these tampered shares will either result in the original m or something independent of m. Since their introduction, non-malleable secret sharing schemes sparked a very impressive line of research.
In this work, we introduce a feature of local reconstructability in NMSS, which allows reconstruction of any portion of a secret by reading just a few locations of the shares. This is a useful feature, especially when the secret is long or when the shares are stored in a distributed manner on a communication network. In this work, we give a compiler that takes in any non-malleable secret sharing scheme and compiles it into a locally reconstructable non-malleable secret sharing scheme. To secret share a message consisting of k blocks of length ρ each, our scheme would only require reading ρ + log k bits (in addition to a few more bits, whose quantity is independent of ρ and k) from each party’s share (of a reconstruction set) to locally reconstruct a single block of the message.
We show an application of our locally reconstructable non-malleable secret sharing scheme to a computational non-malleable secure message transmission scheme in the pre-processing model, with an improved communication complexity, when transmitting multiple messages.
Cite as
Bhavana Kanukurthi, Sai Lakshmi Bhavana Obbattu, Sruthi Sekar, and Jenit Tomy. Locally Reconstructable Non-Malleable Secret Sharing. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{kanukurthi_et_al:LIPIcs.ITC.2021.11,
author = {Kanukurthi, Bhavana and Obbattu, Sai Lakshmi Bhavana and Sekar, Sruthi and Tomy, Jenit},
title = {{Locally Reconstructable Non-Malleable Secret Sharing}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {11:1--11:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.11},
URN = {urn:nbn:de:0030-drops-143302},
doi = {10.4230/LIPIcs.ITC.2021.11},
annote = {Keywords: Information Theoretic Cryptography, Secret Sharing, Non-malleability, Local Reconstructability}
}
Document
Linear Threshold Secret-Sharing with Binary Reconstruction
Abstract
Motivated in part by applications in lattice-based cryptography, we initiate the study of the size of linear threshold (`t-out-of-n') secret-sharing where the linear reconstruction function is restricted to coefficients in {0,1}. We also study the complexity of such schemes with the additional requirement that the joint distribution of the shares of any unauthorized set of parties is not only independent of the secret, but also uniformly distributed. We prove upper and lower bounds on the share size of such schemes, where the size is measured by the total number of field elements distributed to the parties. We prove our results by defining and investigating an equivalent variant of Karchmer and Wigderson’s Monotone Span Programs [CCC, 1993].
One ramification of our results is that a natural variant of Shamir’s classic scheme [Comm. of ACM, 1979], where bit-decomposition is applied to each share, is optimal for when the underlying field has characteristic 2. Another ramification is that schemes obtained from monotone formulae are optimal for certain threshold values when the field’s characteristic is any constant.
For schemes with the uniform distribution requirement, we show that they must use Ω(nlog n) field elements, for all thresholds 2 < t < n and regardless of the field. Moreover, this is tight up to constant factors for the special cases where any t = n-1 parties can reconstruct, as well as for any threshold when the field characteristic is 2.
Cite as
Marshall Ball, Alper Çakan, and Tal Malkin. Linear Threshold Secret-Sharing with Binary Reconstruction. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{ball_et_al:LIPIcs.ITC.2021.12,
author = {Ball, Marshall and \c{C}akan, Alper and Malkin, Tal},
title = {{Linear Threshold Secret-Sharing with Binary Reconstruction}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {12:1--12:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.12},
URN = {urn:nbn:de:0030-drops-143313},
doi = {10.4230/LIPIcs.ITC.2021.12},
annote = {Keywords: Secret sharing, Span programs, Lattice-based cryptography}
}
Document
Doubly-Affine Extractors, and Their Applications
Abstract
In this work we challenge the common misconception that information-theoretic (IT) privacy is too impractical to be used in the real-world: we propose to build simple and reusable IT-encryption solutions whose only efficiency penalty (compared to computationally-secure schemes) comes from a large secret key size, which is often a rather minor inconvenience, as storage is cheap. In particular, our solutions are stateless and locally computable at the optimal rate, meaning that honest parties do not maintain state and read only (optimally) small portions of their large keys with every use.
Moreover, we also propose a novel architecture for outsourcing the storage of these long keys to a network of semi-trusted servers, trading the need to store large secrets with the assumption that it is hard to simultaneously compromise too many publicly accessible ad-hoc servers. Our architecture supports everlasting privacy and post-application security of the derived one-time keys, resolving two major limitations of a related model for outsourcing key storage, called bounded storage model.
Both of these results come from nearly optimal constructions of so called doubly-affine extractors: locally-computable, seeded extractors Ext(X,S) which are linear functions of X (for any fixed seed S), and protect against bounded affine leakage on X. This holds unconditionally, even if (a) affine leakage may adaptively depend on the extracted key R = Ext(X,S); and (b) the seed S is only computationally secure. Neither of these properties are possible with general-leakage extractors.
Cite as
Yevgeniy Dodis and Kevin Yeo. Doubly-Affine Extractors, and Their Applications. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{dodis_et_al:LIPIcs.ITC.2021.13,
author = {Dodis, Yevgeniy and Yeo, Kevin},
title = {{Doubly-Affine Extractors, and Their Applications}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {13:1--13:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.13},
URN = {urn:nbn:de:0030-drops-143320},
doi = {10.4230/LIPIcs.ITC.2021.13},
annote = {Keywords: extractors, information-theoretic privacy, everlasting privacy}
}
Document
Online Linear Extractors for Independent Sources
Abstract
In this work, we characterize linear online extractors. In other words, given a matrix A ∈ F₂^{n×n}, we study the convergence of the iterated process S ← AS⊕X, where X∼D is repeatedly sampled independently from some fixed (but unknown) distribution D with (min)-entropy k. Here, we think of S ∈ {0,1}ⁿ as the state of an online extractor, and X ∈ {0,1}ⁿ as its input.
As our main result, we show that the state S converges to the uniform distribution for all input distributions D with entropy k > 0 if and only if the matrix A has no non-trivial invariant subspace (i.e., a non-zero subspace V ⊊ F₂ⁿ such that AV ⊆ V). In other words, a matrix A yields a linear online extractor if and only if A has no non-trivial invariant subspace. For example, the linear transformation corresponding to multiplication by a generator of the field F_{2ⁿ} yields a good linear online extractor. Furthermore, for any such matrix convergence takes at most Õ(n²(k+1)/k²) steps.
We also study the more general notion of condensing - that is, we ask when this process converges to a distribution with entropy at least l, when the input distribution has entropy at least k. (Extractors corresponding to the special case when l = n.) We show that a matrix gives a good condenser if there are relatively few vectors w ∈ F₂ⁿ such that w, A^Tw, …, (A^T)^{n-k}w are linearly dependent. As an application, we show that the very simple cyclic rotation transformation A(x₁,…, x_n) = (x_n,x₁,…, x_{n-1}) condenses to l = n-1 bits for any k > 1 if n is a prime satisfying a certain simple number-theoretic condition.
Our proofs are Fourier-analytic and rely on a novel lemma, which gives a tight bound on the product of certain Fourier coefficients of any entropic distribution.
Cite as
Yevgeniy Dodis, Siyao Guo, Noah Stephens-Davidowitz, and Zhiye Xie. Online Linear Extractors for Independent Sources. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{dodis_et_al:LIPIcs.ITC.2021.14,
author = {Dodis, Yevgeniy and Guo, Siyao and Stephens-Davidowitz, Noah and Xie, Zhiye},
title = {{Online Linear Extractors for Independent Sources}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {14:1--14:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.14},
URN = {urn:nbn:de:0030-drops-143339},
doi = {10.4230/LIPIcs.ITC.2021.14},
annote = {Keywords: feasibility of randomness extraction, randomness condensers, Fourier analysis}
}
Document
Code Offset in the Exponent
Abstract
Fuzzy extractors derive stable keys from noisy sources. They are a fundamental tool for key derivation from biometric sources. This work introduces a new construction, code offset in the exponent. This construction is the first reusable fuzzy extractor that simultaneously supports structured, low entropy distributions with correlated symbols and confidence information. These properties are specifically motivated by the most pertinent applications - key derivation from biometrics and physical unclonable functions - which typically demonstrate low entropy with additional statistical correlations and benefit from extractors that can leverage confidence information for efficiency.
Code offset in the exponent is a group encoding of the code offset construction (Juels and Wattenberg, CCS 1999). A random codeword of a linear error-correcting code is used as a one-time pad for a sampled value from the noisy source. Rather than encoding this directly, code offset in the exponent encodes by exponentiation of a generator in a cryptographically strong group. We introduce and characterize a condition on noisy sources that directly translates to security of our construction in the generic group model. Our condition requires the inner product between the source distribution and all vectors in the null space of the code to be unpredictable.
Cite as
Luke Demarest, Benjamin Fuller, and Alexander Russell. Code Offset in the Exponent. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 15:1-15:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{demarest_et_al:LIPIcs.ITC.2021.15,
author = {Demarest, Luke and Fuller, Benjamin and Russell, Alexander},
title = {{Code Offset in the Exponent}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {15:1--15:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.15},
URN = {urn:nbn:de:0030-drops-143348},
doi = {10.4230/LIPIcs.ITC.2021.15},
annote = {Keywords: fuzzy extractors, code offset, learning with errors, error-correction, generic group model}
}
Document
P₄-free Partition and Cover Numbers & Applications
Abstract
P₄-free graphs- also known as cographs, complement-reducible graphs, or hereditary Dacey graphs-have been well studied in graph theory. Motivated by computer science and information theory applications, our work encodes (flat) joint probability distributions and Boolean functions as bipartite graphs and studies bipartite P₄-free graphs. For these applications, the graph properties of edge partitioning and covering a bipartite graph using the minimum number of these graphs are particularly relevant. Previously, such graph properties have appeared in leakage-resilient cryptography and (variants of) coloring problems.
Interestingly, our covering problem is closely related to the well-studied problem of product (a.k.a., Prague) dimension of loopless undirected graphs, which allows us to employ algebraic lower-bounding techniques for the product/Prague dimension. We prove that computing these numbers is NP-complete, even for bipartite graphs. We establish a connection to the (unsolved) Zarankiewicz problem to show that there are bipartite graphs with size-N partite sets such that these numbers are at least ε⋅N^{1-2ε}, for ε ∈ {1/3,1/4,1/5,...}. Finally, we accurately estimate these numbers for bipartite graphs encoding well-studied Boolean functions from circuit complexity, such as set intersection, set disjointness, and inequality.
For applications in information theory and communication & cryptographic complexity, we consider a system where a setup samples from a (flat) joint distribution and gives the participants, Alice and Bob, their portion from this joint sample. Alice and Bob’s objective is to non-interactively establish a shared key and extract the left-over entropy from their portion of the samples as independent private randomness. A genie, who observes the joint sample, provides appropriate assistance to help Alice and Bob with their objective. Lower bounds to the minimum size of the genie’s assistance translate into communication and cryptographic lower bounds. We show that (the log₂ of) the P₄-free partition number of a graph encoding the joint distribution that the setup uses is equivalent to the size of the genie’s assistance. Consequently, the joint distributions corresponding to the bipartite graphs constructed above with high P₄-free partition numbers correspond to joint distributions requiring more assistance from the genie.
As a representative application in non-deterministic communication complexity, we study the communication complexity of nondeterministic protocols augmented by access to the equality oracle at the output. We show that (the log₂ of) the P₄-free cover number of the bipartite graph encoding a Boolean function f is equivalent to the minimum size of the nondeterministic input required by the parties (referred to as the communication complexity of f in this model). Consequently, the functions corresponding to the bipartite graphs with high P₄-free cover numbers have high communication complexity. Furthermore, there are functions with communication complexity close to the naïve protocol where the nondeterministic input reveals a party’s input. Finally, the access to the equality oracle reduces the communication complexity of computing set disjointness by a constant factor in contrast to the model where parties do not have access to the equality oracle. To compute the inequality function, we show an exponential reduction in the communication complexity, and this bound is optimal. On the other hand, access to the equality oracle is (nearly) useless for computing set intersection.
Cite as
Alexander R. Block, Simina Brânzei, Hemanta K. Maji, Himanshi Mehta, Tamalika Mukherjee, and Hai H. Nguyen. P₄-free Partition and Cover Numbers & Applications. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 16:1-16:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{block_et_al:LIPIcs.ITC.2021.16,
author = {Block, Alexander R. and Br\^{a}nzei, Simina and Maji, Hemanta K. and Mehta, Himanshi and Mukherjee, Tamalika and Nguyen, Hai H.},
title = {{P₄-free Partition and Cover Numbers \& Applications}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {16:1--16:25},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.16},
URN = {urn:nbn:de:0030-drops-143357},
doi = {10.4230/LIPIcs.ITC.2021.16},
annote = {Keywords: Secure keys, Secure private randomness, Gray-Wyner system, Cryptographic complexity, Nondeterministic communication complexity, Leakage-resilience, Combinatorial optimization, Product dimension, Zarankiewicz problem, Algebraic lower-bounding techniques, P₄-free partition number, P₄-free cover number}
}
Document
Replacing Probability Distributions in Security Games via Hellinger Distance
Abstract
Security of cryptographic primitives is usually proved by assuming "ideal" probability distributions. We need to replace them with approximated "real" distributions in the real-world systems without losing the security level. We demonstrate that the Hellinger distance is useful for this problem, while the statistical distance is mainly used in the cryptographic literature. First, we show that for preserving λ-bit security of a given security game, the closeness of 2^{-λ/2} to the ideal distribution is sufficient for the Hellinger distance, whereas 2^{-λ} is generally required for the statistical distance. The result can be applied to both search and decision primitives through the bit security framework of Micciancio and Walter (Eurocrypt 2018). We also show that the Hellinger distance gives a tighter evaluation of closeness than the max-log distance when the distance is small. Finally, we show that the leftover hash lemma can be strengthened to the Hellinger distance. Namely, a universal family of hash functions gives a strong randomness extractor with optimal entropy loss for the Hellinger distance. Based on the results, a λ-bit entropy loss in randomness extractors is sufficient for preserving λ-bit security. The current understanding based on the statistical distance is that a 2λ-bit entropy loss is necessary.
Cite as
Kenji Yasunaga. Replacing Probability Distributions in Security Games via Hellinger Distance. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{yasunaga:LIPIcs.ITC.2021.17,
author = {Yasunaga, Kenji},
title = {{Replacing Probability Distributions in Security Games via Hellinger Distance}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {17:1--17:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.17},
URN = {urn:nbn:de:0030-drops-143361},
doi = {10.4230/LIPIcs.ITC.2021.17},
annote = {Keywords: Security proof, Hellinger distance, randomness extractor, entropy loss}
}
Document
Differentially Private Approximations of a Convex Hull in Low Dimensions
Abstract
We give the first differentially private algorithms that estimate a variety of geometric features of points in the Euclidean space, such as diameter, width, volume of convex hull, min-bounding box, min-enclosing ball, etc. Our work relies heavily on the notion of Tukey-depth. Instead of (non-privately) approximating the convex-hull of the given set of points P, our algorithms approximate the geometric features of D_{P}(κ) - the κ-Tukey region induced by P (all points of Tukey-depth κ or greater). Moreover, our approximations are all bi-criteria: for any geometric feature μ our (α,Δ)-approximation is a value "sandwiched" between (1-α)μ(D_P(κ)) and (1+α)μ(D_P(κ-Δ)).
Our work is aimed at producing a (α,Δ)-kernel of D_P(κ), namely a set 𝒮 such that (after a shift) it holds that (1-α)D_P(κ) ⊂ CH(𝒮) ⊂ (1+α)D_P(κ-Δ). We show that an analogous notion of a bi-critera approximation of a directional kernel, as originally proposed by [Pankaj K. Agarwal et al., 2004], fails to give a kernel, and so we result to subtler notions of approximations of projections that do yield a kernel. First, we give differentially private algorithms that find (α,Δ)-kernels for a "fat" Tukey-region. Then, based on a private approximation of the min-bounding box, we find a transformation that does turn D_P(κ) into a "fat" region but only if its volume is proportional to the volume of D_P(κ-Δ). Lastly, we give a novel private algorithm that finds a depth parameter κ for which the volume of D_P(κ) is comparable to the volume of D_P(κ-Δ). We hope our work leads to the further study of the intersection of differential privacy and computational geometry.
Cite as
Yue Gao and Or Sheffet. Differentially Private Approximations of a Convex Hull in Low Dimensions. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{gao_et_al:LIPIcs.ITC.2021.18,
author = {Gao, Yue and Sheffet, Or},
title = {{Differentially Private Approximations of a Convex Hull in Low Dimensions}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {18:1--18:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.18},
URN = {urn:nbn:de:0030-drops-143377},
doi = {10.4230/LIPIcs.ITC.2021.18},
annote = {Keywords: Differential Privacy, Computational Geometry, Tukey Depth}
}
Document
Differentially Oblivious Database Joins: Overcoming the Worst-Case Curse of Fully Oblivious Algorithms
Abstract
Numerous high-profile works have shown that access patterns to even encrypted databases can leak secret information and sometimes even lead to reconstruction of the entire database. To thwart access pattern leakage, the literature has focused on oblivious algorithms, where obliviousness requires that the access patterns leak nothing about the input data.
In this paper, we consider the Join operator, an important database primitive that has been extensively studied and optimized. Unfortunately, any fully oblivious Join algorithm would require always padding the result to the worst-case length which is quadratic in the data size N. In comparison, an insecure baseline incurs only O(R + N) cost where R is the true result length, and in the common case in practice, R is relatively short. As a typical example, when R = O(N), any fully oblivious algorithm must inherently incur a prohibitive, N-fold slowdown relative to the insecure baseline. Indeed, the (non-private) database and algorithms literature invariably focuses on studying the instance-specific rather than worst-case performance of database algorithms. Unfortunately, the stringent notion of full obliviousness precludes the design of efficient algorithms with non-trivial instance-specific performance.
To overcome this worst-case performance barrier of full obliviousness and enable algorithms with good instance-specific performance, we consider a relaxed notion of access pattern privacy called (ε, δ)-differential obliviousness (DO), originally proposed in the seminal work of Chan et al. (SODA'19). Rather than insisting that the access patterns leak no information whatsoever, the relaxed DO notion requires that the access patterns satisfy (ε, δ)-differential privacy. We show that by adopting the relaxed DO notion, we can obtain efficient database Join mechanisms whose instance-specific performance approximately matches the insecure baseline, while still offering a meaningful notion of privacy to individual users. Complementing our upper bound results, we also prove new lower bounds regarding the performance of any DO Join algorithm.
Differential obliviousness (DO) is a new notion and is a relatively unexplored territory. Following the pioneering investigations by Chan et al. and others, our work is among the very first to formally explore how DO can help overcome the worst-case performance curse of full obliviousness; moreover, we motivate our work with database applications. Our work shows new evidence why DO might be a promising notion, and opens up several exciting future directions.
Cite as
Shumo Chu, Danyang Zhuo, Elaine Shi, and T-H. Hubert Chan. Differentially Oblivious Database Joins: Overcoming the Worst-Case Curse of Fully Oblivious Algorithms. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{chu_et_al:LIPIcs.ITC.2021.19,
author = {Chu, Shumo and Zhuo, Danyang and Shi, Elaine and Chan, T-H. Hubert},
title = {{Differentially Oblivious Database Joins: Overcoming the Worst-Case Curse of Fully Oblivious Algorithms}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {19:1--19:24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.19},
URN = {urn:nbn:de:0030-drops-143386},
doi = {10.4230/LIPIcs.ITC.2021.19},
annote = {Keywords: differentially oblivious, database join, instance-specific performance}
}
Document
Communication Complexity of Private Simultaneous Quantum Messages Protocols
Abstract
The private simultaneous messages (PSM) model is a non-interactive version of the multiparty secure computation (MPC), which has been intensively studied to examine the communication cost of the secure computation. We consider its quantum counterpart, the private simultaneous quantum messages (PSQM) model, and examine the advantages of quantum communication and prior entanglement of this model.
In the PSQM model, k parties P₁,…,P_k initially share a common random string (or entangled states in a stronger setting), and they have private classical inputs x₁,…, x_k. Every P_i generates a quantum message from the private input x_i and the shared random string (entangled states), and then sends it to the referee R. Receiving the messages from the k parties, R computes F(x₁,…,x_k) from the messages. Then, R learns nothing except for F(x₁,…,x_k) as the privacy condition.
We obtain the following results for this PSQM model. (i) We demonstrate that the privacy condition inevitably increases the communication cost in the two-party PSQM model as well as in the classical case presented by Applebaum, Holenstein, Mishra, and Shayevitz [Journal of Cryptology(3), 916-953 (2020)]. In particular, we prove a lower bound (3-o(1))n of the communication complexity in PSQM protocols with a shared random string for random Boolean functions of 2n-bit input, which is larger than the trivial upper bound 2n of the communication complexity without the privacy condition. (ii) We demonstrate a factor two gap between the communication complexity of PSQM protocols with shared entangled states and with shared random strings by designing a multiparty PSQM protocol with shared entangled states for a total function that extends the two-party equality function. (iii) We demonstrate an exponential gap between the communication complexity of PSQM protocols with shared entangled states and with shared random strings for a two-party partial function.
Cite as
Akinori Kawachi and Harumichi Nishimura. Communication Complexity of Private Simultaneous Quantum Messages Protocols. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{kawachi_et_al:LIPIcs.ITC.2021.20,
author = {Kawachi, Akinori and Nishimura, Harumichi},
title = {{Communication Complexity of Private Simultaneous Quantum Messages Protocols}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {20:1--20:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.20},
URN = {urn:nbn:de:0030-drops-143393},
doi = {10.4230/LIPIcs.ITC.2021.20},
annote = {Keywords: Communication complexity, private simultaneous messages, quantum protocols, secure multi-party computation}
}
Document
Quantum-Access Security of the Winternitz One-Time Signature Scheme
Abstract
Quantum-access security, where an attacker is granted superposition access to secret-keyed functionalities, is a fundamental security model and its study has inspired results in post-quantum security. We revisit, and fill a gap in, the quantum-access security analysis of the Lamport one-time signature scheme (OTS) in the quantum random oracle model (QROM) by Alagic et al. (Eurocrypt 2020). We then go on to generalize the technique to the Winternitz OTS. Along the way, we develop a tool for the analysis of hash chains in the QROM based on the superposition oracle technique by Zhandry (Crypto 2019) which might be of independent interest.
Cite as
Christian Majenz, Chanelle Matadah Manfouo, and Maris Ozols. Quantum-Access Security of the Winternitz One-Time Signature Scheme. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{majenz_et_al:LIPIcs.ITC.2021.21,
author = {Majenz, Christian and Manfouo, Chanelle Matadah and Ozols, Maris},
title = {{Quantum-Access Security of the Winternitz One-Time Signature Scheme}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {21:1--21:22},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.21},
URN = {urn:nbn:de:0030-drops-143406},
doi = {10.4230/LIPIcs.ITC.2021.21},
annote = {Keywords: quantum cryptography, one-time signature schemes, quantum random oracle model, post-quantum cryptography, quantum world, hash-based signatures, information-theoretic security}
}
Document
On the Security of Proofs of Sequential Work in a Post-Quantum World
Abstract
A Proof of Sequential Work (PoSW) allows a prover to convince a resource-bounded verifier that the prover invested a substantial amount of sequential time to perform some underlying computation. PoSWs have many applications including time-stamping, blockchain design, and universally verifiable CPU benchmarks. Mahmoody, Moran, and Vadhan (ITCS 2013) gave the first construction of a PoSW in the random oracle model though the construction relied on expensive depth-robust graphs. In a recent breakthrough, Cohen and Pietrzak (EUROCRYPT 2018) gave an efficient PoSW construction that does not require expensive depth-robust graphs.
In the classical parallel random oracle model, it is straightforward to argue that any successful PoSW attacker must produce a long ℋ-sequence and that any malicious party running in sequential time T-1 will fail to produce an ℋ-sequence of length T except with negligible probability. In this paper, we prove that any quantum attacker running in sequential time T-1 will fail to produce an ℋ-sequence except with negligible probability - even if the attacker submits a large batch of quantum queries in each round. The proof is substantially more challenging and highlights the power of Zhandry’s recent compressed oracle technique (CRYPTO 2019). We further extend this result to establish post-quantum security of a non-interactive PoSW obtained by applying the Fiat-Shamir transform to Cohen and Pietrzak’s efficient construction (EUROCRYPT 2018).
Cite as
Jeremiah Blocki, Seunghoon Lee, and Samson Zhou. On the Security of Proofs of Sequential Work in a Post-Quantum World. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 22:1-22:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{blocki_et_al:LIPIcs.ITC.2021.22,
author = {Blocki, Jeremiah and Lee, Seunghoon and Zhou, Samson},
title = {{On the Security of Proofs of Sequential Work in a Post-Quantum World}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {22:1--22:27},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.22},
URN = {urn:nbn:de:0030-drops-143415},
doi = {10.4230/LIPIcs.ITC.2021.22},
annote = {Keywords: Proof of Sequential Work, Parallel Quantum Random Oracle Model, Lower Bounds}
}
Document
Fooling an Unbounded Adversary with a Short Key, Repeatedly: The Honey Encryption Perspective
Abstract
This article is motivated by the classical results from Shannon that put the simple and elegant one-time pad away from practice: key length has to be as large as message length and the same key could not be used more than once. In particular, we consider encryption algorithm to be defined relative to specific message distributions in order to trade for unconditional security. Such a notion named honey encryption (HE) was originally proposed for achieving best possible security for password based encryption where secrete key may have very small amount of entropy.
Exploring message distributions as in HE indeed helps circumvent the classical restrictions on secret keys.We give a new and very simple honey encryption scheme satisfying the unconditional semantic security (for the targeted message distribution) in the standard model (all previous constructions are in the random oracle model, even for message recovery security only). Our new construction can be paired with an extremely simple yet "tighter" analysis, while all previous analyses (even for message recovery security only) were fairly complicated and require stronger assumptions. We also show a concrete instantiation further enables the secret key to be used for encrypting multiple messages.
Cite as
Xinze Li, Qiang Tang, and Zhenfeng Zhang. Fooling an Unbounded Adversary with a Short Key, Repeatedly: The Honey Encryption Perspective. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{li_et_al:LIPIcs.ITC.2021.23,
author = {Li, Xinze and Tang, Qiang and Zhang, Zhenfeng},
title = {{Fooling an Unbounded Adversary with a Short Key, Repeatedly: The Honey Encryption Perspective}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {23:1--23:21},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.23},
URN = {urn:nbn:de:0030-drops-143425},
doi = {10.4230/LIPIcs.ITC.2021.23},
annote = {Keywords: unconditional security, information theoretic encryption, honey encryption}
}
Document
T₅: Hashing Five Inputs with Three Compression Calls
Abstract
Given 2n-to-n compression functions h₁,h₂,h₃, we build a new 5n-to-n compression function T₅, using only 3 compression calls:
T₅(m₁, m₂, m₃, m₄, m₅) : = h₃(h₁(m₁, m₂)⊕ m₅ , h₂(m₃, m₄)⊕ m₅) ⊕ m₅
We prove that this construction matches Stam’s bound, by providing Õ(q²/2ⁿ) collision security and O(q³/2^{2n}+ nq/2ⁿ) preimage security (the latter term dominates in the region of interest, when q < 2^{n/2}). In particular, it provides birthday security for hashing 5 inputs using three 2n-to-n compression calls, instead of only 4 inputs in prior constructions. Thus, we get a sequential variant of the Merkle-Damgård (MD) hashing, where t message blocks are hashed using only 3t/4 calls to the 2n-to-n compression functions; a 25% saving over traditional hash function constructions. This time reduces to t/4 (resp. t/2) sequential calls using 3 (resp. 2) parallel execution units; saving a factor of 4 (resp. 2) over the traditional MD-hashing, where parallelism does not help to process one message. We also get a novel variant of a Merkle tree, where t message blocks can be processed using 0.75(t-1) compression function calls and depth 0.86 log₂ t, thereby saving 25% in the number of calls and 14% in the update time over Merkle trees. We provide two modes for a local opening of a particular message block: conservative and aggressive. The former retains the birthday security, but provides longer proofs and local verification time than the traditional Merkle tree. For the aggressive variant, we reduce the proof length to a 29% overhead compared to Merkle trees (1.29log₂ t vs log₂ t), but the verification time is now 14% faster (0.86log₂ t vs log₂ t). However, birthday security is only shown under a plausible conjecture related to the 3-XOR problem, and only for the (common, but not universal) setting where the root of the Merkle tree is known to correspond to a valid t-block message.
Cite as
Yevgeniy Dodis, Dmitry Khovratovich, Nicky Mouha, and Mridul Nandi. T₅: Hashing Five Inputs with Three Compression Calls. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 24:1-24:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{dodis_et_al:LIPIcs.ITC.2021.24,
author = {Dodis, Yevgeniy and Khovratovich, Dmitry and Mouha, Nicky and Nandi, Mridul},
title = {{T₅: Hashing Five Inputs with Three Compression Calls}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {24:1--24:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.24},
URN = {urn:nbn:de:0030-drops-143430},
doi = {10.4230/LIPIcs.ITC.2021.24},
annote = {Keywords: hash functions, Merkle trees, Merkle-Damg\r{a}rd, collision resistance}
}
Document
Post-Compromise Security in Self-Encryption
Abstract
In self-encryption, a device encrypts some piece of information for itself to decrypt in the future. We are interested in security of self-encryption when the state occasionally leaks. Applications that use self-encryption include cloud storage, when a client encrypts files to be stored, and in 0-RTT session resumptions, when a server encrypts a resumption key to be kept by the client. Previous works focused on forward security and resistance to replay attacks. In our work, we study post-compromise security (PCS). PCS was achieved in ratcheted instant messaging schemes, at the price of having an inflating state size. An open question was whether state inflation was necessary. In our results, we prove that post-compromise security implies a super-linear state size in terms of the number of active ciphertexts which can still be decrypted. We apply our result to self-encryption for cloud storage, 0-RTT session resumption, and secure messaging. We further show how to construct a secure scheme matching our bound on the state size up to a constant factor.
Cite as
Gwangbae Choi, F. Betül Durak, and Serge Vaudenay. Post-Compromise Security in Self-Encryption. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 25:1-25:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{choi_et_al:LIPIcs.ITC.2021.25,
author = {Choi, Gwangbae and Durak, F. Bet\"{u}l and Vaudenay, Serge},
title = {{Post-Compromise Security in Self-Encryption}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {25:1--25:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.25},
URN = {urn:nbn:de:0030-drops-143447},
doi = {10.4230/LIPIcs.ITC.2021.25},
annote = {Keywords: Encryption, Ratchet, Post-Compromise Security, Instant Messaging, Session Resumption, Cloud Storage}
}
Document
Generic-Group Identity-Based Encryption: A Tight Impossibility Result
Abstract
Following the pioneering work of Boneh and Franklin (CRYPTO '01), the challenge of constructing an identity-based encryption scheme based on the Diffie-Hellman assumption remained unresolved for more than 15 years. Evidence supporting this lack of success was provided by Papakonstantinou, Rackoff and Vahlis (ePrint '12), who ruled out the existence of generic-group identity-based encryption schemes supporting an identity space of sufficiently large polynomial size. Nevertheless, the breakthrough result of Döttling and Garg (CRYPTO '17) settled this long-standing challenge via a non-generic construction.
We prove a tight impossibility result for generic-group identity-based encryption, ruling out the existence of any non-trivial construction: We show that any scheme whose public parameters include n_pp group elements may support at most n_pp identities. This threshold is trivially met by any generic-group public-key encryption scheme whose public keys consist of a single group element (e.g., ElGamal encryption).
In the context of algebraic constructions, generic realizations are often both conceptually simpler and more efficient than non-generic ones. Thus, identifying exact thresholds for the limitations of generic groups is not only of theoretical significance but may in fact have practical implications when considering concrete security parameters.
Cite as
Gili Schul-Ganz and Gil Segev. Generic-Group Identity-Based Encryption: A Tight Impossibility Result. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 26:1-26:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{schulganz_et_al:LIPIcs.ITC.2021.26,
author = {Schul-Ganz, Gili and Segev, Gil},
title = {{Generic-Group Identity-Based Encryption: A Tight Impossibility Result}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {26:1--26:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.26},
URN = {urn:nbn:de:0030-drops-143455},
doi = {10.4230/LIPIcs.ITC.2021.26},
annote = {Keywords: Identity-based encryption, generic-group model}
}