DROPS

Document

DOI: 10.4230/LIPIcs.ITC.2024.3

Are Your Keys Protected? Time Will Tell

Authors: Yoav Ben Dov, Liron David, Moni Naor, and Elad Tzalik

Published in: LIPIcs, Volume 304, 5th Conference on Information-Theoretic Cryptography (ITC 2024)

Abstract

Side channel attacks, and in particular timing attacks, are a fundamental obstacle to obtaining secure implementation of algorithms and cryptographic protocols, and have been widely researched for decades. While cryptographic definitions for the security of cryptographic systems have been well established for decades, none of these accepted definitions take into account the running time information leaked from executing the system. In this work, we give the foundation of new cryptographic definitions for cryptographic systems that take into account information about their leaked running time, focusing mainly on keyed functions such as signature and encryption schemes. Specifically, [(1)] 1) We define several cryptographic properties to express the claim that the timing information does not help an adversary to extract sensitive information, e.g. the key or the queries made. We highlight the definition of key-obliviousness, which means that an adversary cannot tell whether it received the timing of the queries with the actual key or the timing of the same queries with a random key. 2) We present a construction of key-oblivious pseudorandom permutations on a small or medium-sized domain. This construction is not "fixed-time," and at the same time is secure against any number of queries even in case the adversary knows the running time exactly. Our construction, which we call Janus Sometimes Recurse, is a variant of the "Sometimes Recurse" shuffle by Morris and Rogaway. 3) We suggest a new security notion for keyed functions, called noticeable security, and prove that cryptographic schemes that have noticeable security remain secure even when the exact timings are leaked, provided the implementation is key-oblivious. We show that our notion applies to cryptographic signatures, private key encryption and PRPs.

Cite as

Yoav Ben Dov, Liron David, Moni Naor, and Elad Tzalik. Are Your Keys Protected? Time Will Tell. In 5th Conference on Information-Theoretic Cryptography (ITC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 304, pp. 3:1-3:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bendov_et_al:LIPIcs.ITC.2024.3,
  author =	{Ben Dov, Yoav and David, Liron and Naor, Moni and Tzalik, Elad},
  title =	{{Are Your Keys Protected? Time Will Tell}},
  booktitle =	{5th Conference on Information-Theoretic Cryptography (ITC 2024)},
  pages =	{3:1--3:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-333-1},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{304},
  editor =	{Aggarwal, Divesh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2024.3},
  URN =		{urn:nbn:de:0030-drops-205119},
  doi =		{10.4230/LIPIcs.ITC.2024.3},
  annote =	{Keywords: Side channel attacks, Timing attacks, Keyed functions, Key oblivious, Noticeable security}
}

Document

DOI: 10.4230/LIPIcs.ITC.2024.6

Information-Theoretic Single-Server PIR in the Shuffle Model

Authors: Yuval Ishai, Mahimna Kelkar, Daniel Lee, and Yiping Ma

Published in: LIPIcs, Volume 304, 5th Conference on Information-Theoretic Cryptography (ITC 2024)

Abstract

We revisit the problem of private information retrieval (PIR) in the shuffle model, where queries can be made anonymously by multiple clients. We present the first single-server PIR protocol in this model that has sublinear per-client communication and information-theoretic security. Moreover, following one-time preprocessing on the server side, our protocol only requires sublinear per-client computation. Concretely, for every γ > 0, the protocol has O(n^{γ}) communication and computation costs per (stateless) client, with 1/poly(n) statistical security, assuming that a size-n database is simultaneously accessed by poly(n) clients. This should be contrasted with the recent breakthrough result of Lin, Mook, and Wichs (STOC 2023) on doubly efficient PIR in the standard model, which is (inherently) limited to computational security.

Cite as

Yuval Ishai, Mahimna Kelkar, Daniel Lee, and Yiping Ma. Information-Theoretic Single-Server PIR in the Shuffle Model. In 5th Conference on Information-Theoretic Cryptography (ITC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 304, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ishai_et_al:LIPIcs.ITC.2024.6,
  author =	{Ishai, Yuval and Kelkar, Mahimna and Lee, Daniel and Ma, Yiping},
  title =	{{Information-Theoretic Single-Server PIR in the Shuffle Model}},
  booktitle =	{5th Conference on Information-Theoretic Cryptography (ITC 2024)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-333-1},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{304},
  editor =	{Aggarwal, Divesh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2024.6},
  URN =		{urn:nbn:de:0030-drops-205142},
  doi =		{10.4230/LIPIcs.ITC.2024.6},
  annote =	{Keywords: Private information retrieval, Shuffle model}
}

Document

DOI: 10.4230/LIPIcs.ITC.2024.10

Secure Multiparty Computation of Symmetric Functions with Polylogarithmic Bottleneck Complexity and Correlated Randomness

Authors: Reo Eriguchi

Published in: LIPIcs, Volume 304, 5th Conference on Information-Theoretic Cryptography (ITC 2024)

Abstract

Bottleneck complexity is an efficiency measure of secure multiparty computation (MPC) protocols introduced to achieve load-balancing in large-scale networks, which is defined as the maximum communication complexity required by any one player within the protocol execution. Towards the goal of achieving low bottleneck complexity, prior works proposed MPC protocols for computing symmetric functions in the correlated randomness model, where players are given input-independent correlated randomness in advance. However, the previous protocols with polylogarithmic bottleneck complexity in the number n of players require a large amount of correlated randomness that is linear in n, which limits the per-party efficiency as receiving and storing correlated randomness are the bottleneck for efficiency. In this work, we present for the first time MPC protocols for symmetric functions such that bottleneck complexity and the amount of correlated randomness are both polylogarithmic in n, assuming semi-honest adversaries colluding with at most n-o(n) players. Furthermore, one of our protocols is even computationally efficient in that each player performs only polylog(n) arithmetic operations while the computational complexity of the previous protocols is O(n). Technically, our efficiency improvements come from novel protocols based on ramp secret sharing to realize basic functionalities with low bottleneck complexity, which we believe may be of interest beyond their applications to secure computation of symmetric functions.

Cite as

Reo Eriguchi. Secure Multiparty Computation of Symmetric Functions with Polylogarithmic Bottleneck Complexity and Correlated Randomness. In 5th Conference on Information-Theoretic Cryptography (ITC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 304, pp. 10:1-10:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{eriguchi:LIPIcs.ITC.2024.10,
  author =	{Eriguchi, Reo},
  title =	{{Secure Multiparty Computation of Symmetric Functions with Polylogarithmic Bottleneck Complexity and Correlated Randomness}},
  booktitle =	{5th Conference on Information-Theoretic Cryptography (ITC 2024)},
  pages =	{10:1--10:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-333-1},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{304},
  editor =	{Aggarwal, Divesh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2024.10},
  URN =		{urn:nbn:de:0030-drops-205182},
  doi =		{10.4230/LIPIcs.ITC.2024.10},
  annote =	{Keywords: Secure multiparty computation, Bottleneck complexity, Secret sharing}
}

Document

DOI: 10.4230/LIPIcs.CCC.2024.11

Linear-Size Boolean Circuits for Multiselection

Authors: Justin Holmgren and Ron Rothblum

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

We study the circuit complexity of the multiselection problem: given an input string x ∈ {0,1}ⁿ along with indices i_1,… ,i_q ∈ [n], output (x_{i_1},… ,x_{i_q}). A trivial lower bound for the circuit size is the input length n + q⋅log(n), but the straightforward construction has size Θ(q⋅n). Our main result is an O(n+q⋅log³(n))-size and O(log(n+q))-depth circuit for multiselection. In particular, for any q ≤ n/log³(n) the circuit has linear size and logarithmic depth. Prior to our work no linear-size circuit for multiselection was known for any q = ω(1) and regardless of depth.

Cite as

Justin Holmgren and Ron Rothblum. Linear-Size Boolean Circuits for Multiselection. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{holmgren_et_al:LIPIcs.CCC.2024.11,
  author =	{Holmgren, Justin and Rothblum, Ron},
  title =	{{Linear-Size Boolean Circuits for Multiselection}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.11},
  URN =		{urn:nbn:de:0030-drops-204070},
  doi =		{10.4230/LIPIcs.CCC.2024.11},
  annote =	{Keywords: Private Information Retrieval, Batch Selection, Boolean Circuits}
}

Document

DOI: 10.4230/LIPIcs.CCC.2024.19

Information Dissemination via Broadcasts in the Presence of Adversarial Noise

Authors: Klim Efremenko, Gillat Kol, Dmitry Paramonov, Ran Raz, and Raghuvansh R. Saxena

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

We initiate the study of error correcting codes over the multi-party adversarial broadcast channel. Specifically, we consider the classic information dissemination problem where n parties, each holding an input bit, wish to know each other’s input. For this, they communicate in rounds, where, in each round, one designated party sends a bit to all other parties over a channel governed by an adversary that may corrupt a constant fraction of the received communication. We mention that the dissemination problem was studied in the stochastic noise model since the 80’s. While stochastic noise in multi-party channels has received quite a bit of attention, the case of adversarial noise has largely been avoided, as such channels cannot handle more than a 1/n-fraction of errors. Indeed, this many errors allow an adversary to completely corrupt the incoming or outgoing communication for one of the parties and fail the protocol. Curiously, we show that by eliminating these "trivial" attacks, one can get a simple protocol resilient to a constant fraction of errors. Thus, a model that rules out such attacks is both necessary and sufficient to get a resilient protocol. The main shortcoming of our dissemination protocol is its length: it requires Θ(n²) communication rounds whereas n rounds suffice in the absence of noise. Our main result is a matching lower bound of Ω(n²) on the length of any dissemination protocol in our model. Our proof first "gets rid" of the channel noise by converting it to a form of "input noise", showing that a noisy dissemination protocol implies a (noiseless) protocol for a version of the direct sum gap-majority problem. We conclude the proof with a tight lower bound for the latter problem, which may be of independent interest.

Cite as

Klim Efremenko, Gillat Kol, Dmitry Paramonov, Ran Raz, and Raghuvansh R. Saxena. Information Dissemination via Broadcasts in the Presence of Adversarial Noise. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 19:1-19:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{efremenko_et_al:LIPIcs.CCC.2024.19,
  author =	{Efremenko, Klim and Kol, Gillat and Paramonov, Dmitry and Raz, Ran and Saxena, Raghuvansh R.},
  title =	{{Information Dissemination via Broadcasts in the Presence of Adversarial Noise}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{19:1--19:33},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.19},
  URN =		{urn:nbn:de:0030-drops-204159},
  doi =		{10.4230/LIPIcs.CCC.2024.19},
  annote =	{Keywords: Radio Networks, Interactive Coding, Error Correcting Codes}
}

Document

DOI: 10.4230/LIPIcs.CCC.2024.21

Public-Key Pseudoentanglement and the Hardness of Learning Ground State Entanglement Structure

Authors: Adam Bouland, Bill Fefferman, Soumik Ghosh, Tony Metger, Umesh Vazirani, Chenyi Zhang, and Zixin Zhou

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

Given a local Hamiltonian, how difficult is it to determine the entanglement structure of its ground state? We show that this problem is computationally intractable even if one is only trying to decide if the ground state is volume-law vs near area-law entangled. We prove this by constructing strong forms of pseudoentanglement in a public-key setting, where the circuits used to prepare the states are public knowledge. In particular, we construct two families of quantum circuits which produce volume-law vs near area-law entangled states, but nonetheless the classical descriptions of the circuits are indistinguishable under the Learning with Errors (LWE) assumption. Indistinguishability of the circuits then allows us to translate our construction to Hamiltonians. Our work opens new directions in Hamiltonian complexity, for example whether it is difficult to learn certain phases of matter.

Cite as

Adam Bouland, Bill Fefferman, Soumik Ghosh, Tony Metger, Umesh Vazirani, Chenyi Zhang, and Zixin Zhou. Public-Key Pseudoentanglement and the Hardness of Learning Ground State Entanglement Structure. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 21:1-21:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bouland_et_al:LIPIcs.CCC.2024.21,
  author =	{Bouland, Adam and Fefferman, Bill and Ghosh, Soumik and Metger, Tony and Vazirani, Umesh and Zhang, Chenyi and Zhou, Zixin},
  title =	{{Public-Key Pseudoentanglement and the Hardness of Learning Ground State Entanglement Structure}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{21:1--21:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.21},
  URN =		{urn:nbn:de:0030-drops-204175},
  doi =		{10.4230/LIPIcs.CCC.2024.21},
  annote =	{Keywords: Quantum computing, Quantum complexity theory, entanglement}
}

Document

DOI: 10.4230/LIPIcs.CCC.2024.24

Distribution-Free Proofs of Proximity

Authors: Hugo Aaronson, Tom Gur, Ninad Rajgopal, and Ron D. Rothblum

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

Motivated by the fact that input distributions are often unknown in advance, distribution-free property testing considers a setting in which the algorithmic task is to accept functions f: [n] → {0,1} having a certain property Π and reject functions that are ε-far from Π, where the distance is measured according to an arbitrary and unknown input distribution 𝒟 ∼ [n]. As usual in property testing, the tester is required to do so while making only a sublinear number of input queries, but as the distribution is unknown, we also allow a sublinear number of samples from the distribution 𝒟. In this work we initiate the study of distribution-free interactive proofs of proximity (df-IPPs) in which the distribution-free testing algorithm is assisted by an all powerful but untrusted prover. Our main result is that for any problem Π ∈ NC, any proximity parameter ε > 0, and any (trade-off) parameter τ ≤ √n, we construct a df-IPP for Π with respect to ε, that has query and sample complexities τ+O(1/ε), and communication complexity Õ(n/τ + 1/ε). For τ as above and sufficiently large ε (namely, when ε > τ/n), this result matches the parameters of the best-known general purpose IPPs in the standard uniform setting. Moreover, for such τ, its parameters are optimal up to poly-logarithmic factors under reasonable cryptographic assumptions for the same regime of ε as the uniform setting, i.e., when ε ≥ 1/τ. For smaller values of ε (i.e., when ε < τ/n), our protocol has communication complexity Ω(1/ε), which is worse than the Õ(n/τ) communication complexity of the uniform IPPs (with the same query complexity). With the aim of improving on this gap, we further show that for IPPs over specialised, but large distribution families, such as sufficiently smooth distributions and product distributions, the communication complexity can be reduced to Õ(n/τ^{1-o(1)}). In addition, we show that for certain natural families of languages, such as symmetric and (relaxed) self-correctable languages, it is possible to further improve the efficiency of distribution-free IPPs.

Cite as

Hugo Aaronson, Tom Gur, Ninad Rajgopal, and Ron D. Rothblum. Distribution-Free Proofs of Proximity. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{aaronson_et_al:LIPIcs.CCC.2024.24,
  author =	{Aaronson, Hugo and Gur, Tom and Rajgopal, Ninad and Rothblum, Ron D.},
  title =	{{Distribution-Free Proofs of Proximity}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{24:1--24:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.24},
  URN =		{urn:nbn:de:0030-drops-204204},
  doi =		{10.4230/LIPIcs.CCC.2024.24},
  annote =	{Keywords: Property Testing, Interactive Proofs, Distribution-Free Property Testing}
}

Document

DOI: 10.4230/LIPIcs.CCC.2024.36

Gap MCSP Is Not (Levin) NP-Complete in Obfustopia

Authors: Noam Mazor and Rafael Pass

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract

We demonstrate that under believable cryptographic hardness assumptions, Gap versions of standard meta-complexity problems, such as the Minimum Circuit Size Problem (MCSP) and the Minimum Time-Bounded Kolmogorov Complexity problem (MKTP) are not NP-complete w.r.t. Levin (i.e., witness-preserving many-to-one) reductions. In more detail: - Assuming the existence of indistinguishability obfuscation, and subexponentially-secure one-way functions, an appropriate Gap version of MCSP is not NP-complete under randomized Levin-reductions. - Assuming the existence of subexponentially-secure indistinguishability obfuscation, subexponentially-secure one-way functions and injective PRGs, an appropriate Gap version of MKTP is not NP-complete under randomized Levin-reductions.

Cite as

Noam Mazor and Rafael Pass. Gap MCSP Is Not (Levin) NP-Complete in Obfustopia. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 36:1-36:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mazor_et_al:LIPIcs.CCC.2024.36,
  author =	{Mazor, Noam and Pass, Rafael},
  title =	{{Gap MCSP Is Not (Levin) NP-Complete in Obfustopia}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{36:1--36:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.36},
  URN =		{urn:nbn:de:0030-drops-204322},
  doi =		{10.4230/LIPIcs.CCC.2024.36},
  annote =	{Keywords: Kolmogorov complexity, MCSP, Levin Reduction}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.92

Algorithms for the Generalized Poset Sorting Problem

Authors: Shaofeng H.-C. Jiang, Wenqian Wang, Yubo Zhang, and Yuhao Zhang

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

We consider a generalized poset sorting problem (GPS), in which we are given a query graph G = (V, E) and an unknown poset 𝒫(V, ≺) that is defined on the same vertex set V, and the goal is to make as few queries as possible to edges in G in order to fully recover 𝒫, where each query (u, v) returns the relation between u, v, i.e., u ≺ v, v ≺ u or u ̸ ∼ v. This generalizes both the poset sorting problem [Faigle et al., SICOMP 88] and the generalized sorting problem [Huang et al., FOCS 11]. We give algorithms with Õ(n poly(k)) query complexity when G is a complete bipartite graph or G is stochastic under the Erdős-Rényi model, where k is the width of the poset, and these generalize [Daskalakis et al., SICOMP 11] which only studies complete graph G. Both results are based on a unified framework that reduces the poset sorting to partitioning the vertices with respect to a given pivot element, which may be of independent interest. Moreover, we also propose novel algorithms to implement this partition oracle. Notably, we suggest a randomized BFS with vertex skipping for the stochastic G, and it yields a nearly-tight bound even for the special case of generalized sorting (for stochastic G) which is comparable to the main result of a recent work [Kuszmaul et al., FOCS 21] but is conceptually different and simplified. Our study of GPS also leads to a new Õ(n^{1 - 1 / (2W)}) competitive ratio for the so-called weighted generalized sorting problem where W is the number of distinct weights in the query graph. This problem was considered as an open question in [Charikar et al., JCSS 02], and our result makes important progress as it yields the first nontrivial sublinear ratio for general weighted query graphs (for any bounded W). We obtain this via an Õ(nk + n^{1.5}) query complexity algorithm for the case where every edge in G is guaranteed to be comparable in the poset, which generalizes a Õ(n^{1.5}) bound for generalized sorting [Huang et al., FOCS 11].

Cite as

Shaofeng H.-C. Jiang, Wenqian Wang, Yubo Zhang, and Yuhao Zhang. Algorithms for the Generalized Poset Sorting Problem. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 92:1-92:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{jiang_et_al:LIPIcs.ICALP.2024.92,
  author =	{Jiang, Shaofeng H.-C. and Wang, Wenqian and Zhang, Yubo and Zhang, Yuhao},
  title =	{{Algorithms for the Generalized Poset Sorting Problem}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{92:1--92:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.92},
  URN =		{urn:nbn:de:0030-drops-202359},
  doi =		{10.4230/LIPIcs.ICALP.2024.92},
  annote =	{Keywords: sorting, poset sorting, generalized sorting}
}

Document

DOI: 10.4230/LIPIcs.ITC.2022.10

Refuting the Dream XOR Lemma via Ideal Obfuscation and Resettable MPC

Authors: Saikrishna Badrinarayanan, Yuval Ishai, Dakshita Khurana, Amit Sahai, and Daniel Wichs

Published in: LIPIcs, Volume 230, 3rd Conference on Information-Theoretic Cryptography (ITC 2022)

Abstract

We provide counterexamples to the "dream" version of Yao’s XOR Lemma. In particular, we put forward explicit candidates for hard predicates, such that the advantage of predicting the XOR of many independent copies does not decrease beyond some fixed negligible function, even as the number of copies gets arbitrarily large. We provide two such constructions: - Our first construction is in the ideal obfuscation model (alternatively, assuming virtual black-box obfuscation for a concrete class of circuits). It develops a general framework that may be of broader interest, and allows us to embed an instance of a resettably-secure multiparty computation protocol into a one-way function. Along the way, we design the first resettably-secure multiparty computation protocol for general functionalities in the plain model with super-polynomial simulation, under standard assumptions. - The second construction relies on public-coin differing-inputs obfuscation (PCdiO) along with a certain form of hash-function security called extended second-preimage resistance (ESPR). It starts with a previously known counterexample to the dream direct-product hardness amplification based on ESPR, and uses PCdiO to upgrade it into a counterexample for the XOR lemma. Prior to our work, even completely heuristic counterexamples of this type were not known.

Cite as

Saikrishna Badrinarayanan, Yuval Ishai, Dakshita Khurana, Amit Sahai, and Daniel Wichs. Refuting the Dream XOR Lemma via Ideal Obfuscation and Resettable MPC. In 3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{badrinarayanan_et_al:LIPIcs.ITC.2022.10,
  author =	{Badrinarayanan, Saikrishna and Ishai, Yuval and Khurana, Dakshita and Sahai, Amit and Wichs, Daniel},
  title =	{{Refuting the Dream XOR Lemma via Ideal Obfuscation and Resettable MPC}},
  booktitle =	{3rd Conference on Information-Theoretic Cryptography (ITC 2022)},
  pages =	{10:1--10:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-238-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{230},
  editor =	{Dachman-Soled, Dana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2022.10},
  URN =		{urn:nbn:de:0030-drops-164885},
  doi =		{10.4230/LIPIcs.ITC.2022.10},
  annote =	{Keywords: XOR Lemma, Resettable MPC, Obfuscation}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.FSTTCS.2021.4

Indistinguishability Obfuscation from Well-Founded Assumptions (Invited Talk)

Authors: Huijia (Rachel) Lin

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract

Indistinguishability obfuscation, introduced by Barak et al. [Crypto 2001], aims to compile programs into unintelligible ones while preserving functionality. It is a fascinating and powerful object that has been shown to enable a host of new cryptographic goals and beyond. However, constructions of indistinguishability obfuscation have remained elusive, with all other proposals relying on heuristics or newly conjectured hardness assumptions. In this work, we show how to construct indistinguishability obfuscation from the subexponential hardness of three well-founded assumptions. We prove the following. Theorem (Informal) Assume sub-exponential hardness for the following: - the Learning Parity with Noise (LPN) assumption over general prime fields 𝔽_p with polynomially many LPN samples and error rate 1/k^δ, where k is the dimension of the LPN secret, and δ > 0 is any constant; - the existence of a Boolean Pseudo-Random Generator (PRG) in NC⁰ with stretch n^(1+τ), where n is the length of the PRG seed, and τ > 0 is any constant; - the Decision Linear (DLIN) assumption on symmetric bilinear groups of prime order. Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exist. As a corollary, all cryptographic goals that can be achieved using indistinguishability obfuscation can now be achieved assuming the above three assumptions. This includes fully homomorphic encryption, functional encryption, multiparty non-interactive key-exchange, succinct garbled random access machine, and many others. This is joint work with Aayush Jain (UCLA and NTT Research) and Amit Sahai (UCLA).

Cite as

Huijia (Rachel) Lin. Indistinguishability Obfuscation from Well-Founded Assumptions (Invited Talk). In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lin:LIPIcs.FSTTCS.2021.4,
  author =	{Lin, Huijia (Rachel)},
  title =	{{Indistinguishability Obfuscation from Well-Founded Assumptions}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{4:1--4:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.4},
  URN =		{urn:nbn:de:0030-drops-155154},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.4},
  annote =	{Keywords: Cryptography, indistinguishability obfuscation}
}

Document

DOI: 10.4230/LIPIcs.ITC.2020.6

Expander Graphs Are Non-Malleable Codes

Authors: Peter Michael Reichstein Rasmussen and Amit Sahai

Published in: LIPIcs, Volume 163, 1st Conference on Information-Theoretic Cryptography (ITC 2020)

Abstract

Any d-regular graph on n vertices with spectral expansion λ satisfying n = Ω(d³log(d)/λ) yields a O((λ^{3/2})/d)-non-malleable code for single-bit messages in the split-state model.

Cite as

Peter Michael Reichstein Rasmussen and Amit Sahai. Expander Graphs Are Non-Malleable Codes. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 6:1-6:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{rasmussen_et_al:LIPIcs.ITC.2020.6,
  author =	{Rasmussen, Peter Michael Reichstein and Sahai, Amit},
  title =	{{Expander Graphs Are Non-Malleable Codes}},
  booktitle =	{1st Conference on Information-Theoretic Cryptography (ITC 2020)},
  pages =	{6:1--6:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-151-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{163},
  editor =	{Tauman Kalai, Yael and Smith, Adam D. and Wichs, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2020.6},
  URN =		{urn:nbn:de:0030-drops-121114},
  doi =		{10.4230/LIPIcs.ITC.2020.6},
  annote =	{Keywords: Non-Malleable Code, Expander Graph, Mixing Lemma}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2020.82

Affine Determinant Programs: A Framework for Obfuscation and Witness Encryption

Authors: James Bartusek, Yuval Ishai, Aayush Jain, Fermi Ma, Amit Sahai, and Mark Zhandry

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract

An affine determinant program ADP: {0,1}^n → {0,1} is specified by a tuple (A,B_1,…,B_n) of square matrices over ?_q and a function Eval: ?_q → {0,1}, and evaluated on x ∈ {0,1}^n by computing Eval(det(A + ∑_{i∈[n]} x_i B_i)). In this work, we suggest ADPs as a new framework for building general-purpose obfuscation and witness encryption. We provide evidence to suggest that constructions following our ADP-based framework may one day yield secure, practically feasible obfuscation. As a proof-of-concept, we give a candidate ADP-based construction of indistinguishability obfuscation (i?) for all circuits along with a simple witness encryption candidate. We provide cryptanalysis demonstrating that our schemes resist several potential attacks, and leave further cryptanalysis to future work. Lastly, we explore practically feasible applications of our witness encryption candidate, such as public-key encryption with near-optimal key generation.

Cite as

James Bartusek, Yuval Ishai, Aayush Jain, Fermi Ma, Amit Sahai, and Mark Zhandry. Affine Determinant Programs: A Framework for Obfuscation and Witness Encryption. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 82:1-82:39, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bartusek_et_al:LIPIcs.ITCS.2020.82,
  author =	{Bartusek, James and Ishai, Yuval and Jain, Aayush and Ma, Fermi and Sahai, Amit and Zhandry, Mark},
  title =	{{Affine Determinant Programs: A Framework for Obfuscation and Witness Encryption}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{82:1--82:39},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.82},
  URN =		{urn:nbn:de:0030-drops-117679},
  doi =		{10.4230/LIPIcs.ITCS.2020.82},
  annote =	{Keywords: Obfuscation, Witness Encryption}
}

Document

DOI: 10.4230/LIPIcs.CCC.2018.23

A Tight Lower Bound for Entropy Flattening

Authors: Yi-Hsiu Chen, Mika Göös, Salil P. Vadhan, and Jiapeng Zhang

Published in: LIPIcs, Volume 102, 33rd Computational Complexity Conference (CCC 2018)

Abstract

We study entropy flattening: Given a circuit C_X implicitly describing an n-bit source X (namely, X is the output of C_X on a uniform random input), construct another circuit C_Y describing a source Y such that (1) source Y is nearly flat (uniform on its support), and (2) the Shannon entropy of Y is monotonically related to that of X. The standard solution is to have C_Y evaluate C_X altogether Theta(n^2) times on independent inputs and concatenate the results (correctness follows from the asymptotic equipartition property). In this paper, we show that this is optimal among black-box constructions: Any circuit C_Y for entropy flattening that repeatedly queries C_X as an oracle requires Omega(n^2) queries. Entropy flattening is a component used in the constructions of pseudorandom generators and other cryptographic primitives from one-way functions [Johan Håstad et al., 1999; John Rompel, 1990; Thomas Holenstein, 2006; Iftach Haitner et al., 2006; Iftach Haitner et al., 2009; Iftach Haitner et al., 2013; Iftach Haitner et al., 2010; Salil P. Vadhan and Colin Jia Zheng, 2012]. It is also used in reductions between problems complete for statistical zero-knowledge [Tatsuaki Okamoto, 2000; Amit Sahai and Salil P. Vadhan, 1997; Oded Goldreich et al., 1999; Vadhan, 1999]. The Theta(n^2) query complexity is often the main efficiency bottleneck. Our lower bound can be viewed as a step towards proving that the current best construction of pseudorandom generator from arbitrary one-way functions by Vadhan and Zheng (STOC 2012) has optimal efficiency.

Cite as

Yi-Hsiu Chen, Mika Göös, Salil P. Vadhan, and Jiapeng Zhang. A Tight Lower Bound for Entropy Flattening. In 33rd Computational Complexity Conference (CCC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 102, pp. 23:1-23:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{chen_et_al:LIPIcs.CCC.2018.23,
  author =	{Chen, Yi-Hsiu and G\"{o}\"{o}s, Mika and Vadhan, Salil P. and Zhang, Jiapeng},
  title =	{{A Tight Lower Bound for Entropy Flattening}},
  booktitle =	{33rd Computational Complexity Conference (CCC 2018)},
  pages =	{23:1--23:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-069-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{102},
  editor =	{Servedio, Rocco A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2018.23},
  URN =		{urn:nbn:de:0030-drops-88669},
  doi =		{10.4230/LIPIcs.CCC.2018.23},
  annote =	{Keywords: Entropy, One-way function}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2017.8

Hierarchical Functional Encryption

Authors: Zvika Brakerski, Nishanth Chandran, Vipul Goyal, Aayush Jain, Amit Sahai, and Gil Segev

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Abstract

Functional encryption provides fine-grained access control for encrypted data, allowing each user to learn only specific functions of the encrypted data. We study the notion of hierarchical functional encryption, which augments functional encryption with delegation capabilities, offering significantly more expressive access control. We present a generic transformation that converts any general-purpose public-key functional encryption scheme into a hierarchical one without relying on any additional assumptions. This significantly refines our understanding of the power of functional encryption, showing that the existence of functional encryption is equivalent to that of its hierarchical generalization. Instantiating our transformation with the existing functional encryption schemes yields a variety of hierarchical schemes offering various trade-offs between their delegation capabilities (i.e., the depth and width of their hierarchical structures) and underlying assumptions. When starting with a scheme secure against an unbounded number of collusions, we can support arbitrary hierarchical structures. In addition, even when starting with schemes that are secure against a bounded number of collusions (which are known to exist under rather minimal assumptions such as the existence of public-key encryption and shallow pseudorandom generators), we can support hierarchical structures of bounded depth and width.

Cite as

Zvika Brakerski, Nishanth Chandran, Vipul Goyal, Aayush Jain, Amit Sahai, and Gil Segev. Hierarchical Functional Encryption. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 8:1-8:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{brakerski_et_al:LIPIcs.ITCS.2017.8,
  author =	{Brakerski, Zvika and Chandran, Nishanth and Goyal, Vipul and Jain, Aayush and Sahai, Amit and Segev, Gil},
  title =	{{Hierarchical Functional Encryption}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{8:1--8:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.8},
  URN =		{urn:nbn:de:0030-drops-81992},
  doi =		{10.4230/LIPIcs.ITCS.2017.8},
  annote =	{Keywords: Functional Encryption, Delegatable Encryption, Cryptography}
}

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