17 Search Results for "Guo, Siyao"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.62
Improved Rate for Non-Malleable Codes and Time-Lock Puzzles

Authors: Cody Freitag, Ilan Komargodski, Manu Kondapaneni, and Jad Silbak

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Non-malleable codes allow a sender to transmit a message to a receiver, while providing a "best-possible" integrity guarantee to ensure that no attacker - who cannot already decode the message - can meaningfully tamper the message in transit. If tampered, the received message should either be invalid or unrelated to the original message. Non-malleable time-lock puzzles (TLPs) are a special case of non-malleable codes for bounded polynomial-depth tampering with very efficient encoding. In this work, we give generic techniques for constructing non-malleable codes and non-malleable TLPs with improved rate, which captures the ratio of a message’s length to its encoding length. A key contribution of our work is identifying a security notion for non-malleability, which we term "CCA-hiding", sufficient for our compilers. CCA-hiding is a relaxation of CCA-security for encryption or commitments to the fine-grained setting of codes, and requires that the encoded message remains hidden, even given a decoding oracle for any other codeword. Intriguingly, CCA-hiding does not imply non-malleability in the fine-grained setting, as is the case for encryption and commitments. Using our new techniques, we give the following constructions: - Rate-1 CCA-hiding TLPs in the plain model. - Rate-1 non-malleable codes for bounded polynomial-depth tampering in the auxiliary-input random oracle model (AI-ROM). - Rate-(1/2) non-malleable TLPs in the AI-ROM.
Cite as

Cody Freitag, Ilan Komargodski, Manu Kondapaneni, and Jad Silbak. Improved Rate for Non-Malleable Codes and Time-Lock Puzzles. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 62:1-62:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{freitag_et_al:LIPIcs.ITCS.2026.62,
  author =	{Freitag, Cody and Komargodski, Ilan and Kondapaneni, Manu and Silbak, Jad},
  title =	{{Improved Rate for Non-Malleable Codes and Time-Lock Puzzles}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{62:1--62:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.62},
  URN =		{urn:nbn:de:0030-drops-253490},
  doi =		{10.4230/LIPIcs.ITCS.2026.62},
  annote =	{Keywords: Non-malleable codes, Time-lock puzzles}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.116
Decentralized Data Archival: New Definitions and Constructions

Authors: Elaine Shi, Rose Silver, and Changrui Mu

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We initiate the study of a new abstraction called incremental decentralized data archival (iDDA). Specifically, imagine that there is an ever-growing, massive database such as a blockchain, a comprehensive human knowledge base like Wikipedia, or the Internet archive. We want to build a decentralized archival system for such datasets to ensure long-term robustness and sustainability. We identify several important properties that an iDDA scheme should satisfy. First, to promote heterogeneity and decentralization, we want to encourage even weak nodes with limited space (e.g., users' home computers) to contribute. The minimum space requirement to contribute should be approximately independent of the data size. Second, if a collection of nodes together receive rewards commensurate with contributing a total of m blocks of space, then we want the following reassurances: 1) if m is at least the database size, we should be able to reconstruct the entire dataset; and 2) these nodes should actually be committing roughly m space in aggregate - specifically, when m is much larger than the data size, these nodes cannot store only one copy of the database, and be able to impersonate arbitrarily many pseudonyms and get unbounded rewards. We propose new definitions that mathematically formalize the aforementioned requirements of an iDDA scheme. We also devise an efficient construction in the random oracle model which satisfies the desired security requirements. Our scheme incurs only Õ(1) audit cost, as well as Õ(1) update cost for both the publisher and each node, where Õ(⋅) hides polylogarithmic factors. Further, the minimum space provisioning required to contribute is as small as polylogarithmic. Our construction exposes several interesting technical challenges. Specifically, we show that a straightforward application of the standard hierarchical data structure fails, since both our security definition and the underlying cryptographic primitives we employ lack the desired compositional guarantees. We devise novel techniques to overcome these compositional issues, resulting in a construction with provable security while still retaining efficiency. Finally, our new definitions also make a conceptual contribution, and lay the theoretical groundwork for the study of iDDA. We raise several interesting open problems along this direction.
Cite as

Elaine Shi, Rose Silver, and Changrui Mu. Decentralized Data Archival: New Definitions and Constructions. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 116:1-116:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{shi_et_al:LIPIcs.ITCS.2026.116,
  author =	{Shi, Elaine and Silver, Rose and Mu, Changrui},
  title =	{{Decentralized Data Archival: New Definitions and Constructions}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{116:1--116:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.116},
  URN =		{urn:nbn:de:0030-drops-254037},
  doi =		{10.4230/LIPIcs.ITCS.2026.116},
  annote =	{Keywords: Decentralized Data Archival}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.112
Lower Bounds Beyond DNF of Parities

Authors: Artur Riazanov, Anastasia Sofronova, and Dmitry Sokolov

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We consider a subclass of AC⁰[2] circuits that simultaneously captures DNF∘Xor and depth-3 AC⁰ circuits. For this class we show a technique for proving lower bounds inspired by the top-down approach. We give lower bounds for the middle slice function, inner product function, and affine dispersers.
Cite as

Artur Riazanov, Anastasia Sofronova, and Dmitry Sokolov. Lower Bounds Beyond DNF of Parities. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 112:1-112:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{riazanov_et_al:LIPIcs.ITCS.2026.112,
  author =	{Riazanov, Artur and Sofronova, Anastasia and Sokolov, Dmitry},
  title =	{{Lower Bounds Beyond DNF of Parities}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{112:1--112:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.112},
  URN =		{urn:nbn:de:0030-drops-253996},
  doi =		{10.4230/LIPIcs.ITCS.2026.112},
  annote =	{Keywords: boolean circuits, top-down, unpredictability}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.55
Lifting to Randomized Parity Decision Trees

Authors: Farzan Byramji and Russell Impagliazzo

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We prove a lifting theorem from randomized decision tree depth to randomized parity decision tree (PDT) size. We use the same property of the gadget, stifling, which was introduced by Chattopadhyay, Mande, Sanyal and Sherif [ITCS 23] to prove a lifting theorem for deterministic PDTs. Moreover, even the milder condition that the gadget has minimum parity certificate complexity at least 2 suffices for lifting to randomized PDT size. To improve the dependence on the gadget g in the lower bounds for composed functions, we consider a related problem g_* whose inputs are certificates of g. It is implicit in the work of Chattopadhyay et al. that for any function f, lower bounds for the *-depth of f_* give lower bounds for the PDT size of f. We make this connection explicit in the deterministic case and show that it also holds for randomized PDTs. We then combine this with composition theorems for *-depth, which follow by adapting known composition theorems for decision trees. As a corollary, we get tight lifting theorems when the gadget is Indexing, Inner Product or Disjointness.
Cite as

Farzan Byramji and Russell Impagliazzo. Lifting to Randomized Parity Decision Trees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 55:1-55:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{byramji_et_al:LIPIcs.APPROX/RANDOM.2025.55,
  author =	{Byramji, Farzan and Impagliazzo, Russell},
  title =	{{Lifting to Randomized Parity Decision Trees}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{55:1--55:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.55},
  URN =		{urn:nbn:de:0030-drops-244213},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.55},
  annote =	{Keywords: Parity decision trees, composition}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.33
A Min-Entropy Approach to Multi-Party Communication Lower Bounds

Authors: Mi-Ying (Miryam) Huang, Xinyu Mao, Shuo Wang, Guangxu Yang, and Jiapeng Zhang

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
Information complexity is one of the most powerful techniques to prove information-theoretical lower bounds, in which Shannon entropy plays a central role. Though Shannon entropy has some convenient properties, such as the chain rule, it still has inherent limitations. One of the most notable barriers is the square-root loss, which appears in the square-root gap between entropy gaps and statistical distances, e.g., Pinsker’s inequality. To bypass this barrier, we introduce a new method based on min-entropy analysis. Building on this new method, we prove the following results. - An Ω(N^{∑_i α_i - max_i {α_i}}/k) randomized communication lower bound of the k-party set-intersection problem where the i-th party holds a random set of size ≈ N^{1-α_i}. - A tight Ω(n/k) randomized lower bound of the k-party Tree Pointer Jumping problems, improving an Ω(n/k²) lower bound by Chakrabarti, Cormode, and McGregor (STOC 08). - An Ω(n/k+√n) lower bound of the Chained Index problem, improving an Ω(n/k²) lower bound by Cormode, Dark, and Konrad (ICALP 19). Since these problems served as hard problems for numerous applications in streaming lower bounds and cryptography, our new lower bounds directly improve these streaming lower bounds and cryptography lower bounds. On the technical side, min-entropy does not have nice properties such as the chain rule. To address this issue, we enhance the structure-vs-pseudorandomness decomposition used by Göös, Pitassi, and Watson (FOCS 17) and Yang and Zhang (STOC 24); both papers used this decomposition to prove communication lower bounds. In this paper, we give a new breath to this method in the multi-party setting, presenting a new toolkit for proving multi-party communication lower bounds.
Cite as

Mi-Ying (Miryam) Huang, Xinyu Mao, Shuo Wang, Guangxu Yang, and Jiapeng Zhang. A Min-Entropy Approach to Multi-Party Communication Lower Bounds. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 33:1-33:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{huang_et_al:LIPIcs.CCC.2025.33,
  author =	{Huang, Mi-Ying (Miryam) and Mao, Xinyu and Wang, Shuo and Yang, Guangxu and Zhang, Jiapeng},
  title =	{{A Min-Entropy Approach to Multi-Party Communication Lower Bounds}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{33:1--33:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.33},
  URN =		{urn:nbn:de:0030-drops-237273},
  doi =		{10.4230/LIPIcs.CCC.2025.33},
  annote =	{Keywords: communication complexity, lifting theorems, set intersection, chained index}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.30
Online Condensing of Unpredictable Sources via Random Walks

Authors: Dean Doron, Dana Moshkovitz, Justin Oh, and David Zuckerman

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
A natural model of a source of randomness consists of a long stream of symbols X = X_1∘…∘X_t, with some guarantee on the entropy of X_i conditioned on the outcome of the prefix x_1,… ,x_{i-1}. We study unpredictable sources, a generalization of the almost Chor-Goldreich (CG) sources considered in [Doron et al., 2023]. In an unpredictable source X, for a typical draw of x ∼ X, for most i-s, the element x_i has a low probability of occurring given x_1,… ,x_{i-1}. Such a model relaxes the often unrealistic assumption of a CG source that for every i, and every x_1,… ,x_{i-1}, the next symbol X_i has sufficiently large entropy. Unpredictable sources subsume all previously considered notions of almost CG sources, including notions that [Doron et al., 2023] failed to analyze, and including those that are equivalent to general sources with high min entropy. For a lossless expander G = (V,E) with m = log |V|, we consider a random walk V_0,V_1,…,V_t on G using unpredictable instructions that have sufficient entropy with respect to m. Our main theorem is that for almost all the steps t/2 ≤ i ≤ t in the walk, the vertex V_i is close to a distribution with min-entropy at least m-O(1). As a result, we obtain seeded online condensers with constant entropy gap, and seedless (deterministic) condensers outputting a constant fraction of the entropy. In particular, our condensers run in space comparable to the output entropy, as opposed to the size of the stream, and even when the length t of the stream is not known ahead of time. As another corollary, we obtain a new extractor based on expander random walks handling lower entropy than the classic expander based construction relying on spectral techniques [Gillman, 1998]. As our main technical tool, we provide a novel analysis covering a key case of adversarial random walks on lossless expanders that [Doron et al., 2023] fails to address. As part of the analysis, we provide a "chain rule for vertex probabilities". The standard chain rule states that for every x ∼ X and i, Pr(x_1,… ,x_i) = Pr[X_i = x_i|X_[1,i-1] = x_1,… ,x_{i-1}] ⋅ Pr(x_1,… ,x_{i-1}). If W(x₁,… ,x_i) is the vertex reached using x₁,… ,x_i, then the chain rule for vertex probabilities essentially states that the same phenomena occurs for a typical x: Pr [V_i = W(x_1,… ,x_i)] ≲ Pr[X_i = x_i|X_[1,i-1] = x_1,… ,x_{i-1}] ⋅ Pr[V_{i-1} = W(x_1,… ,x_{i-1})], where V_i is the vertex distribution of the random walk at step i using X.
Cite as

Dean Doron, Dana Moshkovitz, Justin Oh, and David Zuckerman. Online Condensing of Unpredictable Sources via Random Walks. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 30:1-30:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{doron_et_al:LIPIcs.CCC.2025.30,
  author =	{Doron, Dean and Moshkovitz, Dana and Oh, Justin and Zuckerman, David},
  title =	{{Online Condensing of Unpredictable Sources via Random Walks}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{30:1--30:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.30},
  URN =		{urn:nbn:de:0030-drops-237243},
  doi =		{10.4230/LIPIcs.CCC.2025.30},
  annote =	{Keywords: Randomness Extractors, Expander Graphs}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.16
Direct Sums for Parity Decision Trees

Authors: Tyler Besselman, Mika Göös, Siyao Guo, Gilbert Maystre, and Weiqiang Yuan

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
Direct sum theorems state that the cost of solving k instances of a problem is at least Ω(k) times the cost of solving a single instance. We prove the first such results in the randomised parity decision tree model. We show that a direct sum theorem holds whenever (1) the lower bound for parity decision trees is proved using the discrepancy method; or (2) the lower bound is proved relative to a product distribution.
Cite as

Tyler Besselman, Mika Göös, Siyao Guo, Gilbert Maystre, and Weiqiang Yuan. Direct Sums for Parity Decision Trees. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 16:1-16:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{besselman_et_al:LIPIcs.CCC.2025.16,
  author =	{Besselman, Tyler and G\"{o}\"{o}s, Mika and Guo, Siyao and Maystre, Gilbert and Yuan, Weiqiang},
  title =	{{Direct Sums for Parity Decision Trees}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{16:1--16:38},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.16},
  URN =		{urn:nbn:de:0030-drops-237105},
  doi =		{10.4230/LIPIcs.CCC.2025.16},
  annote =	{Keywords: direct sum, parity decision trees, query complexity}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICALP.2025.2
Let’s Try to Be More Tolerant: On Tolerant Property Testing and Distance Approximation (Invited Talk)

Authors: Dana Ron

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
This short paper accompanies an invited talk given at ICALP2025. It is an informal, high-level presentation of tolerant testing and distance approximation. It includes some general results as well as a few specific ones, with the aim of providing a taste of this research direction within the area of sublinear algorithms.
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Dana Ron. Let’s Try to Be More Tolerant: On Tolerant Property Testing and Distance Approximation (Invited Talk). In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 2:1-2:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ron:LIPIcs.ICALP.2025.2,
  author =	{Ron, Dana},
  title =	{{Let’s Try to Be More Tolerant: On Tolerant Property Testing and Distance Approximation}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{2:1--2:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.2},
  URN =		{urn:nbn:de:0030-drops-233798},
  doi =		{10.4230/LIPIcs.ICALP.2025.2},
  annote =	{Keywords: Sublinear Algorithms, Tolerant Property Testing, Distance Approximation}
}
Document
DOI: 10.4230/LIPIcs.ITC.2024.9
Time-Space Tradeoffs for Finding Multi-Collisions in Merkle-Damgård Hash Functions

Authors: Akshima

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

Abstract
We analyze the multi-collision resistance of Merkle-Damgård hash function construction in the auxiliary input random oracle model. Finding multi-collisions or m-way collisions, for some parameter m, in a hash function consists of m distinct input that have the same output under the hash function. This is a natural generalization of the collision finding problem in hash functions, which is basically finding 2-way collisions. Hardness of finding collisions, or collision resistance, is an important security assumption in cryptography. While the time-space trade-offs for collision resistance of hash functions has received considerable attention, this is the first work that studies time-space trade-offs for the multi-collision resistance property of hash functions based on the popular and widely used Merkle-Damgård (MD) constructions. In this work, we study how the advantage of finding m-way collisions depends on the parameter m. We believe understanding whether multi-collision resistance is a strictly easier property than collision resistance is a fundamental problem and our work facilitates this for adversaries with auxiliary information against MD based hash functions. Furthermore, in this work we study how the advantage varies with the bound on length of the m colliding inputs. Prior works [Akshima et al., 2020; Ashrujit Ghoshal and Ilan Komargodski, 2022; Akshima et al., 2022] have shown that finding "longer" collisions with auxiliary input in MD based hash functions becomes easier. More precisely, the advantage of finding collisions linearly depends on the bound on the length of colliding inputs. In this work, we show similar dependence for m-way collision finding, for any m ≥ 2. We show a simple attack for finding 1-block m-way collisions which achieves an advantage of Ω̃(S/mN). For 2 ≤ B < log m, we give the best known attack for finding B-blocks m-way collision which achieves an advantage of Ω̃(ST/m^{1/(B-1)}N) when m^{1/(B-1)}-way collisions exist on every salt. For B > log m, our attack achieves an advantage of Ω̃(STB/N) which is optimal when SB ≥ T and ST² ≤ N. The main results of this work is showing that our attacks are optimal for B = 1 and B = 2. This implies that in the auxiliary-input random oracle model, the advantage decreases by a multiplicative factor of m for finding 1-block and 2-block m-way collisions (compared to collision finding) in Merkle-Damgård based hash functions.
Cite as

Akshima. Time-Space Tradeoffs for Finding Multi-Collisions in Merkle-Damgård Hash Functions. In 5th Conference on Information-Theoretic Cryptography (ITC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 304, pp. 9:1-9:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{akshima:LIPIcs.ITC.2024.9,
  author =	{Akshima},
  title =	{{Time-Space Tradeoffs for Finding Multi-Collisions in Merkle-Damg\r{a}rd Hash Functions}},
  booktitle =	{5th Conference on Information-Theoretic Cryptography (ITC 2024)},
  pages =	{9:1--9:22},
  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.2024.9},
  URN =		{urn:nbn:de:0030-drops-205171},
  doi =		{10.4230/LIPIcs.ITC.2024.9},
  annote =	{Keywords: Collision, hash functions, multi-collisions, Merkle-Damg\r{a}rd, pre-computation, auxiliary input}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.10
The (Im)possibility of Simple Search-To-Decision Reductions for Approximation Problems

Authors: Alexander Golovnev, Siyao Guo, Spencer Peters, and Noah Stephens-Davidowitz

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
We study the question of when an approximate search optimization problem is harder than the associated decision problem. Specifically, we study a natural and quite general model of black-box search-to-decision reductions, which we call branch-and-bound reductions (in analogy with branch-and-bound algorithms). In this model, an algorithm attempts to minimize (or maximize) a function f: D → ℝ_{≥ 0} by making oracle queries to h_f : 𝒮 → ℝ_{≥ 0} satisfying min_{x ∈ S} f(x) ≤ h_f(S) ≤ γ ⋅ min_{x ∈ S} f(x) (*) for some γ ≥ 1 and any subset S in some allowed class of subsets 𝒮 of the domain D. (When the goal is to maximize f, h_f instead yields an approximation to the maximal value of f over S.) We show tight upper and lower bounds on the number of queries q needed to find even a γ'-approximate minimizer (or maximizer) for quite large γ' in a number of interesting settings, as follows. - For arbitrary functions f : {0,1}ⁿ → ℝ_{≥ 0}, where 𝒮 contains all subsets of the domain, we show that no branch-and-bound reduction can achieve γ' ≲ γ^{n/log q}, while a simple greedy approach achieves essentially γ^{n/log q}. - For a large class of MAX-CSPs, where 𝒮 := {S_w} contains each set of assignments to the variables induced by a partial assignment w, we show that no branch-and-bound reduction can do significantly better than essentially a random guess, even when the oracle h_f guarantees an approximation factor of γ ≈ 1+√{log(q)/n}. - For the Traveling Salesperson Problem (TSP), where 𝒮 := {S_p} contains each set of tours extending a path p, we show that no branch-and-bound reduction can achieve γ' ≲ (γ-1) n/log q. We also prove a nearly matching upper bound in our model. These results show an oracle model in which approximate search and decision are strongly separated. (In particular, our result for TSP can be viewed as a negative answer to a question posed by Bellare and Goldwasser (SIAM J. Comput. 1994), though only in an oracle model.) We also note two alternative interpretations of our results. First, if we view h_f as a data structure, then our results unconditionally rule out black-box search-to-decision reductions for certain data structure problems. Second, if we view h_f as an efficiently computable heuristic, then our results show that any reasonably efficient branch-and-bound algorithm requires more guarantees from its heuristic than simply Eq. (*). Behind our results is a "useless oracle lemma," which allows us to argue that under certain conditions the oracle h_f is "useless," and which might be of independent interest. See also the full version [Alexander Golovnev et al., 2022].
Cite as

Alexander Golovnev, Siyao Guo, Spencer Peters, and Noah Stephens-Davidowitz. The (Im)possibility of Simple Search-To-Decision Reductions for Approximation Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{golovnev_et_al:LIPIcs.APPROX/RANDOM.2023.10,
  author =	{Golovnev, Alexander and Guo, Siyao and Peters, Spencer and Stephens-Davidowitz, Noah},
  title =	{{The (Im)possibility of Simple Search-To-Decision Reductions for Approximation Problems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.10},
  URN =		{urn:nbn:de:0030-drops-188351},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.10},
  annote =	{Keywords: search-to-decision reductions, oracles, constraint satisfaction, traveling salesman, discrete optimization}
}
Document
DOI: 10.4230/LIPIcs.ITC.2022.6
On the Distributed Discrete Logarithm Problem with Preprocessing

Authors: Pavel Hubáček, Ľubica Jančová, and Veronika Králová

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

Abstract
Protocols solving the Distributed Discrete Logarithm (DDLog) problem are a core component of many recent constructions of group-based homomorphic secret sharing schemes. On a high-level, these protocols enable two parties to transform multiplicative shares of a secret into additive share locally without any communication. Due to their important applications, various generic optimized DDLog protocols were proposed in the literature, culminating in the asymptotically optimal generic protocol of Dinur, Keller, and Klein (J. Cryptol. 2020) solving DDLog in time T with error probability O(W/T²) when the magnitude of the secret is bounded by W. Given that DDLog is solved repeatedly with respect to a fixed group in its applications, a natural approach for improving the efficiency of DDLog protocols could be via leveraging some precomputed group-specific advice. To understand the limitations of this approach, we revisit the distributed discrete logarithm problem in the preprocessing model and study the possible time-space trade-offs for DDLog in the generic group model. As our main result, we show that, in a group of size N, any generic DDLog protocol for secrets of magnitude W with parties running in time T using precomputed group-specific advice of size S has success probability ε = O (T²/W + max{S,log W} ⋅ T²/N) . Thus, assuming N ≥ W log W, we get a lower bound ST² = Ω(ε N) on the time-space trade-off for DDLog protocols using large advice of size S = Ω(N/W). Interestingly, for DDLog protocols using small advice of size S = O(N/W), we get a lower bound T² = Ω(ε W) on the running time, which, in the constant-error regime, asymptotically matches the running time of the DDLog protocol without any advice of Dinur et al. (J. Cryptol. 2020). In other words, we show that generic DDLog protocols achieving constant success probability do not benefit from any advice of size S = O(N/W) in the online phase of the DDLog problem.
Cite as

Pavel Hubáček, Ľubica Jančová, and Veronika Králová. On the Distributed Discrete Logarithm Problem with Preprocessing. In 3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{hubacek_et_al:LIPIcs.ITC.2022.6,
  author =	{Hub\'{a}\v{c}ek, Pavel and Jan\v{c}ov\'{a}, \v{L}ubica and Kr\'{a}lov\'{a}, Veronika},
  title =	{{On the Distributed Discrete Logarithm Problem with Preprocessing}},
  booktitle =	{3rd Conference on Information-Theoretic Cryptography (ITC 2022)},
  pages =	{6:1--6:19},
  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.2022.6},
  URN =		{urn:nbn:de:0030-drops-164847},
  doi =		{10.4230/LIPIcs.ITC.2022.6},
  annote =	{Keywords: Distributed discrete logarithm problem, preprocessing, generic group model}
}
Document
DOI: 10.4230/LIPIcs.ITC.2021.14
Online Linear Extractors for Independent Sources

Authors: Yevgeniy Dodis, Siyao Guo, Noah Stephens-Davidowitz, and Zhiye Xie

Published in: LIPIcs, Volume 199, 2nd Conference on Information-Theoretic Cryptography (ITC 2021)

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
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.1
Extractor Lower Bounds, Revisited

Authors: Divesh Aggarwal, Siyao Guo, Maciej Obremski, João Ribeiro, and Noah Stephens-Davidowitz

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
We revisit the fundamental problem of determining seed length lower bounds for strong extractors and natural variants thereof. These variants stem from a "change in quantifiers" over the seeds of the extractor: While a strong extractor requires that the average output bias (over all seeds) is small for all input sources with sufficient min-entropy, a somewhere extractor only requires that there exists a seed whose output bias is small. More generally, we study what we call probable extractors, which on input a source with sufficient min-entropy guarantee that a large enough fraction of seeds have small enough associated output bias. Such extractors have played a key role in many constructions of pseudorandom objects, though they are often defined implicitly and have not been studied extensively. Prior known techniques fail to yield good seed length lower bounds when applied to the variants above. Our novel approach yields significantly improved lower bounds for somewhere and probable extractors. To complement this, we construct a somewhere extractor that implies our lower bound for such functions is tight in the high min-entropy regime. Surprisingly, this means that a random function is far from an optimal somewhere extractor in this regime. The techniques that we develop also yield an alternative, simpler proof of the celebrated optimal lower bound for strong extractors originally due to Radhakrishnan and Ta-Shma (SIAM J. Discrete Math., 2000).
Cite as

Divesh Aggarwal, Siyao Guo, Maciej Obremski, João Ribeiro, and Noah Stephens-Davidowitz. Extractor Lower Bounds, Revisited. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{aggarwal_et_al:LIPIcs.APPROX/RANDOM.2020.1,
  author =	{Aggarwal, Divesh and Guo, Siyao and Obremski, Maciej and Ribeiro, Jo\~{a}o and Stephens-Davidowitz, Noah},
  title =	{{Extractor Lower Bounds, Revisited}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.1},
  URN =		{urn:nbn:de:0030-drops-126041},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.1},
  annote =	{Keywords: randomness extractors, lower bounds, explicit constructions}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.86
On the Complexity of Decomposable Randomized Encodings, Or: How Friendly Can a Garbling-Friendly PRF Be?

Authors: Marshall Ball, Justin Holmgren, Yuval Ishai, Tianren Liu, and Tal Malkin

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

Abstract
Garbling schemes, also known as decomposable randomized encodings (DRE), have found many applications in cryptography. However, despite a large body of work on constructing such schemes, very little is known about their limitations. We initiate a systematic study of the DRE complexity of Boolean functions, obtaining the following main results: - Near-quadratic lower bounds. We use a classical lower bound technique of Nečiporuk [Dokl. Akad. Nauk SSSR '66] to show an Ω(n²/log n) lower bound on the size of any DRE for many explicit Boolean functions. For some natural functions, we obtain a corresponding upper bound, thus settling their DRE complexity up to polylogarithmic factors. Prior to our work, no superlinear lower bounds were known, even for non-explicit functions. - Garbling-friendly PRFs. We show that any exponentially secure PRF has Ω(n²/log n) DRE size, and present a plausible candidate for a "garbling-optimal" PRF that nearly meets this bound. This candidate establishes a barrier for super-quadratic DRE lower bounds via natural proof techniques. In contrast, we show a candidate for a weak PRF with near-exponential security and linear DRE size. Our results establish several qualitative separations, including near-quadratic separations between computational and information-theoretic DRE size of Boolean functions, and between DRE size of weak vs. strong PRFs.
Cite as

Marshall Ball, Justin Holmgren, Yuval Ishai, Tianren Liu, and Tal Malkin. On the Complexity of Decomposable Randomized Encodings, Or: How Friendly Can a Garbling-Friendly PRF Be?. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 86:1-86:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ball_et_al:LIPIcs.ITCS.2020.86,
  author =	{Ball, Marshall and Holmgren, Justin and Ishai, Yuval and Liu, Tianren and Malkin, Tal},
  title =	{{On the Complexity of Decomposable Randomized Encodings, Or: How Friendly Can a Garbling-Friendly PRF Be?}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{86:1--86:22},
  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.2020.86},
  URN =		{urn:nbn:de:0030-drops-117714},
  doi =		{10.4230/LIPIcs.ITCS.2020.86},
  annote =	{Keywords: Randomized Encoding, Private Simultaneous Messages}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.30
Optimal Deterministic Extractors for Generalized Santha-Vazirani Sources

Authors: Salman Beigi, Andrej Bogdanov, Omid Etesami, and Siyao Guo

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
Let F be a finite alphabet and D be a finite set of distributions over F. A Generalized Santha-Vazirani (GSV) source of type (F, D), introduced by Beigi, Etesami and Gohari (ICALP 2015, SICOMP 2017), is a random sequence (F_1, ..., F_n) in F^n, where F_i is a sample from some distribution d in D whose choice may depend on F_1, ..., F_{i-1}. We show that all GSV source types (F, D) fall into one of three categories: (1) non-extractable; (2) extractable with error n^{-Theta(1)}; (3) extractable with error 2^{-Omega(n)}. We provide essentially randomness-optimal extraction algorithms for extractable sources. Our algorithm for category (2) sources extracts one bit with error epsilon from n = poly(1/epsilon) samples in time linear in n. Our algorithm for category (3) sources extracts m bits with error epsilon from n = O(m + log 1/epsilon) samples in time min{O(m2^m * n),n^{O(|F|)}}. We also give algorithms for classifying a GSV source type (F, D): Membership in category (1) can be decided in NP, while membership in category (3) is polynomial-time decidable.
Cite as

Salman Beigi, Andrej Bogdanov, Omid Etesami, and Siyao Guo. Optimal Deterministic Extractors for Generalized Santha-Vazirani Sources. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{beigi_et_al:LIPIcs.APPROX-RANDOM.2018.30,
  author =	{Beigi, Salman and Bogdanov, Andrej and Etesami, Omid and Guo, Siyao},
  title =	{{Optimal Deterministic Extractors for Generalized Santha-Vazirani Sources}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{30:1--30:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.30},
  URN =		{urn:nbn:de:0030-drops-94349},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.30},
  annote =	{Keywords: feasibility of randomness extraction, extractor lower bounds, martingales}
}
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