65 Search Results for "Reingold, Omer"

Document
Survey
DOI: 10.4230/TGDK.3.2.1
Resilience in Knowledge Graph Embeddings

Authors: Arnab Sharma, N'Dah Jean Kouagou, and Axel-Cyrille Ngonga Ngomo

Published in: TGDK, Volume 3, Issue 2 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 2

Abstract
In recent years, knowledge graphs have gained interest and witnessed widespread applications in various domains, such as information retrieval, question-answering, recommendation systems, amongst others. Large-scale knowledge graphs to this end have demonstrated their utility in effectively representing structured knowledge. To further facilitate the application of machine learning techniques, knowledge graph embedding models have been developed. Such models can transform entities and relationships within knowledge graphs into vectors. However, these embedding models often face challenges related to noise, missing information, distribution shift, adversarial attacks, etc. This can lead to sub-optimal embeddings and incorrect inferences, thereby negatively impacting downstream applications. While the existing literature has focused so far on adversarial attacks on KGE models, the challenges related to the other critical aspects remain unexplored. In this paper, we, first of all, give a unified definition of resilience, encompassing several factors such as generalisation, in-distribution generalization, distribution adaption, and robustness. After formalizing these concepts for machine learning in general, we define them in the context of knowledge graphs. To find the gap in the existing works on resilience in the context of knowledge graphs, we perform a systematic survey, taking into account all these aspects mentioned previously. Our survey results show that most of the existing works focus on a specific aspect of resilience, namely robustness. After categorizing such works based on their respective aspects of resilience, we discuss the challenges and future research directions.
Cite as

Arnab Sharma, N'Dah Jean Kouagou, and Axel-Cyrille Ngonga Ngomo. Resilience in Knowledge Graph Embeddings. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 2, pp. 1:1-1:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{sharma_et_al:TGDK.3.2.1,
  author =	{Sharma, Arnab and Kouagou, N'Dah Jean and Ngomo, Axel-Cyrille Ngonga},
  title =	{{Resilience in Knowledge Graph Embeddings}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{1:1--1:38},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{2},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.2.1},
  URN =		{urn:nbn:de:0030-drops-248117},
  doi =		{10.4230/TGDK.3.2.1},
  annote =	{Keywords: Knowledge graphs, Resilience, Robustness}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ESA.2025.2
Securing Dynamic Data: A Primer on Differentially Private Data Structures (Invited Talk)

Authors: Monika Henzinger and Roodabeh Safavi

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We give an introduction into differential privacy in the dynamic setting, called the continual observation setting.
Cite as

Monika Henzinger and Roodabeh Safavi. Securing Dynamic Data: A Primer on Differentially Private Data Structures (Invited Talk). In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 2:1-2:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{henzinger_et_al:LIPIcs.ESA.2025.2,
  author =	{Henzinger, Monika and Safavi, Roodabeh},
  title =	{{Securing Dynamic Data: A Primer on Differentially Private Data Structures}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{2:1--2:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.2},
  URN =		{urn:nbn:de:0030-drops-244702},
  doi =		{10.4230/LIPIcs.ESA.2025.2},
  annote =	{Keywords: Differential privacy, continual observation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.70
Improved Parallel Derandomization via Finite Automata with Applications

Authors: Jeff Giliberti and David G. Harris

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
A central approach to algorithmic derandomization is the construction of small-support probability distributions that "fool” randomized algorithms, often enabling efficient parallel (NC) implementations. An abstraction of this idea is fooling polynomial-space statistical tests computed via finite automata [Sivakumar STOC'02]; this encompasses a wide range of properties including k-wise independence and sums of random variables. We present new parallel algorithms to fool finite-state automata, with significantly reduced processor complexity. Briefly, our approach is to iteratively sparsify distributions using a work-efficient lattice rounding routine and maintain accuracy by tracking an aggregate weighted error that is determined by the Lipschitz value of the statistical tests being fooled. We illustrate with improved applications to the Gale-Berlekamp Switching Game and to approximate MAX-CUT via SDP rounding. These involve further several optimizations, such as the truncation of the state space of the automata and FFT-based convolutions to compute transition probabilities efficiently.
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Jeff Giliberti and David G. Harris. Improved Parallel Derandomization via Finite Automata with Applications. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 70:1-70:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{giliberti_et_al:LIPIcs.ESA.2025.70,
  author =	{Giliberti, Jeff and Harris, David G.},
  title =	{{Improved Parallel Derandomization via Finite Automata with Applications}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{70:1--70:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.70},
  URN =		{urn:nbn:de:0030-drops-245381},
  doi =		{10.4230/LIPIcs.ESA.2025.70},
  annote =	{Keywords: Parallel Algorithms, Derandomization, MAX-CUT, Gale-Berlekamp Switching Game}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.91
Near-Optimal Differentially Private Graph Algorithms via the Multidimensional AboveThreshold Mechanism

Authors: Laxman Dhulipala, Monika Henzinger, George Z. Li, Quanquan C. Liu, A. R. Sricharan, and Leqi Zhu

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Many differentially private and classical non-private graph algorithms rely crucially on determining whether some property of each vertex meets a threshold. For example, for the k-core decomposition problem, the classic peeling algorithm iteratively removes a vertex if its induced degree falls below a threshold. The sparse vector technique (SVT) is generally used to transform non-private threshold queries into private ones with only a small additive loss in accuracy. However, a naive application of SVT in the graph setting leads to an amplification of the error by a factor of n due to composition, as SVT is applied to every vertex. In this paper, we resolve this problem by formulating a novel generalized sparse vector technique which we call the Multidimensional AboveThreshold (MAT) Mechanism which generalizes SVT (applied to vectors with one dimension) to vectors with multiple dimensions. When applied to vectors with n dimensions, we solve a number of important graph problems with better bounds than previous work. Specifically, we apply our MAT mechanism to obtain a set of improved bounds for a variety of problems including k-core decomposition, densest subgraph, low out-degree ordering, and vertex coloring. We give a tight local edge differentially private (LEDP) algorithm for k-core decomposition that results in an approximation with O(ε^{-1} log n) additive error and no multiplicative error in O(n) rounds. We also give a new (2+η)-factor multiplicative, O(ε^{-1} log n) additive error algorithm in O(log² n) rounds for any constant η > 0. Both of these results are asymptotically tight against our new lower bound of Ω(log n) for any constant-factor approximation algorithm for k-core decomposition. Our new algorithms for k-core decomposition also directly lead to new algorithms for the related problems of densest subgraph and low out-degree ordering. Finally, we give novel LEDP differentially private defective coloring algorithms that use number of colors given in terms of the arboricity of the graph.
Cite as

Laxman Dhulipala, Monika Henzinger, George Z. Li, Quanquan C. Liu, A. R. Sricharan, and Leqi Zhu. Near-Optimal Differentially Private Graph Algorithms via the Multidimensional AboveThreshold Mechanism. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 91:1-91:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dhulipala_et_al:LIPIcs.ESA.2025.91,
  author =	{Dhulipala, Laxman and Henzinger, Monika and Li, George Z. and Liu, Quanquan C. and Sricharan, A. R. and Zhu, Leqi},
  title =	{{Near-Optimal Differentially Private Graph Algorithms via the Multidimensional AboveThreshold Mechanism}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{91:1--91:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.91},
  URN =		{urn:nbn:de:0030-drops-245601},
  doi =		{10.4230/LIPIcs.ESA.2025.91},
  annote =	{Keywords: differential privacy, abovethreshold, densest subgraph}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.40
Sublinear Space Graph Algorithms in the Continual Release Model

Authors: Alessandro Epasto, Quanquan C. Liu, Tamalika Mukherjee, and Felix Zhou

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

Abstract
The graph continual release model of differential privacy seeks to produce differentially private solutions to graph problems under a stream of edge updates where new private solutions are released after each update. Thus far, previously known edge-differentially private algorithms for most graph problems including densest subgraph and matchings in the continual release setting only output real-value estimates (not vertex subset solutions) and do not use sublinear space. Instead, they rely on computing exact graph statistics on the input [Hendrik Fichtenberger et al., 2021; Shuang Song et al., 2018]. In this paper, we leverage sparsification to address the above shortcomings for edge-insertion streams. Our edge-differentially private algorithms use sublinear space with respect to the number of edges in the graph while some also achieve sublinear space in the number of vertices in the graph. In addition, for the densest subgraph problem, we also output edge-differentially private vertex subset solutions; no previous graph algorithms in the continual release model output such subsets. We make novel use of assorted sparsification techniques from the non-private streaming and static graph algorithms literature to achieve new results in the sublinear space, continual release setting. This includes algorithms for densest subgraph, maximum matching, as well as the first continual release k-core decomposition algorithm. We also develop a novel sparse level data structure for k-core decomposition that may be of independent interest. To complement our insertion-only algorithms, we conclude with polynomial additive error lower bounds for edge-privacy in the fully dynamic setting, where only logarithmic lower bounds were previously known.
Cite as

Alessandro Epasto, Quanquan C. Liu, Tamalika Mukherjee, and Felix Zhou. Sublinear Space Graph Algorithms in the Continual Release Model. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 40:1-40:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{epasto_et_al:LIPIcs.APPROX/RANDOM.2025.40,
  author =	{Epasto, Alessandro and Liu, Quanquan C. and Mukherjee, Tamalika and Zhou, Felix},
  title =	{{Sublinear Space Graph Algorithms in the Continual Release Model}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{40:1--40:27},
  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.2025.40},
  URN =		{urn:nbn:de:0030-drops-244064},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.40},
  annote =	{Keywords: Differential Privacy, Continual Release, Densest Subgraph, k-Core Decomposition, Maximum Matching}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.41
What Is the Minimum Number of Random Bits Required for Computability and Efficiency in Anonymous Networks?

Authors: Dariusz R. Kowalski, Piotr Krysta, and Shay Kutten

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

Abstract
Angluin (STOC'80) and Yamashita and Kameda (PODC'88) show that some useful distributed tasks are impossible (for deterministic algorithms) in a general network if nodes do not possess unique identifiers. However, any task decidable in the non-distributed context, can be solved deterministically if the network has a unique leader. Alternatively, much research has been devoted to randomized distributed algorithms in anonymous networks. We present tight upper and lower bounds for the fundamental question: How much randomness is necessary and sufficient to solve Leader Election (LE) in anonymous networks, i.e., to transform an anonymous network into a non-anonymous one? We prove that at least one random bit per node is required in some cases. Surprisingly, a single random bit is also enough, for a total of n bits, where n is the number of nodes. However, the time complexity of our (total of) n random bits algorithm for general networks turned out to be impractically high. Hence, we also developed time-efficient algorithms for the very symmetric graphs of cliques and cycles, paying only an additional cost of o(n) random bits. The primary steps of our algorithms are of independent interest. At first glance, it seems that using one random bit per node, any algorithm can distinguish only two sets of nodes: those with 0 and those with 1. Our algorithms manage to partition the nodes into more than two sets with high probability. In some sense, they perform the task of a "distributed pseudorandom generator", for example, one of our algorithms turns n bits, one per node, into n unique (with high probability) numbers. Even though a complete graph looks very symmetric, the algorithms explore interesting asymmetries inherent in any n permutations (of n values each), if each describes the assignment (by the adversary) of ports in a node to edges leading to neighbors. Finally, we show how to transform any randomized algorithm that generates xn+o(n) random bits in total to one where each node generates at most x+1 bits. Our results apply to both synchronous and asynchronous networks.
Cite as

Dariusz R. Kowalski, Piotr Krysta, and Shay Kutten. What Is the Minimum Number of Random Bits Required for Computability and Efficiency in Anonymous Networks?. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 41:1-41:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kowalski_et_al:LIPIcs.APPROX/RANDOM.2025.41,
  author =	{Kowalski, Dariusz R. and Krysta, Piotr and Kutten, Shay},
  title =	{{What Is the Minimum Number of Random Bits Required for Computability and Efficiency in Anonymous Networks?}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{41:1--41:24},
  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.2025.41},
  URN =		{urn:nbn:de:0030-drops-244071},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.41},
  annote =	{Keywords: Distributed computability, Anonymous Networks, Randomness, Leader Election}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.35
Fooling Near-Maximal Decision Trees

Authors: William M. Hoza and Zelin Lv

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

Abstract
For any constant α > 0, we construct an explicit pseudorandom generator (PRG) that fools n-variate decision trees of size m with error ε and seed length (1 + α) ⋅ log₂ m + O(log(1/ε) + log log n). For context, one can achieve seed length (2 + o(1)) ⋅ log₂ m + O(log(1/ε) + log log n) using well-known constructions and analyses of small-bias distributions, but such a seed length is trivial when m ≥ 2^{n/2}. Our approach is to develop a new variant of the classic concept of almost k-wise independence, which might be of independent interest. We say that a distribution X over {0, 1}ⁿ is k-wise ε-probably uniform if every Boolean function f that depends on only k variables satisfies 𝔼[f(X)] ≥ (1 - ε) ⋅ 𝔼[f]. We show how to sample a k-wise ε-probably uniform distribution using a seed of length (1 + α) ⋅ k + O(log(1/ε) + log log n). Meanwhile, we also show how to construct a set H ⊆ 𝔽₂ⁿ such that every feasible system of k linear equations in n variables over 𝔽₂ has a solution in H. The cardinality of H and the time complexity of enumerating H are at most 2^{k + o(k) + polylog n}, whereas small-bias distributions would give a bound of 2^{2k + O(log(n/k))}. By combining our new constructions with work by Chen and Kabanets (TCS 2016), we obtain nontrivial PRGs and hitting sets for linear-size Boolean circuits. Specifically, we get an explicit PRG with seed length (1 - Ω(1)) ⋅ n that fools circuits of size 2.99 ⋅ n over the U₂ basis, and we get a hitting set with time complexity 2^{(1 - Ω(1)) ⋅ n} for circuits of size 2.49 ⋅ n over the B₂ basis.
Cite as

William M. Hoza and Zelin Lv. Fooling Near-Maximal Decision Trees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 35:1-35:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hoza_et_al:LIPIcs.APPROX/RANDOM.2025.35,
  author =	{Hoza, William M. and Lv, Zelin},
  title =	{{Fooling Near-Maximal Decision Trees}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{35:1--35:24},
  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.2025.35},
  URN =		{urn:nbn:de:0030-drops-244019},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.35},
  annote =	{Keywords: almost k-wise independence, decision trees, pseudorandom generators}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.33
Bit-Fixing Extractors for Almost-Logarithmic Entropy

Authors: Dean Doron and Ori Fridman

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

Abstract
An oblivious bit-fixing source is a distribution over {0,1}ⁿ, where k bits are uniform and independent and the rest n-k are fixed a priori to some constant value. Extracting (close to) true randomness from an oblivious bit-fixing source has been studied since the 1980s, with applications in cryptography and complexity theory. We construct explicit extractors for oblivious bit-fixing source that support k = Õ(log n), outputting almost all the entropy with low error. The previous state-of-the-art construction that outputs many bits is due to Rao [Rao, CCC '09], and requires entropy k ≥ log^{c} n for some large constant c. The two key components in our constructions are new low-error affine condensers for poly-logarithmic entropies (that we achieve using techniques from the nonmalleable extractors literature), and a dual use of linear condensers for OBF sources.
Cite as

Dean Doron and Ori Fridman. Bit-Fixing Extractors for Almost-Logarithmic Entropy. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 33:1-33:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{doron_et_al:LIPIcs.APPROX/RANDOM.2025.33,
  author =	{Doron, Dean and Fridman, Ori},
  title =	{{Bit-Fixing Extractors for Almost-Logarithmic Entropy}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{33:1--33:19},
  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.2025.33},
  URN =		{urn:nbn:de:0030-drops-243994},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.33},
  annote =	{Keywords: Seedless extractors, oblivious bit-fixing sources}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.28
Implications of Better PRGs for Permutation Branching Programs

Authors: Dean Doron and William M. Hoza

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

Abstract
We study the challenge of derandomizing constant-width standard-order read-once branching programs (ROBPs). Let c ∈ [1, 2) be any constant. We prove that if there are explicit pseudorandom generators (PRGs) for width-6 length-n permutation ROBPs with error 1/n and seed length Õ(log^c n), then there are explicit hitting set generators (HSGs) for width-4 length-n ROBPs with threshold 1/polylog(n) and seed length Õ(log^c n). For context, there are known explicit PRGs that fool constant-width permutation ROBPs with error ε and seed length O(log(n)⋅log(1/ε)) (Koucký, Nimbhorkar, and Pudlák STOC 2011; De CCC 2011; Steinke ECCC 2012). When ε = 1/n, there are known constructions of weighted pseudorandom generators (WPRGs) that fool polynomial-width permutation ROBPs with seed length Õ(log^{3/2} n) (Pyne and Vadhan CCC 2021; Chen, Hoza, Lyu, Tal, and Wu FOCS 2023; Chattopadhyay and Liao ITCS 2024), but unweighted PRGs with seed length o(log² n) remain elusive. Meanwhile, for width-4 ROBPs, there are no known explicit PRGs, WPRGs, or HSGs with seed length o(log²n). Our reduction can be divided into two parts. First, we show that explicit low-error PRGs for width-6 permutation ROBPs with seed length Õ(log^c n) would imply explicit low-error PRGs for width-3 ROBPs with seed length Õ(log^c n). This would improve Meka, Reingold, and Tal’s PRG (STOC 2019), which has seed length o(log²n) only when the error parameter is relatively large. Second, we show that for any w, n, s, and ε, an explicit PRG for width-w ROBPs with error 0.01/n and seed length s would imply an explicit ε-HSG for width-(w + 1) ROBPs with seed length O(s + log(n)⋅log(1/ε)).
Cite as

Dean Doron and William M. Hoza. Implications of Better PRGs for Permutation Branching Programs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{doron_et_al:LIPIcs.APPROX/RANDOM.2025.28,
  author =	{Doron, Dean and Hoza, William M.},
  title =	{{Implications of Better PRGs for Permutation Branching Programs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{28:1--28:20},
  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.2025.28},
  URN =		{urn:nbn:de:0030-drops-243946},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.28},
  annote =	{Keywords: hitting set generators, pseudorandom generators, read-once branching programs}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.67
On Sums of INW Pseudorandom Generators

Authors: William M. Hoza and Zelin Lv

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

Abstract
We study a new approach for constructing pseudorandom generators (PRGs) that fool constant-width standard-order read-once branching programs (ROBPs). Let X be the n-bit output distribution of the INW PRG (Impagliazzo, Nisan, and Wigderson, STOC 1994), instantiated using expansion parameter λ. We prove that the bitwise XOR of t independent copies of X fools width-w programs with error n^{log(w + 1)} ⋅ (λ⋅log n)^t. Notably, this error bound is meaningful even for relatively large values of λ such as λ = 1/O(log n). Admittedly, our analysis does not yet imply any improvement in the bottom-line overall seed length required for fooling such programs - it just gives a new way of re-proving the well-known O(log² n) bound. Furthermore, we prove that this shortcoming is not an artifact of our analysis, but rather is an intrinsic limitation of our "XOR of INW" approach. That is, no matter how many copies of the INW generator we XOR together, and no matter how we set the expansion parameters, if the generator fools width-3 programs and the proof of correctness does not use any properties of the expander graphs except their spectral expansion, then we prove that the seed length of the generator is inevitably Ω(log² n). Still, we hope that our work might be a step toward constructing near-optimal PRGs fooling constant-width ROBPs. We suggest that one could try running the INW PRG on t correlated seeds, sampled via another PRG, and taking the bitwise XOR of the outputs.
Cite as

William M. Hoza and Zelin Lv. On Sums of INW Pseudorandom Generators. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 67:1-67:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hoza_et_al:LIPIcs.APPROX/RANDOM.2025.67,
  author =	{Hoza, William M. and Lv, Zelin},
  title =	{{On Sums of INW Pseudorandom Generators}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{67:1--67:24},
  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.2025.67},
  URN =		{urn:nbn:de:0030-drops-244330},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.67},
  annote =	{Keywords: INW generator, pseudorandomness, space-bounded computation, XOR Lemmas}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.66
Testing Isomorphism of Boolean Functions over Finite Abelian Groups

Authors: Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy

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

Abstract
Let f and g be Boolean functions over a finite Abelian group 𝒢, where g is fully known and f is accessible via queries; that is, given any x ∈ 𝒢, we can obtain the value f(x). We study the problem of tolerant isomorphism testing: given parameters ε ≥ 0 and τ > 0, the goal is to determine, using as few queries as possible, whether there exists an automorphism σ of 𝒢 such that the fractional Hamming distance between f∘σ and g is at most ε, or whether for every automorphism σ, the distance is at least ε + τ. We design an efficient tolerant property testing algorithm for this problem over finite Abelian groups with constant exponent. The exponent of a finite group refers to the largest order of any element in the group. The query complexity of our algorithm is polynomial in s and 1/τ, where s bounds the spectral norm of the function g, and τ is the tolerance parameter. In addition, we present an improved algorithm in the case where g is Fourier sparse, meaning that its Fourier expansion contains only a small number of nonzero coefficients. Our approach draws on key ideas from Abelian group theory and Fourier analysis, including the annihilator of a subgroup, Pontryagin duality, and a pseudo inner product defined over finite Abelian groups. We believe that these techniques will be useful more broadly in the design of property testing algorithms.
Cite as

Swarnalipa Datta, Arijit Ghosh, Chandrima Kayal, Manaswi Paraashar, and Manmatha Roy. Testing Isomorphism of Boolean Functions over Finite Abelian Groups. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 66:1-66:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{datta_et_al:LIPIcs.APPROX/RANDOM.2025.66,
  author =	{Datta, Swarnalipa and Ghosh, Arijit and Kayal, Chandrima and Paraashar, Manaswi and Roy, Manmatha},
  title =	{{Testing Isomorphism of Boolean Functions over Finite Abelian Groups}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{66:1--66:22},
  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.2025.66},
  URN =		{urn:nbn:de:0030-drops-244328},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.66},
  annote =	{Keywords: Analysis of Boolean functions, Abelian groups, Automorphism group, Function isomorphism, Spectral norm}
}
Document
DOI: 10.4230/LIPIcs.ITC.2025.8
On the Definition of Malicious Private Information Retrieval

Authors: Bar Alon and Amos Beimel

Published in: LIPIcs, Volume 343, 6th Conference on Information-Theoretic Cryptography (ITC 2025)

Abstract
A multi-server private information retrieval (PIR) protocol allows a client to obtain an entry of its choice from a database, held by one or more servers, while hiding the identity of the entry from small enough coalitions of servers. In this paper, we study PIR protocols in which some of the servers are malicious and may not send messages according to the pre-described protocol. In previous papers, such protocols were defined by requiring that they are correct, private, and robust to malicious servers, i.e., by listing 3 properties that they should satisfy. However, 40 years of experience in studying secure multiparty protocols taught us that defining the security of protocols by a list of required properties is problematic. In this paper, we rectify this situation and define the security of PIR protocols with malicious servers using the real vs. ideal paradigm. We study the relationship between the property-based definition of PIR protocols and the real vs. ideal definition, showing the following results: - We prove that if we require full security from PIR protocols, e.g., the client outputs the correct value of the database entry with high probability even if a minority of the servers are malicious, then the two definitions are equivalent. This implies that constructions of such protocols that were proven secure using the property-based definition are actually secure under the "correct" definition of security. - We show that if we require security-with-abort from PIR protocols (called PIR protocols with error-detection in previous papers), i.e., protocols in which the user either outputs the correct value or an abort symbol, then there are protocols that are secure under the property-based definition; however, they do not satisfy the real vs. ideal definition, that is, they can be attacked allowing selective abort. This shows that the property-based definition of PIR protocols with security-with-abort is problematic. - We consider the compiler of Eriguchi et al. (TCC 22) that starts with a PIR protocol that is secure against semi-honest servers and constructs a PIR protocol with security-with-abort; this compiler implies the best-known PIR protocols with security-with-abort. We show that applying this compiler does not result in PIR protocols that are secure according to the real vs. ideal definition. However, we prove that a simple modification of this compiler results in PIR protocols that are secure according to the real vs. ideal definition.
Cite as

Bar Alon and Amos Beimel. On the Definition of Malicious Private Information Retrieval. In 6th Conference on Information-Theoretic Cryptography (ITC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 343, pp. 8:1-8:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{alon_et_al:LIPIcs.ITC.2025.8,
  author =	{Alon, Bar and Beimel, Amos},
  title =	{{On the Definition of Malicious Private Information Retrieval}},
  booktitle =	{6th Conference on Information-Theoretic Cryptography (ITC 2025)},
  pages =	{8:1--8:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-385-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{343},
  editor =	{Gilboa, Niv},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2025.8},
  URN =		{urn:nbn:de:0030-drops-243581},
  doi =		{10.4230/LIPIcs.ITC.2025.8},
  annote =	{Keywords: Private information retrieval, secure multiparty computation}
}
Document
DOI: 10.4230/LIPIcs.ITC.2025.12
Key-Agreement with Perfect Completeness from Random Oracles

Authors: Noam Mazor

Published in: LIPIcs, Volume 343, 6th Conference on Information-Theoretic Cryptography (ITC 2025)

Abstract
In the Random Oracle Model (ROM) all parties have oracle access to a common random function, and the parties are limited in the number of queries they can make to the oracle. The Merkle’s Puzzles protocol, introduced by Merkle [CACM '78], is a key-agreement protocol in the ROM with a quadratic gap between the query complexity of the honest parties and the eavesdropper. This quadratic gap is known to be optimal, by the works of Impagliazzo and Rudich [STOC ’89] and Barak and Mahmoody [Crypto ’09]. When the oracle function is injective or a permutation, Merkle’s Puzzles has perfect completeness. That is, it is certain that the protocol results in agreement between the parties. However, without such an assumption on the random function, there is a small error probability, and the parties may end up holding different keys. This fact raises the question: Is there a key-agreement protocol with perfect completeness and super-linear security in the ROM? In this paper we give a positive answer to the above question, showing that changes to the query distribution of the parties in Merkle’s Puzzles, yield a protocol with perfect completeness and roughly the same security.
Cite as

Noam Mazor. Key-Agreement with Perfect Completeness from Random Oracles. In 6th Conference on Information-Theoretic Cryptography (ITC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 343, pp. 12:1-12:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mazor:LIPIcs.ITC.2025.12,
  author =	{Mazor, Noam},
  title =	{{Key-Agreement with Perfect Completeness from Random Oracles}},
  booktitle =	{6th Conference on Information-Theoretic Cryptography (ITC 2025)},
  pages =	{12:1--12:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-385-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{343},
  editor =	{Gilboa, Niv},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2025.12},
  URN =		{urn:nbn:de:0030-drops-243628},
  doi =		{10.4230/LIPIcs.ITC.2025.12},
  annote =	{Keywords: Key-Agreement, Random Oracle, Merkle’s Puzzles, Perfect Completeness}
}
Document
DOI: 10.4230/LIPIcs.ITC.2025.3
Leakage-Resilience of Shamir’s Secret Sharing: Identifying Secure Evaluation Places

Authors: Jihun Hwang, Hemanta K. Maji, Hai H. Nguyen, and Xiuyu Ye

Published in: LIPIcs, Volume 343, 6th Conference on Information-Theoretic Cryptography (ITC 2025)

Abstract
Can Shamir’s secret-sharing protect its secret even when all shares are partially compromised? For instance, repairing Reed-Solomon codewords, when possible, recovers the entire secret in the corresponding Shamir’s secret sharing. Yet, Shamir’s secret sharing mitigates various side-channel threats, depending on where its "secret-sharing polynomial" is evaluated. Although most evaluation places yield secure schemes, none are known explicitly; even techniques to identify them are unknown. Our work initiates research into such classifier constructions and derandomization objectives. In this work, we focus on Shamir’s scheme over prime fields, where every share is required to reconstruct the secret. We investigate the security of these schemes against single-bit probes into shares stored in their native binary representation. Technical analysis is particularly challenging when dealing with Reed-Solomon codewords over prime fields, as observed recently in the code repair literature. Furthermore, ensuring the statistical independence of the leakage from the secret necessitates the elimination of any subtle correlations between them. In this context, we present: 1) An efficient algorithm to classify evaluation places as secure or vulnerable against the least-significant-bit leakage. 2) Modulus choices where the classifier above extends to any single-bit probe per share. 3) Explicit modulus choices and secure evaluation places for them. On the way, we discover new bit-probing attacks on Shamir’s scheme, revealing surprising correlations between the leakage and the secret, leading to vulnerabilities when choosing evaluation places naïvely. Our results rely on new techniques to analyze the security of secret-sharing schemes against side-channel threats. We connect their leakage resilience to the orthogonality of square wave functions, which, in turn, depends on the 2-adic valuation of rational approximations. These techniques, novel to the security analysis of secret sharings, can potentially be of broader interest.
Cite as

Jihun Hwang, Hemanta K. Maji, Hai H. Nguyen, and Xiuyu Ye. Leakage-Resilience of Shamir’s Secret Sharing: Identifying Secure Evaluation Places. In 6th Conference on Information-Theoretic Cryptography (ITC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 343, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hwang_et_al:LIPIcs.ITC.2025.3,
  author =	{Hwang, Jihun and Maji, Hemanta K. and Nguyen, Hai H. and Ye, Xiuyu},
  title =	{{Leakage-Resilience of Shamir’s Secret Sharing: Identifying Secure Evaluation Places}},
  booktitle =	{6th Conference on Information-Theoretic Cryptography (ITC 2025)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-385-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{343},
  editor =	{Gilboa, Niv},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2025.3},
  URN =		{urn:nbn:de:0030-drops-243531},
  doi =		{10.4230/LIPIcs.ITC.2025.3},
  annote =	{Keywords: Shamir’s secret sharing, leakage resilience, physical bit probing, secure evaluation places, secure modulus choice, square wave families, LLL algorithm, Fourier analysis}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.25
Quantum LDPC Codes of Almost Linear Distance via Iterated Homological Products

Authors: Louis Golowich and Venkatesan Guruswami

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

Abstract
The first linear-distance quantum LDPC codes were recently constructed by a line of breakthrough works (culminating in the result of Panteleev & Kalachev, 2021). All such constructions, even when allowing for almost-linear distance, are based on an operation called a balanced (or lifted) product, which is used in a one-shot manner to combine a pair of large classical codes possessing a group symmetry. We present a new construction of almost-linear distance quantum LDPC codes that is iterative in nature. Our construction is based on a more basic and widely used product, namely the homological product (i.e. the tensor product of chain complexes). Specifically, for every ε > 0, we obtain a family of [[N,N^{1-ε},N^{1-ε}]] (subsystem) quantum LDPC codes via repeated homological products of a constant-sized quantum locally testable code. Our key idea is to remove certain low-weight codewords using subsystem codes (while still maintaining constant stabilizer weight), in order to circumvent a particular obstruction that limited the distance of many prior homological product code constructions to at most Õ(√N).
Cite as

Louis Golowich and Venkatesan Guruswami. Quantum LDPC Codes of Almost Linear Distance via Iterated Homological Products. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 25:1-25:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{golowich_et_al:LIPIcs.CCC.2025.25,
  author =	{Golowich, Louis and Guruswami, Venkatesan},
  title =	{{Quantum LDPC Codes of Almost Linear Distance via Iterated Homological Products}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{25:1--25:11},
  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.2025.25},
  URN =		{urn:nbn:de:0030-drops-237196},
  doi =		{10.4230/LIPIcs.CCC.2025.25},
  annote =	{Keywords: Quantum Error Correction, Quantum LDPC Code, Homological Product, Iterative Construction}
}
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