37 Search Results for "Green, Ben J."

Document
DOI: 10.4230/LIPIcs.ITCS.2026.103
A General Framework for Low Soundness Homomorphism Testing

Authors: Tushant Mittal and Sourya Roy

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

Abstract
We introduce a general framework to design and analyze algorithms for the problem of testing homomorphisms between finite groups in the low-soundness regime. In this regime, we give the first constant-query tests for various families of groups. These include tests for: (i) homomorphisms between arbitrary cyclic groups, (ii) homomorphisms between any finite group and ℤ_p, (iii) automorphisms of dihedral and symmetric groups, (iv) inner automorphisms of non-abelian finite simple groups and extraspecial groups, and (v) testing linear characters of GL_n(F_q), and finite-dimensional Lie algebras over F_q. We also recover the result of Kiwi [TCS'03] for testing homomorphisms between F_qⁿ and F_q. Prior to this work, such tests were only known for abelian groups with a constant maximal order (such as F_qⁿ). No tests were known for non-abelian groups. As an additional corollary, our framework gives combinatorial list decoding bounds for cyclic groups with list size dependence of O(ε^{-2}) (for agreement parameter ε). This improves upon the currently best-known bound of O(ε^{-105}) due to Dinur, Grigorescu, Kopparty, and Sudan [STOC'08], and Guo and Sudan [RANDOM'14].
Cite as

Tushant Mittal and Sourya Roy. A General Framework for Low Soundness Homomorphism Testing. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 103:1-103:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{mittal_et_al:LIPIcs.ITCS.2026.103,
  author =	{Mittal, Tushant and Roy, Sourya},
  title =	{{A General Framework for Low Soundness Homomorphism Testing}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{103:1--103:18},
  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.2026.103},
  URN =		{urn:nbn:de:0030-drops-253901},
  doi =		{10.4230/LIPIcs.ITCS.2026.103},
  annote =	{Keywords: Property Testing, Coding Theory}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.82
Dimension Reduction for Clustering: The Curious Case of Discrete Centers

Authors: Shaofeng H.-C. Jiang, Robert Krauthgamer, Shay Sapir, Sandeep Silwal, and Di Yue

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

Abstract
The Johnson-Lindenstrauss transform is a fundamental method for dimension reduction in Euclidean spaces, that can map any dataset of n points into dimension O(log n) with low distortion of their distances. This dimension bound is tight in general, but one can bypass it for specific problems. Indeed, tremendous progress has been made for clustering problems, especially in the continuous setting where centers can be picked from the ambient space ℝ^d. Most notably, for k-median and k-means, the dimension bound was improved to O(log k) [Makarychev, Makarychev and Razenshteyn, STOC 2019]. We explore dimension reduction for clustering in the discrete setting, where centers can only be picked from the dataset, and present two results that are both parameterized by the doubling dimension of the dataset, denoted as ddim. The first result shows that dimension O_{ε}(ddim + log k + log log n) suffices, and is moreover tight, to guarantee that the cost is preserved within factor 1±ε for every set of centers. Our second result eliminates the log log n term in the dimension through a relaxation of the guarantee (namely, preserving the cost only for all approximately-optimal sets of centers), which maintains its usefulness for downstream applications. Overall, we achieve strong dimension reduction in the discrete setting, and find that it differs from the continuous setting not only in the dimension bound, which depends on the doubling dimension, but also in the guarantees beyond preserving the optimal value, such as which clusterings are preserved.
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Shaofeng H.-C. Jiang, Robert Krauthgamer, Shay Sapir, Sandeep Silwal, and Di Yue. Dimension Reduction for Clustering: The Curious Case of Discrete Centers. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 82:1-82:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{jiang_et_al:LIPIcs.ITCS.2026.82,
  author =	{Jiang, Shaofeng H.-C. and Krauthgamer, Robert and Sapir, Shay and Silwal, Sandeep and Yue, Di},
  title =	{{Dimension Reduction for Clustering: The Curious Case of Discrete Centers}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{82:1--82:23},
  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.2026.82},
  URN =		{urn:nbn:de:0030-drops-253698},
  doi =		{10.4230/LIPIcs.ITCS.2026.82},
  annote =	{Keywords: dimension reduction, clustering, k-median, k-means, doubling dimension}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.76
Ideal Private Simultaneous Messages Schemes and Their Applications

Authors: Keitaro Hiwatashi and Reo Eriguchi

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

Abstract
Private Simultaneous Messages (PSM) is a minimal model for secure computation, where two parties, Alice and Bob, have private inputs x,y and a shared random string. Each of them sends a single message to an external party, Charlie, who can compute f(x,y) for a public function f but learns nothing else. The problem of narrowing the gap between upper and lower bounds on the communication complexity of PSM has been widely studied, but the gap still remains exponential. In this work, we study the communication complexity of PSM from a different perspective and introduce a special class of PSM, referred to as ideal PSM, in which each party’s message length attains the minimum, that is, their messages are taken from the same domain as inputs. We initiate a systematic study of ideal PSM with a complete characterization, several positive results, and applications. First, we provide a characterization of the class of functions that admit ideal PSM, based on permutation groups acting on the input domain. This characterization allows us to derive asymptotic upper bounds on the total number of such functions and a complete list for small domains. We also present several infinite families of functions of practical interest that admit ideal PSM. Interestingly, by simply restricting the input domains of these ideal PSM schemes, we can recover most of the existing PSM schemes that achieve the best known communication complexity in various computation models. As applications, we show that these ideal PSM schemes yield novel communication-efficient PSM schemes for functions with sparse or dense truth-tables and those with low-rank truth-tables. Furthermore, we obtain a PSM scheme for general functions that improves the constant factor in the dominant term of the best known communication complexity. An additional advantage is that our scheme simplifies the existing construction by avoiding the hierarchical design of internally invoking PSM schemes for smaller functions.
Cite as

Keitaro Hiwatashi and Reo Eriguchi. Ideal Private Simultaneous Messages Schemes and Their Applications. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 76:1-76:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hiwatashi_et_al:LIPIcs.ITCS.2026.76,
  author =	{Hiwatashi, Keitaro and Eriguchi, Reo},
  title =	{{Ideal Private Simultaneous Messages Schemes and Their Applications}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{76:1--76:23},
  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.2026.76},
  URN =		{urn:nbn:de:0030-drops-253633},
  doi =		{10.4230/LIPIcs.ITCS.2026.76},
  annote =	{Keywords: secure computation, private simultaneous messages, communication complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.61
Random Unitaries in Constant (Quantum) Time

Authors: Ben Foxman, Natalie Parham, Francisca Vasconcelos, and Henry Yuen

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

Abstract
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries (PRUs) using Θ(log log n)-depth unitary circuits with two-qubit gates. In this work, we show that unitary designs and PRUs can be efficiently constructed in several well-studied models of constant-time quantum computation (i.e., the time complexity on the quantum computer is independent of the system size). These models are constant-depth circuits augmented with certain nonlocal operations, such as (a) many-qubit TOFFOLI gates, (b) many-qubit FANOUT gates, or (c) mid-circuit measurements with classical feedforward control. Recent advances in quantum computing hardware suggest experimental feasibility of these models in the near future. Our results demonstrate that unitary designs and PRUs can be constructed in much weaker circuit models than previously thought. Furthermore, our construction of PRUs in constant-depth with many-qubit TOFFOLI gates shows that, under cryptographic assumptions, there is no polynomial-time learning algorithm for the circuit class QAC⁰. Finally, our results suggest a new approach towards proving that PARITY is not computable in QAC⁰, a long-standing question in quantum complexity theory.
Cite as

Ben Foxman, Natalie Parham, Francisca Vasconcelos, and Henry Yuen. Random Unitaries in Constant (Quantum) Time. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 61:1-61:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{foxman_et_al:LIPIcs.ITCS.2026.61,
  author =	{Foxman, Ben and Parham, Natalie and Vasconcelos, Francisca and Yuen, Henry},
  title =	{{Random Unitaries in Constant (Quantum) Time}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{61:1--61:25},
  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.2026.61},
  URN =		{urn:nbn:de:0030-drops-253481},
  doi =		{10.4230/LIPIcs.ITCS.2026.61},
  annote =	{Keywords: Quantum Information, Pseudorandomness, Circuit Complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.71
Lower Bounds on FSS from Dynamic Data Structures

Authors: Niv Gilboa and Daniel Weber

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

Abstract
In Function Secret Sharing (FSS), a dealer with a given function f: {0,1}ⁿ → 𝔾 from n bits to a commutative group 𝔾 such that f is in a function class ℱ shares succinct keys with two properties. Evaluating each key separately on a common input x results in additive shares of f(x) and any subset of the keys does not provide information on f. Two-party FSS schemes which are reducible to One-way Functions (OWF) have applications in cryptography, complexity, and in practical data security systems. We establish a two-way transformation between a two-party FSS scheme for a function class ℱ, which is black-box reducible to an OWF, or even black-box reducible to a family of Pseudo-Random Functions (PRF) and a dynamic data structure that supports range queries on ℱ. A data structure of this type enables dynamically adding functions to a multiset of functions F ⊆ ℱ, and answering range queries on the output of F, i.e., returning ∑_{f ∈ F} f(x) for a query x. The data structures are defined in one of several models which abstract RAM. The correspondence together with known lower bounds on the update time and the query time in data structures leads to the first non-trivial lower bounds on FSS schemes which are black-box reducible to PRF. These lower bounds apply to FSS schemes with polynomial key size and include: - For ℱ^d_{box}, the class of all functions which assign a constant group element β ∈ 𝔾 to any input in a specified d-dimensional box and 0 to all other inputs: if the key sharing function, Gen, runs in time polynomial in n and the evaluation function is Eval then: - If d ≥ 2 and 𝔾 = ℤ₂ then Eval’s running time is Ω ((n^{3/2})/(log³ n)). - If d ≥ 2 and 𝔾 is cyclic such that log |𝔾| = (1 + ε) n then Eval’s running time is Ω ((n/(log n)) ²). - If d > 2 is a constant and further, Gen and Eval correspond to operations on data structures in the Oblivious Group Model (this includes all known FSS from OWF techniques), then the product of Eval’s time and the key size is Ω(n^{d-1}). - For ℱ_{mono}, the class of all monomials ax^b ∈ 𝔽_{2ⁿ}[X] such that b ≤ B, assuming n^{ω(1)} ≤ B ≤ 2^{n/4}: if Gen runs in polynomial time, then Eval’s running time is Ω ((n √{log B})/(log² n)).
Cite as

Niv Gilboa and Daniel Weber. Lower Bounds on FSS from Dynamic Data Structures. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 71:1-71:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gilboa_et_al:LIPIcs.ITCS.2026.71,
  author =	{Gilboa, Niv and Weber, Daniel},
  title =	{{Lower Bounds on FSS from Dynamic Data Structures}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{71:1--71:22},
  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.2026.71},
  URN =		{urn:nbn:de:0030-drops-253585},
  doi =		{10.4230/LIPIcs.ITCS.2026.71},
  annote =	{Keywords: FSS, Data Structures, Lower Bounds, Black-Box Reductions}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.90
Slice Rank and Partition Rank of the Determinant

Authors: Amichai Lampert and Guy Moshkovitz

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

Abstract
The Laplace expansion expresses the n × n determinant det_n as a sum of n products. Do shorter expansions exist? In this paper we: - Fully determine the slice rank decompositions of det_n (where each product must contain a linear factor): In this case, we show that n summands are necessary, and moreover, the only such expansions with n summands are equivalent (in a precise sense) to the Laplace expansion. - Prove a logarithmic lower bound for the partition rank of det_n (where each product is of multilinear forms): In this case, we show that at least log₂(n)+1 summands are needed and we explain why existing techniques fail to yield any nontrivial lower bound. - Separate partition rank from slice rank for det_n: we find a quadratic expansion for det₄, over any field, with fewer summands than the Laplace expansion. This construction is related to a well-known example of Green-Tao and Lovett-Meshulam-Samorodnitsky disproving the naive version of the Gowers Inverse conjecture over small fields. An important motivation for these questions comes from the challenge of separating structure and randomness for tensors. On the one hand, we show that the random construction fails to separate: for a random tensor of partition rank r, the analytic rank is r-o(1) with high probability. On the other hand, our results imply that the determinant yields the first asymptotic separation between partition rank and analytic rank of d-tensors, with their ratio tending to infinity with d.
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Amichai Lampert and Guy Moshkovitz. Slice Rank and Partition Rank of the Determinant. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 90:1-90:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lampert_et_al:LIPIcs.ITCS.2026.90,
  author =	{Lampert, Amichai and Moshkovitz, Guy},
  title =	{{Slice Rank and Partition Rank of the Determinant}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{90:1--90:15},
  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.2026.90},
  URN =		{urn:nbn:de:0030-drops-253779},
  doi =		{10.4230/LIPIcs.ITCS.2026.90},
  annote =	{Keywords: Slice rank, partition rank, determinant}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.6
Foundations of Fiat-Denominated Loans Collateralized by Cryptocurrencies

Authors: Pavel Hubáček, Jan Václavek, and Michelle Yeo

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
The rising importance of cryptocurrencies as financial assets pushed their applicability from an object of speculation closer to standard financial instruments such as loans. In this work, we initiate the study of secure protocols that enable fiat-denominated loans collateralized by cryptocurrencies such as Bitcoin. We provide limited-custodial protocols for such loans relying only on trusted arbitration and provide their game-theoretical analysis. We also highlight various interesting directions for future research.
Cite as

Pavel Hubáček, Jan Václavek, and Michelle Yeo. Foundations of Fiat-Denominated Loans Collateralized by Cryptocurrencies. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hubacek_et_al:LIPIcs.OPODIS.2025.6,
  author =	{Hub\'{a}\v{c}ek, Pavel and V\'{a}clavek, Jan and Yeo, Michelle},
  title =	{{Foundations of Fiat-Denominated Loans Collateralized by Cryptocurrencies}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.6},
  URN =		{urn:nbn:de:0030-drops-251796},
  doi =		{10.4230/LIPIcs.OPODIS.2025.6},
  annote =	{Keywords: Blockchains, Cryptocurrencies, DeFi, Loans, Mechanism design, Subgame Perfect Equilibrium, Rational analysis}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.18
Distributed Download from an External Data Source in Asynchronous Faulty Settings

Authors: John Augustine, Soumyottam Chatterjee, Valerie King, Manish Kumar, Shachar Meir, and David Peleg

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
The distributed Data Retrieval (DR) model consists of k peers connected by a complete peer-to-peer communication network, and a trusted external data source that stores an array X of n bits (n ≫ k). Up to β k of the peers might fail in any execution (for β ∈ [0, 1)). Peers can obtain the information either by inexpensive messages passed among themselves or through expensive queries to the source array X. In the DR model, we focus on designing protocols that minimize the number of queries performed by any nonfaulty peer (a measure referred to as the query complexity) while maximizing the resiliency parameter β. The Download problem requires each nonfaulty peer to correctly learn the entire array X. Earlier work on this problem focused on synchronous communication networks and established several deterministic and randomized upper and lower bounds. Our work is the first to extend the study of distributed data retrieval to asynchronous communication networks. We address the Download problem under both the Byzantine and crash failure models. We present query-optimal deterministic solutions in an asynchronous model that can tolerate any fixed fraction β < 1 of crash faults. In the Byzantine failure model, it is known that deterministic protocols incur a query complexity of Ω(n) per peer, even under synchrony. We extend this lower bound to randomized protocols in the asynchronous model for β ≥ 1/2, and further show that for β < 1/2, a randomized protocol exists with near-optimal query complexity.
Cite as

John Augustine, Soumyottam Chatterjee, Valerie King, Manish Kumar, Shachar Meir, and David Peleg. Distributed Download from an External Data Source in Asynchronous Faulty Settings. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{augustine_et_al:LIPIcs.OPODIS.2025.18,
  author =	{Augustine, John and Chatterjee, Soumyottam and King, Valerie and Kumar, Manish and Meir, Shachar and Peleg, David},
  title =	{{Distributed Download from an External Data Source in Asynchronous Faulty Settings}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.18},
  URN =		{urn:nbn:de:0030-drops-251915},
  doi =		{10.4230/LIPIcs.OPODIS.2025.18},
  annote =	{Keywords: Byzantine Fault Tolerance, Blockchain Oracle, Data Retrieval Model, Distributed Download, asynchrony}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.8
Binary k-Center with Missing Entries: Structure Leads to Tractability

Authors: Tobias Friedrich, Kirill Simonov, and Farehe Soheil

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
k-Center clustering is a fundamental classification problem, where the task is to categorize the given collection of entities into k clusters and come up with a representative for each cluster, so that the maximum distance between an entity and its representative is minimized. In this work, we focus on the setting where the entities are represented by binary vectors with missing entries, which model incomplete categorical data. This version of the problem has wide applications, from predictive analytics to bioinformatics. Our main finding is that the problem, which is notoriously hard from the classical complexity viewpoint, becomes tractable as soon as the known entries are sparse and exhibit a certain structure. Formally, we show fixed-parameter tractable algorithms for the parameters vertex cover, fracture number, and treewidth of the row-column graph, which encodes the positions of the known entries of the matrix. Additionally, we tie the complexity of the 1-cluster variant of the problem, which is famous under the name Closest String, to the complexity of solving integer linear programs with few constraints. This implies, in particular, that improving upon the running times of our algorithms would lead to more efficient algorithms for integer linear programming in general.
Cite as

Tobias Friedrich, Kirill Simonov, and Farehe Soheil. Binary k-Center with Missing Entries: Structure Leads to Tractability. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{friedrich_et_al:LIPIcs.IPEC.2025.8,
  author =	{Friedrich, Tobias and Simonov, Kirill and Soheil, Farehe},
  title =	{{Binary k-Center with Missing Entries: Structure Leads to Tractability}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.8},
  URN =		{urn:nbn:de:0030-drops-251403},
  doi =		{10.4230/LIPIcs.IPEC.2025.8},
  annote =	{Keywords: Clustering, Missing Entries, k-Center, Parameterized Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.19
Traffic-Oblivious Multi-Commodity Flow Network Design

Authors: Markus Chimani and Max Ilsen

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
We consider the Minimum Multi-Commodity Flow Subgraph (MMCFS) problem: given a directed graph G with edge capacities cap and a retention ratio α ∈ (0,1), find an edge-wise minimum subgraph G' ⊆ G such that for all traffic matrices T routable in G using a multi-commodity flow, α⋅ T is routable in G'. This natural yet novel problem is motivated by recent research that investigates how the power consumption in backbone computer networks can be reduced by turning off connections during times of low demand without compromising the quality of service. Since the actual traffic demands are generally not known beforehand, our approach must be traffic-oblivious, i.e., work for all possible sets of simultaneously routable traffic demands in the original network. In this paper we present the problem, relate it to other known problems in literature, and show several structural results, including a reformulation, maximum possible deviations from the optimum, and NP-hardness (as well as a certain inapproximability) already on very restricted instances. The most significant contribution is a max(1/α, 2)-approximation based on a surprisingly simple LP-rounding scheme. We also give instances where this worst-case approximation ratio is met and thus prove that our analysis is tight.
Cite as

Markus Chimani and Max Ilsen. Traffic-Oblivious Multi-Commodity Flow Network Design. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chimani_et_al:LIPIcs.ISAAC.2025.19,
  author =	{Chimani, Markus and Ilsen, Max},
  title =	{{Traffic-Oblivious Multi-Commodity Flow Network Design}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{19:1--19:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.19},
  URN =		{urn:nbn:de:0030-drops-249273},
  doi =		{10.4230/LIPIcs.ISAAC.2025.19},
  annote =	{Keywords: Multi-commodity flow, Digraphs, LP-rounding, Approximation algorithm}
}
Document
DOI: 10.4230/LIPIcs.AFT.2025.3
Fast, Private and Regulated Payments in Asynchronous Networks

Authors: Maxence Brugeres, Victor Languille, Petr Kuznetsov, and Hamza Zarfaoui

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract
We propose a decentralized asset-transfer system that enjoys full privacy: no party can learn the details of a transaction, except for its issuer and its recipient. Furthermore, the recipient is not aware of the sender’s identity. Our system does not rely on consensus or synchrony assumptions, and therefore, it is responsive, since it runs at the actual network speed. Under the hood, every transaction creates a consumable coin equipped with a non-interactive zero-knowledge proof (NIZK) that confirms that the issuer has sufficient funds without revealing any information about her identity, the recipient’s identity, or the payment amount. Moreover, we equip our system with a regulatory enforcement mechanism that can be used to regulate transfer limits or restrict specific addresses from sending or receiving funds, while preserving the system’s privacy guarantees. Finally, we report on PaxPay, our implementation of Fully Private Asset Transfer (FPAT) that uses the Gnark library for the NIZKs. In our benchmark, PaxPay exhibits better performance than earlier proposals that either ensure only partial privacy, require some kind of network synchrony or do not implement regulation features. Our system thus reconciles privacy, responsiveness, regulation enforcement and performance.
Cite as

Maxence Brugeres, Victor Languille, Petr Kuznetsov, and Hamza Zarfaoui. Fast, Private and Regulated Payments in Asynchronous Networks. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 3:1-3:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{brugeres_et_al:LIPIcs.AFT.2025.3,
  author =	{Brugeres, Maxence and Languille, Victor and Kuznetsov, Petr and Zarfaoui, Hamza},
  title =	{{Fast, Private and Regulated Payments in Asynchronous Networks}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{3:1--3:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.3},
  URN =		{urn:nbn:de:0030-drops-247227},
  doi =		{10.4230/LIPIcs.AFT.2025.3},
  annote =	{Keywords: Anonymous, Asset Transfer, Asynchronous System, BFT, CBDC, NIZK, Payment System, Privacy, Regulation, Scalability, zk-SNARK}
}
Document
DOI: 10.4230/LIPIcs.AFT.2025.1
Cache Timing Leakages in Zero-Knowledge Protocols

Authors: Shibam Mukherjee, Christian Rechberger, and Markus Schofnegger

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract
The area of modern zero-knowledge proof systems has seen a significant rise in popularity over the last couple of years, with new techniques and optimized constructions emerging on a regular basis. As the field matures, the aspect of implementation attacks becomes more relevant, however side-channel attacks on zero-knowledge proof systems have seen surprisingly little treatment so far. In this paper, we give an overview of potential attack vectors and show that some of the underlying finite field libraries, and implementations of heavily used components like hash functions using them, are vulnerable w.r.t. cache attacks on CPUs. On the positive side, we demonstrate that the computational overhead to protect against these attacks is relatively small.
Cite as

Shibam Mukherjee, Christian Rechberger, and Markus Schofnegger. Cache Timing Leakages in Zero-Knowledge Protocols. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 1:1-1:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mukherjee_et_al:LIPIcs.AFT.2025.1,
  author =	{Mukherjee, Shibam and Rechberger, Christian and Schofnegger, Markus},
  title =	{{Cache Timing Leakages in Zero-Knowledge Protocols}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{1:1--1:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.1},
  URN =		{urn:nbn:de:0030-drops-247201},
  doi =		{10.4230/LIPIcs.AFT.2025.1},
  annote =	{Keywords: zero-knowledge, protocol, cache timing, side-channel, leakage}
}
Document
DOI: 10.4230/LIPIcs.AFT.2025.2
Zero-Knowledge Authenticator for Blockchain: Policy-Private and Obliviously Updateable

Authors: Kostas Kryptos Chalkias, Deepak Maram, Arnab Roy, Joy Wang, and Aayush Yadav

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract
Transaction details and participant identities on the blockchain are often publicly exposed. In this work, we posit that blockchain’s transparency should not come at the cost of privacy. To that end, we introduce zero-knowledge authenticators (zkAt), a new cryptographic primitive for privacy-preserving authentication on public blockchains. zkAt utilizes zero-knowledge proofs to enable users to authenticate transactions, while keeping the underlying authentication policies private. Prior solutions for such policy-private authentication required the use of threshold signatures, which can only hide the threshold access structure itself. In comparison, zkAt provides privacy for arbitrarily complex authentication policies, and offers a richer interface even within the threshold access structure by, for instance, allowing for the combination of signatures under distinct signature schemes. In order to construct zkAt, we design a compiler that transforms the popular Groth16 non-interactive zero knowledge (NIZK) proof system into a NIZK with equivocable verification keys, a property that we define in this work. Then, for any zkAt constructed using proof systems with this new property, we show that all public information must be independent of the policy, thereby achieving policy-privacy. Next, we give an extension of zkAt, called zkAt^+ wherein, assuming a trusted authority, policies can be updated obliviously in the sense that a third-party learns no new information when a policy is updated by the policy issuer. We also give a theoretical construction for zkAt^+ using recursive NIZKs, and explore the integration of zkAt into modern blockchains. Finally, to evaluate their feasibility, we implement both our schemes for a specific threshold access structure. Our findings show that zkAt achieves comparable performance to traditional threshold signatures, while also attaining privacy for significantly more complex policies with very little overhead.
Cite as

Kostas Kryptos Chalkias, Deepak Maram, Arnab Roy, Joy Wang, and Aayush Yadav. Zero-Knowledge Authenticator for Blockchain: Policy-Private and Obliviously Updateable. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kryptoschalkias_et_al:LIPIcs.AFT.2025.2,
  author =	{Kryptos Chalkias, Kostas and Maram, Deepak and Roy, Arnab and Wang, Joy and Yadav, Aayush},
  title =	{{Zero-Knowledge Authenticator for Blockchain: Policy-Private and Obliviously Updateable}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{2:1--2:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.2},
  URN =		{urn:nbn:de:0030-drops-247218},
  doi =		{10.4230/LIPIcs.AFT.2025.2},
  annote =	{Keywords: Blockchain privacy, authentication schemes, threshold wallets, zero knowledge proofs}
}
Document
DOI: 10.4230/LIPIcs.AFT.2025.16
Nakamoto Consensus from Multiple Resources

Authors: Mirza Ahad Baig, Christoph U. Günther, and Krzysztof Pietrzak

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract
The blocks in the Bitcoin blockchain "record" the amount of work W that went into creating them through proofs of work. When honest parties control a majority of the work, consensus is achieved by picking the chain with the highest recorded weight. Resources other than work have been considered to secure such longest-chain blockchains. In Chia, blocks record the amount of disk-space S (via a proof of space) and sequential computational steps V (through a VDF). In this paper, we ask what weight functions Γ(S,V,W) (that assign a weight to a block as a function of the recorded space, speed, and work) are secure in the sense that whenever the weight of the resources controlled by honest parties is larger than the weight of adversarial parties, the blockchain is secure against private double-spending attacks. We completely classify such functions in an idealized "continuous" model: Γ(S,V,W) is secure against private double-spending attacks if and only if it is homogeneous of degree one in the "timed" resources V and W, i.e., αΓ(S,V,W) = Γ(S,α V, α W). This includes the Bitcoin rule Γ(S,V,W) = W and the Chia rule Γ(S,V,W) = S ⋅ V. In a more realistic model where blocks are created at discrete time-points, one additionally needs some mild assumptions on the dependency on S (basically, the weight should not grow too much if S is slightly increased, say linear as in Chia). Our classification is more general and allows various instantiations of the same resource. It provides a powerful tool for designing new longest-chain blockchains. E.g., consider combining different PoWs to counter centralization, say the Bitcoin PoW W₁ and a memory-hard PoW W₂. Previous work suggested to use W₁+W₂ as weight. Our results show that using e.g., √{W₁}⋅ √{W₂} or min{W₁,W₂} are also secure, and we argue that in practice these are much better choices.
Cite as

Mirza Ahad Baig, Christoph U. Günther, and Krzysztof Pietrzak. Nakamoto Consensus from Multiple Resources. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 16:1-16:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baig_et_al:LIPIcs.AFT.2025.16,
  author =	{Baig, Mirza Ahad and G\"{u}nther, Christoph U. and Pietrzak, Krzysztof},
  title =	{{Nakamoto Consensus from Multiple Resources}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{16:1--16:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.16},
  URN =		{urn:nbn:de:0030-drops-247353},
  doi =		{10.4230/LIPIcs.AFT.2025.16},
  annote =	{Keywords: Nakamoto Consensus, Heaviest-chain Rule, Resource Theory}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.14
Testing Sumsets Is Hard

Authors: Xi Chen, Shivam Nadimpalli, Tim Randolph, Rocco A. Servedio, and Or Zamir

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

Abstract
A subset S of the Boolean hypercube 𝔽₂ⁿ is a sumset if S = {a + b : a, b ∈ A} for some A ⊆ 𝔽₂ⁿ. Sumsets are central objects of study in additive combinatorics, where they play a role in several of the field’s most important results. We prove a lower bound of Ω(2^{n/2}) for the number of queries needed to test whether a Boolean function f:𝔽₂ⁿ → {0,1} is the indicator function of a sumset, ruling out an efficient testing algorithm for sumsets. Our lower bound for testing sumsets follows from sharp bounds on the related problem of shift testing, which may be of independent interest. We also give a near-optimal {2^{n/2} ⋅ poly(n)}-query algorithm for a smoothed analysis formulation of the sumset refutation problem. Finally, we include a simple proof that the number of different sumsets in 𝔽₂ⁿ is 2^{(1±o(1))2^{n-1}}.
Cite as

Xi Chen, Shivam Nadimpalli, Tim Randolph, Rocco A. Servedio, and Or Zamir. Testing Sumsets Is Hard. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ESA.2025.14,
  author =	{Chen, Xi and Nadimpalli, Shivam and Randolph, Tim and Servedio, Rocco A. and Zamir, Or},
  title =	{{Testing Sumsets Is Hard}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{14:1--14:16},
  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.2025.14},
  URN =		{urn:nbn:de:0030-drops-244822},
  doi =		{10.4230/LIPIcs.ESA.2025.14},
  annote =	{Keywords: Sumsets, additive combinatorics, property testing, Boolean functions}
}
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