12 Search Results for "Alagic, Gorjan"

Document
DOI: 10.4230/DagRep.15.10.105
Quantum Cryptanalysis (Dagstuhl Seminar 25431)

Authors: Gorjan Alagic, Simona Etinski, Stacey Jeffery, and Rainer Steinwandt

Published in: Dagstuhl Reports, Volume 15, Issue 10 (2026)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 25431 "Quantum Cryptanalysis". The seminar took place as an in-person event in October 2025 and was the eighth installment of the Dagstuhl Seminar series on Quantum Cryptanalysis. This report describes the motivation and technical scope of the seminar as well as the (updated) organizational structure of this week-long event. We also include abstracts of the seminar presentations given by participants and a description of the activities of the working groups.
Cite as

Gorjan Alagic, Simona Etinski, Stacey Jeffery, and Rainer Steinwandt. Quantum Cryptanalysis (Dagstuhl Seminar 25431). In Dagstuhl Reports, Volume 15, Issue 10, pp. 105-118, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@Article{alagic_et_al:DagRep.15.10.105,
  author =	{Alagic, Gorjan and Etinski, Simona and Jeffery, Stacey and Steinwandt, Rainer},
  title =	{{Quantum Cryptanalysis (Dagstuhl Seminar 25431)}},
  pages =	{105--118},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2026},
  volume =	{15},
  number =	{10},
  editor =	{Alagic, Gorjan and Etinski, Simona and Jeffery, Stacey and Steinwandt, Rainer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.15.10.105},
  URN =		{urn:nbn:de:0030-drops-254138},
  doi =		{10.4230/DagRep.15.10.105},
  annote =	{Keywords: computational algebra, cryptanalysis, post-quantum cryptography, quantum algorithms, quantum resource estimation}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.42
Compressed Data Structures for Heegaard Splitting

Authors: Henrique Ennes and Clément Maria

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Heegaard splittings provide a natural representation of closed 3-manifolds by gluing handlebodies along a common surface. These splittings can be equivalently given by two finite sets of meridians lying on the surface, which define a Heegaard diagram. We present a data structure to effectively represent Heegaard diagrams as normal curves with respect to triangulations of a surface of complexity measured by the space required to express the normal coordinates' vectors in binary. This structure can be significantly more compressed than triangulations of 3-manifolds, giving exponential gains for some families. Even with this succinct definition of complexity, we establish polynomial-time algorithms for comparing and manipulating diagrams, performing stabilizations, detecting trivial stabilizations and reductions, and computing topological invariants of the underlying manifolds, such as their fundamental and homology groups. We also contrast early implementations of our techniques with standard software programs for 3-manifolds, achieving faster algorithms for the average cases and exponential gains in speed for some particular presentations of the inputs.
Cite as

Henrique Ennes and Clément Maria. Compressed Data Structures for Heegaard Splitting. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 42:1-42:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ennes_et_al:LIPIcs.SoCG.2026.42,
  author =	{Ennes, Henrique and Maria, Cl\'{e}ment},
  title =	{{Compressed Data Structures for Heegaard Splitting}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{42:1--42:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.42},
  URN =		{urn:nbn:de:0030-drops-258484},
  doi =		{10.4230/LIPIcs.SoCG.2026.42},
  annote =	{Keywords: 3-manifold, Heegaard splitting, curves on surfaces, surface theory, data structure, computational topology}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.37
Hardness of Computation of Quantum Invariants on 3-Manifolds with Restricted Topology

Authors: Henrique Ennes and Clément Maria

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

Abstract
Quantum invariants in low-dimensional topology offer a wide variety of valuable invariants about knots and 3-manifolds, presented by explicit formulas that are readily computable. Their computational complexity has been actively studied and is tightly connected to topological quantum computing. In this article, we prove that for any 3-manifold quantum invariant in the Reshetikhin-Turaev model, there is a deterministic polynomial time algorithm that, given as input an arbitrary closed 3-manifold M, outputs a closed 3-manifold M' with the same quantum invariant, such that M' is hyperbolic, contains no low genus embedded incompressible surface, and is presented by a strongly irreducible Heegaard diagram. Our construction relies on properties of Heegaard splittings and the Hempel distance. At the level of computational complexity, this proves that the hardness of computing a given quantum invariant of 3-manifolds is preserved even when severely restricting the topology and the combinatorics of the input. This positively answers a question raised by Samperton [Samperton, 2023].
Cite as

Henrique Ennes and Clément Maria. Hardness of Computation of Quantum Invariants on 3-Manifolds with Restricted Topology. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ennes_et_al:LIPIcs.ESA.2025.37,
  author =	{Ennes, Henrique and Maria, Cl\'{e}ment},
  title =	{{Hardness of Computation of Quantum Invariants on 3-Manifolds with Restricted Topology}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{37:1--37:16},
  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.2025.37},
  URN =		{urn:nbn:de:0030-drops-245057},
  doi =		{10.4230/LIPIcs.ESA.2025.37},
  annote =	{Keywords: 3-manifold, Heegaard splitting, Hempel distance, Quantum invariant, polynomial time reduction}
}
Document
DOI: 10.4230/LIPIcs.TQC.2025.9
Efficient Quantum Pseudorandomness from Hamiltonian Phase States

Authors: John Bostanci, Jonas Haferkamp, Dominik Hangleiter, and Alexander Poremba

Published in: LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)

Abstract
Quantum pseudorandomness has found applications in many areas of quantum information, ranging from entanglement theory, to models of scrambling phenomena in chaotic quantum systems, and, more recently, in the foundations of quantum cryptography. Kretschmer (TQC '21) showed that both pseudorandom states and pseudorandom unitaries exist even in a world without classical one-way functions. To this day, however, all known constructions require classical cryptographic building blocks which are themselves synonymous with the existence of one-way functions, and which are also challenging to implement on realistic quantum hardware. In this work, we seek to make progress on both of these fronts simultaneously - by decoupling quantum pseudorandomness from classical cryptography altogether. We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem, which is the task of decoding output states of a random instantaneous quantum polynomial-time (IQP) circuit. Hamiltonian phase states can be generated very efficiently using only Hadamard gates, single-qubit Z rotations and CNOT circuits. We show that the hardness of our problem reduces to a worst-case version of the problem, and we provide evidence that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We also show information-theoretic hardness when only few copies of HPS are available by proving an approximate t-design property of our ensemble. Finally, we show that our HPS assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives, ranging from pseudorandom states, to quantum pseudoentanglement, to pseudorandom unitaries, and even primitives such as public-key encryption with quantum keys.
Cite as

John Bostanci, Jonas Haferkamp, Dominik Hangleiter, and Alexander Poremba. Efficient Quantum Pseudorandomness from Hamiltonian Phase States. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bostanci_et_al:LIPIcs.TQC.2025.9,
  author =	{Bostanci, John and Haferkamp, Jonas and Hangleiter, Dominik and Poremba, Alexander},
  title =	{{Efficient Quantum Pseudorandomness from Hamiltonian Phase States}},
  booktitle =	{20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-392-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{350},
  editor =	{Fefferman, Bill},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.9},
  URN =		{urn:nbn:de:0030-drops-240586},
  doi =		{10.4230/LIPIcs.TQC.2025.9},
  annote =	{Keywords: Quantum pseudorandomness, quantum phase states, quantum cryptography}
}
Document
DOI: 10.4230/LIPIcs.TQC.2025.1
Quantum Search with In-Place Queries

Authors: Blake Holman, Ronak Ramachandran, and Justin Yirka

Published in: LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)

Abstract
Quantum query complexity is typically characterized in terms of xor queries |x,y⟩ ↦ |x,y⊕ f(x)⟩ or phase queries, which ensure that even queries to non-invertible functions are unitary. When querying a permutation, another natural model is unitary: in-place queries |x⟩↦ |f(x)⟩. Some problems are known to require exponentially fewer in-place queries than xor queries, but no separation has been shown in the opposite direction. A candidate for such a separation was the problem of inverting a permutation over N elements. This task, equivalent to unstructured search in the context of permutations, is solvable with O(√N) xor queries but was conjectured to require Ω(N) in-place queries. We refute this conjecture by designing a quantum algorithm for Permutation Inversion using O(√N) in-place queries. Our algorithm achieves the same speedup as Grover’s algorithm despite the inability to efficiently uncompute queries or perform straightforward oracle-controlled reflections. Nonetheless, we show that there are indeed problems which require fewer xor queries than in-place queries. We introduce a subspace-conversion problem called Function Erasure that requires 1 xor query and Θ(√N) in-place queries. Then, we build on a recent extension of the quantum adversary method to characterize exact conditions for a decision problem to exhibit such a separation, and we propose a candidate problem.
Cite as

Blake Holman, Ronak Ramachandran, and Justin Yirka. Quantum Search with In-Place Queries. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{holman_et_al:LIPIcs.TQC.2025.1,
  author =	{Holman, Blake and Ramachandran, Ronak and Yirka, Justin},
  title =	{{Quantum Search with In-Place Queries}},
  booktitle =	{20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
  pages =	{1:1--1:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-392-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{350},
  editor =	{Fefferman, Bill},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.1},
  URN =		{urn:nbn:de:0030-drops-240502},
  doi =		{10.4230/LIPIcs.TQC.2025.1},
  annote =	{Keywords: Quantum algorithms, query complexity, quantum complexity theory, quantum search, Grover’s algorithm, permutation inversion}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.8
Single-Round Proofs of Quantumness from Knowledge Assumptions

Authors: Petia Arabadjieva, Alexandru Gheorghiu, Victor Gitton, and Tony Metger

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
A proof of quantumness is an efficiently verifiable interactive test that an efficient quantum computer can pass, but all efficient classical computers cannot (under some cryptographic assumption). Such protocols play a crucial role in the certification of quantum devices. Existing single-round protocols based solely on a cryptographic hardness assumption (like asking the quantum computer to factor a large number) require large quantum circuits, whereas multi-round ones use smaller circuits but require experimentally challenging mid-circuit measurements. In this work, we construct efficient single-round proofs of quantumness based on existing knowledge assumptions. While knowledge assumptions have not been previously considered in this context, we show that they provide a natural basis for separating classical and quantum computation. Our work also helps in understanding the interplay between black-box/white-box reductions and cryptographic assumptions in the design of proofs of quantumness. Specifically, we show that multi-round protocols based on Decisional Diffie-Hellman (DDH) or Learning With Errors (LWE) can be "compiled" into single-round protocols using a knowledge-of-exponent assumption [Bitansky et al., 2012] or knowledge-of-lattice-point assumption [Loftus et al., 2012], respectively. We also prove an adaptive hardcore-bit statement for a family of claw-free functions based on DDH, which might be of independent interest.
Cite as

Petia Arabadjieva, Alexandru Gheorghiu, Victor Gitton, and Tony Metger. Single-Round Proofs of Quantumness from Knowledge Assumptions. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{arabadjieva_et_al:LIPIcs.ITCS.2025.8,
  author =	{Arabadjieva, Petia and Gheorghiu, Alexandru and Gitton, Victor and Metger, Tony},
  title =	{{Single-Round Proofs of Quantumness from Knowledge Assumptions}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.8},
  URN =		{urn:nbn:de:0030-drops-226364},
  doi =		{10.4230/LIPIcs.ITCS.2025.8},
  annote =	{Keywords: Proofs of quantumness, Knowledge assumptions, Learning with errors, Decisional Diffie-Hellman}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.96
Formulations and Constructions of Remote State Preparation with Verifiability, with Applications

Authors: Jiayu Zhang

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
Remote state preparation with verifiability (RSPV) is an important quantum cryptographic primitive [Alexandru Gheorghiu and Thomas Vidick, 2019; Jiayu Zhang, 2022]. In this primitive, a client would like to prepare a quantum state (sampled or chosen from a state family) on the server side, such that ideally the client knows its full description, while the server holds and only holds the state itself. In this work we make several contributions on its formulations, constructions and applications. In more detail: - We first work on the definitions and abstract properties of the RSPV problem. We select and compare different variants of definitions [Bennett et al., 2001; Alexandru Gheorghiu and Thomas Vidick, 2019; Jiayu Zhang, 2022; Alexandru Gheorghiu et al., 2022], and study their basic properties (like composability and amplification). - We also study a closely related question of how to certify the server’s operations (instead of solely the states). We introduce a new notion named remote operator application with verifiability (ROAV). We compare this notion with related existing definitions [Summers and Werner, 1987; Dominic Mayers and Andrew Chi-Chih Yao, 2004; Zhengfeng Ji et al., 2021; Tony Metger and Thomas Vidick, 2021; Anand Natarajan and Tina Zhang, 2023], study its abstract properties and leave its concrete constructions for further works. - Building on the abstract properties and existing results [Zvika Brakerski et al., 2023], we construct a series of new RSPV protocols. Our constructions not only simplify existing results [Alexandru Gheorghiu and Thomas Vidick, 2019] but also cover new state families, for example, states in the form of 1/√2 (|0⟩ + |x_0⟩ + |1⟩ |x_1⟩). All these constructions rely only on the existence of weak NTCF [Zvika Brakerski et al., 2020; Navid Alamati et al., 2022], without additional requirements like the adaptive hardcore bit property [Zvika Brakerski et al., 2018; Navid Alamati et al., 2022]. - As a further application, we show that the classical verification of quantum computations (CVQC) problem [Dorit Aharonov et al., 2010; Urmila Mahadev, 2018] could be constructed from assumptions on group actions [Navid Alamati et al., 2020]. This is achieved by combining our results on RSPV with group-action-based instantiation of weak NTCF [Navid Alamati et al., 2022], and then with the quantum-gadget-assisted quantum verification protocol [Ferracin et al., 2018].
Cite as

Jiayu Zhang. Formulations and Constructions of Remote State Preparation with Verifiability, with Applications. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 96:1-96:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhang:LIPIcs.ITCS.2025.96,
  author =	{Zhang, Jiayu},
  title =	{{Formulations and Constructions of Remote State Preparation with Verifiability, with Applications}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{96:1--96:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.96},
  URN =		{urn:nbn:de:0030-drops-227245},
  doi =		{10.4230/LIPIcs.ITCS.2025.96},
  annote =	{Keywords: Quantum Cryptography, Remote State Preparation, Self-testing, Verification of Quantum Computations}
}
Document
DOI: 10.4230/DagRep.13.10.65
Quantum Cryptanalysis (Dagstuhl Seminar 23421)

Authors: Gorjan Alagic, Maria Naya-Plasencia, Rainer Steinwandt, and Manasi Shingane

Published in: Dagstuhl Reports, Volume 13, Issue 10 (2024)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23421 "Quantum Cryptanalysis". The seminar took place as an in-person event in October 2023 and was the seventh installment of the Dagstuhl Seminar series on Quantum Cryptanalysis. This report describes the motivation and technical scope of the seminar as well as the (updated) organizational structure of this week-long event. We also include abstracts of the seminar presentations given by participants and a description of the activities of the working groups.
Cite as

Gorjan Alagic, Maria Naya-Plasencia, Rainer Steinwandt, and Manasi Shingane. Quantum Cryptanalysis (Dagstuhl Seminar 23421). In Dagstuhl Reports, Volume 13, Issue 10, pp. 65-75, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{alagic_et_al:DagRep.13.10.65,
  author =	{Alagic, Gorjan and Naya-Plasencia, Maria and Steinwandt, Rainer and Shingane, Manasi},
  title =	{{Quantum Cryptanalysis (Dagstuhl Seminar 23421)}},
  pages =	{65--75},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{10},
  editor =	{Alagic, Gorjan and Naya-Plasencia, Maria and Steinwandt, Rainer and Shingane, Manasi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.10.65},
  URN =		{urn:nbn:de:0030-drops-198345},
  doi =		{10.4230/DagRep.13.10.65},
  annote =	{Keywords: computational algebra, cryptanalysis, post-quantum cryptography, quantum algorithms, quantum resource estimation}
}
Document
DOI: 10.4230/LIPIcs.TQC.2022.9
Approximating Output Probabilities of Shallow Quantum Circuits Which Are Geometrically-Local in Any Fixed Dimension

Authors: Suchetan Dontha, Shi Jie Samuel Tan, Stephen Smith, Sangheon Choi, and Matthew Coudron

Published in: LIPIcs, Volume 232, 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)

Abstract
We present a classical algorithm that, for any D-dimensional geometrically-local, quantum circuit C of polylogarithmic-depth, and any bit string x ∈ {0,1}ⁿ, can compute the quantity |<x|C|0^{⊗ n}>|² to within any inverse-polynomial additive error in quasi-polynomial time, for any fixed dimension D. This is an extension of the result [Nolan J. Coble and Matthew Coudron, 2021], which originally proved this result for D = 3. To see why this is interesting, note that, while the D = 1 case of this result follows from a standard use of Matrix Product States, known for decades, the D = 2 case required novel and interesting techniques introduced in [Sergy Bravyi et al., 2020]. Extending to the case D = 3 was even more laborious, and required further new techniques introduced in [Nolan J. Coble and Matthew Coudron, 2021]. Our work here shows that, while handling each new dimension has historically required a new insight, and fixed algorithmic primitive, based on known techniques for D ≤ 3, we can now handle any fixed dimension D > 3. Our algorithm uses the Divide-and-Conquer framework of [Nolan J. Coble and Matthew Coudron, 2021] to approximate the desired quantity via several instantiations of the same problem type, each involving D-dimensional circuits on about half the number of qubits as the original. This division step is then applied recursively, until the width of the recursively decomposed circuits in the D^{th} dimension is so small that they can effectively be regarded as (D-1)-dimensional problems by absorbing the small width in the D^{th} dimension into the qudit structure at the cost of a moderate increase in runtime. The main technical challenge lies in ensuring that the more involved portions of the recursive circuit decomposition and error analysis from [Nolan J. Coble and Matthew Coudron, 2021] still hold in higher dimensions, which requires small modifications to the analysis in some places. Our work also includes some simplifications, corrections and clarifications of the use of block-encodings within the original classical algorithm in [Nolan J. Coble and Matthew Coudron, 2021].
Cite as

Suchetan Dontha, Shi Jie Samuel Tan, Stephen Smith, Sangheon Choi, and Matthew Coudron. Approximating Output Probabilities of Shallow Quantum Circuits Which Are Geometrically-Local in Any Fixed Dimension. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dontha_et_al:LIPIcs.TQC.2022.9,
  author =	{Dontha, Suchetan and Tan, Shi Jie Samuel and Smith, Stephen and Choi, Sangheon and Coudron, Matthew},
  title =	{{Approximating Output Probabilities of Shallow Quantum Circuits Which Are Geometrically-Local in Any Fixed Dimension}},
  booktitle =	{17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-237-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{232},
  editor =	{Le Gall, Fran\c{c}ois and Morimae, Tomoyuki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.9},
  URN =		{urn:nbn:de:0030-drops-165163},
  doi =		{10.4230/LIPIcs.TQC.2022.9},
  annote =	{Keywords: Low-Depth Quantum Circuits, Matrix Product States, Block-Encoding}
}
Document
DOI: 10.4230/LIPIcs.TQC.2019.1
On Quantum Chosen-Ciphertext Attacks and Learning with Errors

Authors: Gorjan Alagic, Stacey Jeffery, Maris Ozols, and Alexander Poremba

Published in: LIPIcs, Volume 135, 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)

Abstract
Quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model which grants the adversary quantum oracle access to encryption and decryption, but where the latter is restricted to non-adaptive (i.e., pre-challenge) queries only. We define this model formally using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA1 in analogy to the classical CCA1 security model. Using a bound on quantum random-access codes, we show that the standard PRF-based encryption schemes are QCCA1-secure when instantiated with quantum-secure primitives. We then revisit standard IND-CPA-secure Learning with Errors (LWE) encryption and show that leaking just one quantum decryption query (and no other queries or leakage of any kind) allows the adversary to recover the full secret key with constant success probability. In the classical setting, by contrast, recovering the key requires a linear number of decryption queries. The algorithm at the core of our attack is a (large-modulus version of) the well-known Bernstein-Vazirani algorithm. We emphasize that our results should not be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.
Cite as

Gorjan Alagic, Stacey Jeffery, Maris Ozols, and Alexander Poremba. On Quantum Chosen-Ciphertext Attacks and Learning with Errors. In 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 135, pp. 1:1-1:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{alagic_et_al:LIPIcs.TQC.2019.1,
  author =	{Alagic, Gorjan and Jeffery, Stacey and Ozols, Maris and Poremba, Alexander},
  title =	{{On Quantum Chosen-Ciphertext Attacks and Learning with Errors}},
  booktitle =	{14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)},
  pages =	{1:1--1:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-112-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{135},
  editor =	{van Dam, Wim and Man\v{c}inska, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2019.1},
  URN =		{urn:nbn:de:0030-drops-103939},
  doi =		{10.4230/LIPIcs.TQC.2019.1},
  annote =	{Keywords: quantum chosen-ciphertext security, quantum attacks, learning with errors}
}
Document
DOI: 10.4230/LIPIcs.TQC.2014.141
Circuit Obfuscation Using Braids

Authors: Gorjan Alagic, Stacey Jeffery, and Stephen Jordan

Published in: LIPIcs, Volume 27, 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)

Abstract
An obfuscator is an algorithm that translates circuits into functionally-equivalent similarly-sized circuits that are hard to understand. Efficient obfuscators would have many applications in cryptography. Until recently, theoretical progress has mainly been limited to no-go results. Recent works have proposed the first efficient obfuscation algorithms for classical logic circuits, based on a notion of indistinguishability against polynomial-time adversaries. In this work, we propose a new notion of obfuscation, which we call partial-indistinguishability. This notion is based on computationally universal groups with efficiently computable normal forms, and appears to be incomparable with existing definitions. We describe universal gate sets for both classical and quantum computation, in which our definition of obfuscation can be met by polynomial-time algorithms. We also discuss some potential applications to testing quantum computers. We stress that the cryptographic security of these obfuscators, especially when composed with translation from other gate sets, remains an open question.
Cite as

Gorjan Alagic, Stacey Jeffery, and Stephen Jordan. Circuit Obfuscation Using Braids. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 141-160, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{alagic_et_al:LIPIcs.TQC.2014.141,
  author =	{Alagic, Gorjan and Jeffery, Stacey and Jordan, Stephen},
  title =	{{Circuit Obfuscation Using Braids}},
  booktitle =	{9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)},
  pages =	{141--160},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-73-6},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{27},
  editor =	{Flammia, Steven T. and Harrow, Aram W.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.141},
  URN =		{urn:nbn:de:0030-drops-48135},
  doi =		{10.4230/LIPIcs.TQC.2014.141},
  annote =	{Keywords: obfuscation, cryptography, universality, quantum}
}
Document
DOI: 10.4230/LIPIcs.TQC.2014.161
Classical Simulation of Yang-Baxter Gates

Authors: Gorjan Alagic, Aniruddha Bapat, and Stephen Jordan

Published in: LIPIcs, Volume 27, 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)

Abstract
A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group B_n for every n >= 2. If we view such an operator as a quantum-computational gate, then topological braiding corresponds to a quantum circuit. A basic question is when such a representation affords universal quantum computation. In this work, we show how to classically simulate these circuits when the gate in question belongs to certain families of solutions to the Yang-Baxter equation. These include all of the qubit (i.e., d = 2) solutions, and some simple families that include solutions for arbitrary d >= 2. Our main tool is a probabilistic classical algorithm for efficient simulation of a more general class of quantum circuits. This algorithm may be of use outside the present setting.
Cite as

Gorjan Alagic, Aniruddha Bapat, and Stephen Jordan. Classical Simulation of Yang-Baxter Gates. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 161-175, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{alagic_et_al:LIPIcs.TQC.2014.161,
  author =	{Alagic, Gorjan and Bapat, Aniruddha and Jordan, Stephen},
  title =	{{Classical Simulation of Yang-Baxter Gates}},
  booktitle =	{9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)},
  pages =	{161--175},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-73-6},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{27},
  editor =	{Flammia, Steven T. and Harrow, Aram W.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.161},
  URN =		{urn:nbn:de:0030-drops-48143},
  doi =		{10.4230/LIPIcs.TQC.2014.161},
  annote =	{Keywords: Quantum, Yang-Baxter, Braid, Anyon}
}
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