10 Search Results for "Sikora, Jamie"


Document
The Entangled Quantum Polynomial Hierarchy Collapses

Authors: Sabee Grewal and Justin Yirka

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


Abstract
We introduce the entangled quantum polynomial hierarchy, QEPH, as the class of problems that are efficiently verifiable given alternating quantum proofs that may be entangled with each other. We prove QEPH collapses to its second level. In fact, we show that a polynomial number of alternations collapses to just two. As a consequence, QEPH = QRG(1), the class of problems having one-turn quantum refereed games, which is known to be contained in PSPACE. This is in contrast to the unentangled quantum polynomial hierarchy, QPH, which contains QMA(2). We also introduce DistributionQCPH, a generalization of the quantum-classical polynomial hierarchy QCPH where the provers send probability distributions over strings (instead of strings). We prove DistributionQCPH = QCPH, suggesting that only quantum superposition (not classical probability) increases the computational power of these hierarchies. To prove this equality, we generalize a game-theoretic result of Lipton and Young (1994) which says that, without loss of generality, the provers can send uniform distributions over a polynomial-size support. We also prove the analogous result for the polynomial hierarchy, i.e., DistributionPH = PH. Finally, we show that PH and QCPH are contained in QPH, resolving an open question of Gharibian et al. (2022).

Cite as

Sabee Grewal and Justin Yirka. The Entangled Quantum Polynomial Hierarchy Collapses. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{grewal_et_al:LIPIcs.CCC.2024.6,
  author =	{Grewal, Sabee and Yirka, Justin},
  title =	{{The Entangled Quantum Polynomial Hierarchy Collapses}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.6},
  URN =		{urn:nbn:de:0030-drops-204028},
  doi =		{10.4230/LIPIcs.CCC.2024.6},
  annote =	{Keywords: Polynomial hierarchy, Entangled proofs, Correlated proofs, Minimax}
}
Document
A Constant Lower Bound for Any Quantum Protocol for Secure Function Evaluation

Authors: Sarah A. Osborn and Jamie Sikora

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


Abstract
Secure function evaluation is a two-party cryptographic primitive where Bob computes a function of Alice’s and his respective inputs, and both hope to keep their inputs private from the other party. It has been proven that perfect (or near perfect) security is impossible, even for quantum protocols. We generalize this no-go result by exhibiting a constant lower bound on the cheating probabilities for any quantum protocol for secure function evaluation, and present many applications from oblivious transfer to the millionaire’s problem. Constant lower bounds are of practical interest since they imply the impossibility to arbitrarily amplify the security of quantum protocols by any means.

Cite as

Sarah A. Osborn and Jamie Sikora. A Constant Lower Bound for Any Quantum Protocol for Secure Function Evaluation. In 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 232, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{osborn_et_al:LIPIcs.TQC.2022.8,
  author =	{Osborn, Sarah A. and Sikora, Jamie},
  title =	{{A Constant Lower Bound for Any Quantum Protocol for Secure Function Evaluation}},
  booktitle =	{17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)},
  pages =	{8:1--8:14},
  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.2022.8},
  URN =		{urn:nbn:de:0030-drops-165151},
  doi =		{10.4230/LIPIcs.TQC.2022.8},
  annote =	{Keywords: Quantum cryptography, security analysis, secure function evaluation}
}
Document
A Device-Independent Protocol for XOR Oblivious Transfer

Authors: Srijita Kundu, Jamie Sikora, and Ernest Y.-Z. Tan

Published in: LIPIcs, Volume 158, 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)


Abstract
Oblivious transfer is a cryptographic primitive where Alice has two bits and Bob wishes to learn some function of them. Ideally, Alice should not learn Bob’s desired function choice and Bob should not learn any more than logically implied by the function value. While decent quantum protocols for this task are known, many quickly become insecure if an adversary were to control the quantum devices used in the implementation of the protocol. Here we present how some existing protocols fail in this device-independent framework, and give a fully-device independent quantum protocol for XOR oblivious transfer which is provably more secure than any classical protocol.

Cite as

Srijita Kundu, Jamie Sikora, and Ernest Y.-Z. Tan. A Device-Independent Protocol for XOR Oblivious Transfer. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{kundu_et_al:LIPIcs.TQC.2020.12,
  author =	{Kundu, Srijita and Sikora, Jamie and Tan, Ernest Y.-Z.},
  title =	{{A Device-Independent Protocol for XOR Oblivious Transfer}},
  booktitle =	{15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
  pages =	{12:1--12:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-146-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{158},
  editor =	{Flammia, Steven T.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2020.12},
  URN =		{urn:nbn:de:0030-drops-127579},
  doi =		{10.4230/LIPIcs.TQC.2020.12},
  annote =	{Keywords: Quantum cryptography, device independence, oblivious transfer, semidefinite programming, security analysis}
}
Document
Towards Quantum One-Time Memories from Stateless Hardware

Authors: Anne Broadbent, Sevag Gharibian, and Hong-Sheng Zhou

Published in: LIPIcs, Volume 158, 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)


Abstract
A central tenet of theoretical cryptography is the study of the minimal assumptions required to implement a given cryptographic primitive. One such primitive is the one-time memory (OTM), introduced by Goldwasser, Kalai, and Rothblum [CRYPTO 2008], which is a classical functionality modeled after a non-interactive 1-out-of-2 oblivious transfer, and which is complete for one-time classical and quantum programs. It is known that secure OTMs do not exist in the standard model in both the classical and quantum settings. Here, we propose a scheme for using quantum information, together with the assumption of stateless (i.e., reusable) hardware tokens, to build statistically secure OTMs. Via the semidefinite programming-based quantum games framework of Gutoski and Watrous [STOC 2007], we prove security for a malicious receiver, against a linear number of adaptive queries to the token, in the quantum universal composability framework, but leave open the question of security against a polynomial amount of queries. Compared to alternative schemes derived from the literature on quantum money, our scheme is technologically simple since it is of the "prepare-and-measure" type. We also show our scheme is "tight" according to two scenarios.

Cite as

Anne Broadbent, Sevag Gharibian, and Hong-Sheng Zhou. Towards Quantum One-Time Memories from Stateless Hardware. In 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 158, pp. 6:1-6:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{broadbent_et_al:LIPIcs.TQC.2020.6,
  author =	{Broadbent, Anne and Gharibian, Sevag and Zhou, Hong-Sheng},
  title =	{{Towards Quantum One-Time Memories from Stateless Hardware}},
  booktitle =	{15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020)},
  pages =	{6:1--6:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-146-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{158},
  editor =	{Flammia, Steven T.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2020.6},
  URN =		{urn:nbn:de:0030-drops-120654},
  doi =		{10.4230/LIPIcs.TQC.2020.6},
  annote =	{Keywords: quantum cryptography, one-time memories, semi-definite programming}
}
Document
Track A: Algorithms, Complexity and Games
Improvements in Quantum SDP-Solving with Applications

Authors: Joran van Apeldoorn and András Gilyén

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)


Abstract
Following the first paper on quantum algorithms for SDP-solving by Brandão and Svore [Brandão and Svore, 2017] in 2016, rapid developments have been made on quantum optimization algorithms. In this paper we improve and generalize all prior quantum algorithms for SDP-solving and give a simpler and unified framework. We take a new perspective on quantum SDP-solvers and introduce several new techniques. One of these is the quantum operator input model, which generalizes the different input models used in previous work, and essentially any other reasonable input model. This new model assumes that the input matrices are embedded in a block of a unitary operator. In this model we give a O~((sqrt{m}+sqrt{n}gamma)alpha gamma^4) algorithm, where n is the size of the matrices, m is the number of constraints, gamma is the reciprocal of the scale-invariant relative precision parameter, and alpha is a normalization factor of the input matrices. In particular for the standard sparse-matrix access, the above result gives a quantum algorithm where alpha=s. We also improve on recent results of Brandão et al. [Fernando G. S. L. Brandão et al., 2018], who consider the special case when the input matrices are proportional to mixed quantum states that one can query. For this model Brandão et al. [Fernando G. S. L. Brandão et al., 2018] showed that the dependence on n can be replaced by a polynomial dependence on both the rank and the trace of the input matrices. We remove the dependence on the rank and hence require only a dependence on the trace of the input matrices. After we obtain these results we apply them to a few different problems. The most notable of which is the problem of shadow tomography, recently introduced by Aaronson [Aaronson, 2018]. Here we simultaneously improve both the sample and computational complexity of the previous best results. Finally we prove a new Omega~(sqrt{m}alpha gamma) lower bound for solving LPs and SDPs in the quantum operator model, which also implies a lower bound for the model of Brandão et al. [Fernando G. S. L. Brandão et al., 2018].

Cite as

Joran van Apeldoorn and András Gilyén. Improvements in Quantum SDP-Solving with Applications. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 99:1-99:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{vanapeldoorn_et_al:LIPIcs.ICALP.2019.99,
  author =	{van Apeldoorn, Joran and Gily\'{e}n, Andr\'{a}s},
  title =	{{Improvements in Quantum SDP-Solving with Applications}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{99:1--99:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.99},
  URN =		{urn:nbn:de:0030-drops-106750},
  doi =		{10.4230/LIPIcs.ICALP.2019.99},
  annote =	{Keywords: quantum algorithms, semidefinite programming, shadow tomography}
}
Document
Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2)

Authors: Sevag Gharibian, Miklos Santha, Jamie Sikora, Aarthi Sundaram, and Justin Yirka

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)


Abstract
The polynomial-time hierarchy (PH) has proven to be a powerful tool for providing separations in computational complexity theory (modulo standard conjectures such as PH does not collapse). Here, we study whether two quantum generalizations of PH can similarly prove separations in the quantum setting. The first generalization, QCPH, uses classical proofs, and the second, QPH, uses quantum proofs. For the former, we show quantum variants of the Karp-Lipton theorem and Toda's theorem. For the latter, we place its third level, Q Sigma_3, into NEXP using the Ellipsoid Method for efficiently solving semidefinite programs. These results yield two implications for QMA(2), the variant of Quantum Merlin-Arthur (QMA) with two unentangled proofs, a complexity class whose characterization has proven difficult. First, if QCPH=QPH (i.e., alternating quantifiers are sufficiently powerful so as to make classical and quantum proofs "equivalent"), then QMA(2) is in the Counting Hierarchy (specifically, in P^{PP^{PP}}). Second, unless QMA(2)= Q Sigma_3 (i.e., alternating quantifiers do not help in the presence of "unentanglement"), QMA(2) is strictly contained in NEXP.

Cite as

Sevag Gharibian, Miklos Santha, Jamie Sikora, Aarthi Sundaram, and Justin Yirka. Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2). In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 58:1-58:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{gharibian_et_al:LIPIcs.MFCS.2018.58,
  author =	{Gharibian, Sevag and Santha, Miklos and Sikora, Jamie and Sundaram, Aarthi and Yirka, Justin},
  title =	{{Quantum Generalizations of the Polynomial Hierarchy with Applications to QMA(2)}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{58:1--58:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.58},
  URN =		{urn:nbn:de:0030-drops-96409},
  doi =		{10.4230/LIPIcs.MFCS.2018.58},
  annote =	{Keywords: Complexity Theory, Quantum Computing, Polynomial Hierarchy, Semidefinite Programming, QMA(2), Quantum Complexity}
}
Document
Fidelity of Quantum Strategies with Applications to Cryptography

Authors: Gus Gutoski, Ansis Rosmanis, and Jamie Sikora

Published in: LIPIcs, Volume 73, 12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)


Abstract
We introduce a definition of the fidelity function for multi-round quantum strategies, which we call the strategy fidelity, that is a generalization of the fidelity function for quantum states. We provide many interesting properties of the strategy fidelity including a Fuchs-van de Graaf relationship with the strategy norm. We illustrate an operational interpretation of the strategy fidelity in the spirit of Uhlmann's Theorem and discuss its application to the security analysis of quantum protocols for interactive cryptographic tasks such as bit-commitment and oblivious string transfer. Our analysis is very general in the sense that the actions of the protocol need not be fully specified, which is in stark contrast to most other security proofs. Lastly, we provide a semidefinite programming formulation of the strategy fidelity.

Cite as

Gus Gutoski, Ansis Rosmanis, and Jamie Sikora. Fidelity of Quantum Strategies with Applications to Cryptography. In 12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 73, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{gutoski_et_al:LIPIcs.TQC.2017.8,
  author =	{Gutoski, Gus and Rosmanis, Ansis and Sikora, Jamie},
  title =	{{Fidelity of Quantum Strategies with Applications to Cryptography}},
  booktitle =	{12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)},
  pages =	{8:1--8:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-034-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{73},
  editor =	{Wilde, Mark M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2017.8},
  URN =		{urn:nbn:de:0030-drops-85830},
  doi =		{10.4230/LIPIcs.TQC.2017.8},
  annote =	{Keywords: Quantum strategies, cryptography, fidelity, semidefinite programming}
}
Document
Simple, Near-Optimal Quantum Protocols for Die-Rolling

Authors: Jamie Sikora

Published in: LIPIcs, Volume 61, 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)


Abstract
Die-rolling is the cryptographic task where two mistrustful, remote parties wish to generate a random D-sided die-roll over a communication channel. Optimal quantum protocols for this task have been given by Aharon and Silman (New Journal of Physics, 2010) but are based on optimal weak coin-flipping protocols which are currently very complicated and not very well understood. In this paper, we first present very simple classical protocols for die-rolling which have decent (and sometimes optimal) security which is in stark contrast to coin-flipping, bit-commitment, oblivious transfer, and many other two-party cryptographic primitives. We also present quantum protocols based on the idea of integer-commitment, a generalization of bit-commitment, where one wishes to commit to an integer. We analyze these protocols using semidefinite programming and finally give protocols which are very close to Kitaev's lower bound for any D >= 3.

Cite as

Jamie Sikora. Simple, Near-Optimal Quantum Protocols for Die-Rolling. In 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 61, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{sikora:LIPIcs.TQC.2016.4,
  author =	{Sikora, Jamie},
  title =	{{Simple, Near-Optimal Quantum Protocols for Die-Rolling}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  pages =	{4:1--4:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Broadbent, Anne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2016.4},
  URN =		{urn:nbn:de:0030-drops-66851},
  doi =		{10.4230/LIPIcs.TQC.2016.4},
  annote =	{Keywords: Quantum Cryptography, Semidefinite Programming, Die-Rolling, Integer-Commitment}
}
Document
Optimal Bounds for Parity-Oblivious Random Access Codes with Applications

Authors: André Chailloux, Iordanis Kerenidis, Srijita Kundu, and Jamie Sikora

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


Abstract
Random Access Codes is an information task that has been extensively studied and found many applications in quantum information. In this scenario, Alice receives an n-bit string x, and wishes to encode x into a quantum state rho_x, such that Bob, when receiving the state rho_x, can choose any bit i in [n] and recover the input bit x_i with high probability. Here we study a variant called parity-oblivious random acres codes, where we impose the cryptographic property that Bob cannot infer any information about the parity of any subset of bits of the input, apart form the single bits x_i. We provide the optimal quantum parity-oblivious random access codes and show that they are asymptotically better than the optimal classical ones. For this, we relate such encodings to a non-local game and provide tight bounds for the success probability of the non-local game via semi-definite programming. Our results provide a large non-contextuality inequality violation and resolve the main open question in [Spekkens et al., Phys. Review Letters, 2009].

Cite as

André Chailloux, Iordanis Kerenidis, Srijita Kundu, and Jamie Sikora. Optimal Bounds for Parity-Oblivious Random Access Codes with Applications. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 76-87, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


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@InProceedings{chailloux_et_al:LIPIcs.TQC.2014.76,
  author =	{Chailloux, Andr\'{e} and Kerenidis, Iordanis and Kundu, Srijita and Sikora, Jamie},
  title =	{{Optimal Bounds for Parity-Oblivious Random Access Codes with Applications}},
  booktitle =	{9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)},
  pages =	{76--87},
  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.2014.76},
  URN =		{urn:nbn:de:0030-drops-48084},
  doi =		{10.4230/LIPIcs.TQC.2014.76},
  annote =	{Keywords: quantum information theory, contextuality, semidefinite programming}
}
Document
Lower bounds for Quantum Oblivious Transfer

Authors: André Chailloux, Iordanis Kerenidis, and Jamie Sikora

Published in: LIPIcs, Volume 8, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)


Abstract
Oblivious transfer is a fundamental primitive in cryptography. While perfect information theoretic security is impossible, quantum oblivious transfer protocols can limit the dishonest players' cheating. Finding the optimal security parameters in such protocols is an important open question. In this paper we show that every 1-out-of-2 oblivious transfer protocol allows a dishonest party to cheat with probability bounded below by a constant strictly larger than $1/2$. Alice's cheating is defined as her probability of guessing Bob's index, and Bob's cheating is defined as his probability of guessing both input bits of Alice. In our proof, we relate these cheating probabilities to the cheating probabilities of a coin flipping protocol and conclude by using Kitaev's coin flipping lower bound. Then, we present an oblivious transfer protocol with two messages and cheating probabilities at most $3/4$. Last, we extend Kitaev's semidefinite programming formulation to more general primitives, where the security is against a dishonest player trying to force the outcome of the other player, and prove optimal lower and upper bounds for them.

Cite as

André Chailloux, Iordanis Kerenidis, and Jamie Sikora. Lower bounds for Quantum Oblivious Transfer. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 157-168, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{chailloux_et_al:LIPIcs.FSTTCS.2010.157,
  author =	{Chailloux, Andr\'{e} and Kerenidis, Iordanis and Sikora, Jamie},
  title =	{{Lower bounds for Quantum Oblivious Transfer}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)},
  pages =	{157--168},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-23-1},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{8},
  editor =	{Lodaya, Kamal and Mahajan, Meena},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2010.157},
  URN =		{urn:nbn:de:0030-drops-28613},
  doi =		{10.4230/LIPIcs.FSTTCS.2010.157},
  annote =	{Keywords: quantum oblivious transfer, coin flipping protocol, semidefinite programming}
}
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