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**Published in:** LIPIcs, Volume 310, 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)

One of the founding results of lattice based cryptography is a quantum reduction from the Short Integer Solution (SIS) problem to the Learning with Errors (LWE) problem introduced by Regev. It has recently been pointed out by Chen, Liu and Zhandry [Chen et al., 2022] that this reduction can be made more powerful by replacing the LWE problem with a quantum equivalent, where the errors are given in quantum superposition. In parallel, Regev’s reduction has recently been adapted in the context of code-based cryptography by Debris, Remaud and Tillich [Debris-Alazard et al., 2023], who showed a reduction between the Short Codeword Problem and the Decoding Problem (the DRT reduction). This motivates the study of the Quantum Decoding Problem (QDP), which is the Decoding Problem but with errors in quantum superposition and see how it behaves in the DRT reduction.
The purpose of this paper is to introduce and to lay a firm foundation for QDP. We first show QDP is likely to be easier than classical decoding, by proving that it can be solved in quantum polynomial time in a large regime of noise whereas no non-exponential quantum algorithm is known for the classical decoding problem. Then, we show that QDP can even be solved (albeit not necessarily efficiently) beyond the information theoretic Shannon limit for classical decoding. We give precisely the largest noise level where we can solve QDP giving in a sense the information theoretic limit for this new problem. Finally, we study how QDP can be used in the DRT reduction. First, we show that our algorithms can be properly used in the DRT reduction showing that our quantum algorithms for QDP beyond Shannon capacity can be used to find minimal weight codewords in a random code. On the negative side, we show that the DRT reduction cannot be, in all generality, a reduction between finding small codewords and QDP by exhibiting quantum algorithms for QDP where this reduction entirely fails. Our proof techniques include the use of specific quantum measurements, such as q-ary unambiguous state discrimination and pretty good measurements as well as strong concentration bounds on weight distribution of random shifted dual codes, which we relate using quantum Fourier analysis.

André Chailloux and Jean-Pierre Tillich. The Quantum Decoding Problem. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chailloux_et_al:LIPIcs.TQC.2024.6, author = {Chailloux, Andr\'{e} and Tillich, Jean-Pierre}, title = {{The Quantum Decoding Problem}}, booktitle = {19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)}, pages = {6:1--6:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-328-7}, ISSN = {1868-8969}, year = {2024}, volume = {310}, editor = {Magniez, Fr\'{e}d\'{e}ric and Grilo, Alex Bredariol}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2024.6}, URN = {urn:nbn:de:0030-drops-206767}, doi = {10.4230/LIPIcs.TQC.2024.6}, annote = {Keywords: quantum information theory, code-based cryptography, quantum algorithms} }

Document

**Published in:** LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

It is known since the work of [Aaronson and Ambainis, 2014] that for any permutation symmetric function f, the quantum query complexity is at most polynomially smaller than the classical randomized query complexity, more precisely that R(f) = O~(Q^7(f)). In this paper, we improve this result and show that R(f) = O(Q^3(f)) for a more general class of symmetric functions. Our proof is constructive and relies largely on the quantum hardness of distinguishing a random permutation from a random function with small range from Zhandry [Zhandry, 2015].

André Chailloux. A Note on the Quantum Query Complexity of Permutation Symmetric Functions. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 19:1-19:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chailloux:LIPIcs.ITCS.2019.19, author = {Chailloux, Andr\'{e}}, title = {{A Note on the Quantum Query Complexity of Permutation Symmetric Functions}}, booktitle = {10th Innovations in Theoretical Computer Science Conference (ITCS 2019)}, pages = {19:1--19:7}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-095-8}, ISSN = {1868-8969}, year = {2019}, volume = {124}, editor = {Blum, Avrim}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.19}, URN = {urn:nbn:de:0030-drops-101126}, doi = {10.4230/LIPIcs.ITCS.2019.19}, annote = {Keywords: quantum query complexity, permutation symmetric functions} }

Document

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

We introduce a novel technique to give bounds to the entangled value of non-local games. The technique is based on a class of graphs used by Cabello, Severini and Winter in 2010. The upper bound uses the famous Lovàsz theta number and is efficiently computable; the lower one is based on the quantum independence number, which is a quantity used in the study of entanglement-assisted channel capacities and graph homomorphism games.

André Chailloux, Laura Mancinska, Giannicola Scarpa, and Simone Severini. Graph-theoretical Bounds on the Entangled Value of Non-local Games. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 67-75, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{chailloux_et_al:LIPIcs.TQC.2014.67, author = {Chailloux, Andr\'{e} and Mancinska, Laura and Scarpa, Giannicola and Severini, Simone}, title = {{Graph-theoretical Bounds on the Entangled Value of Non-local Games}}, booktitle = {9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)}, pages = {67--75}, 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.2014.67}, URN = {urn:nbn:de:0030-drops-48074}, doi = {10.4230/LIPIcs.TQC.2014.67}, annote = {Keywords: Graph theory, non-locality, entangled games} }

Document

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

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].

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

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

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.

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} }

Document

**Published in:** LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)

In quantum zero knowledge, the assumption was made that the
verifier is only using unitary operations. Under this assumption,
many nice properties have been shown about quantum zero
knowledge, including the fact that Honest-Verifier Quantum
Statistical Zero Knowledge ($HVQSZK$) is equal to
Cheating-Verifier Quantum Statistical Zero Knowledge ($QSZK$)
(see ~\cite{Wat02,Wat06}).
In this paper, we study what happens when we allow an honest
verifier to flip some coins in addition to using unitary
operations. Flipping a coin is a non-unitary operation but
doesn\'t seem at first to enhance the cheating possibilities of
the verifier since a classical honest verifier can flip coins. In
this setting, we show an unexpected result: any classical
Interactive Proof has an Honest-Verifier Quantum Statistical Zero
Knowledge proof with coins. Note that in the classical case,
honest verifier $SZK$ is no more powerful than $SZK$ and hence it
is not believed to contain even $NP$. On the other hand, in the
case of cheating verifiers, we show that Quantum Statistical Zero
Knowledge where the verifier applies any non-unitary operation is
equal to Quantum Zero-Knowledge where the verifier uses only
unitaries.
One can think of our results in two complementary ways. If we
would like to use the honest verifier model as a means to study
the general model by taking advantage of their equivalence, then
it is imperative to use the unitary definition without coins,
since with the general one this equivalence is most probably not
true. On the other hand, if we would like to use quantum zero
knowledge protocols in a cryptographic scenario where the
honest-but-curious model is sufficient, then adding the unitary
constraint severely decreases the power of quantum zero knowledge
protocols.

Andre Chailloux and Iordanis Kerenidis. Increasing the power of the verifier in Quantum Zero Knowledge. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 95-106, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{chailloux_et_al:LIPIcs.FSTTCS.2008.1744, author = {Chailloux, Andre and Kerenidis, Iordanis}, title = {{Increasing the power of the verifier in Quantum Zero Knowledge}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {95--106}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-08-8}, ISSN = {1868-8969}, year = {2008}, volume = {2}, editor = {Hariharan, Ramesh and Mukund, Madhavan and Vinay, V}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1744}, URN = {urn:nbn:de:0030-drops-17446}, doi = {10.4230/LIPIcs.FSTTCS.2008.1744}, annote = {Keywords: Quantum cryptography, zero-knowledge protocols, honest-verifier, quantum semi-honest model, hiddenquantum cryptography, zero-knowledge protocols, honest-verifier, quantum semi-honest model, hidden-bits} }

Document

**Published in:** LIPIcs, Volume 310, 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)

One of the founding results of lattice based cryptography is a quantum reduction from the Short Integer Solution (SIS) problem to the Learning with Errors (LWE) problem introduced by Regev. It has recently been pointed out by Chen, Liu and Zhandry [Chen et al., 2022] that this reduction can be made more powerful by replacing the LWE problem with a quantum equivalent, where the errors are given in quantum superposition. In parallel, Regev’s reduction has recently been adapted in the context of code-based cryptography by Debris, Remaud and Tillich [Debris-Alazard et al., 2023], who showed a reduction between the Short Codeword Problem and the Decoding Problem (the DRT reduction). This motivates the study of the Quantum Decoding Problem (QDP), which is the Decoding Problem but with errors in quantum superposition and see how it behaves in the DRT reduction.
The purpose of this paper is to introduce and to lay a firm foundation for QDP. We first show QDP is likely to be easier than classical decoding, by proving that it can be solved in quantum polynomial time in a large regime of noise whereas no non-exponential quantum algorithm is known for the classical decoding problem. Then, we show that QDP can even be solved (albeit not necessarily efficiently) beyond the information theoretic Shannon limit for classical decoding. We give precisely the largest noise level where we can solve QDP giving in a sense the information theoretic limit for this new problem. Finally, we study how QDP can be used in the DRT reduction. First, we show that our algorithms can be properly used in the DRT reduction showing that our quantum algorithms for QDP beyond Shannon capacity can be used to find minimal weight codewords in a random code. On the negative side, we show that the DRT reduction cannot be, in all generality, a reduction between finding small codewords and QDP by exhibiting quantum algorithms for QDP where this reduction entirely fails. Our proof techniques include the use of specific quantum measurements, such as q-ary unambiguous state discrimination and pretty good measurements as well as strong concentration bounds on weight distribution of random shifted dual codes, which we relate using quantum Fourier analysis.

André Chailloux and Jean-Pierre Tillich. The Quantum Decoding Problem. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chailloux_et_al:LIPIcs.TQC.2024.6, author = {Chailloux, Andr\'{e} and Tillich, Jean-Pierre}, title = {{The Quantum Decoding Problem}}, booktitle = {19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)}, pages = {6:1--6:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-328-7}, ISSN = {1868-8969}, year = {2024}, volume = {310}, editor = {Magniez, Fr\'{e}d\'{e}ric and Grilo, Alex Bredariol}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2024.6}, URN = {urn:nbn:de:0030-drops-206767}, doi = {10.4230/LIPIcs.TQC.2024.6}, annote = {Keywords: quantum information theory, code-based cryptography, quantum algorithms} }

Document

**Published in:** LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

It is known since the work of [Aaronson and Ambainis, 2014] that for any permutation symmetric function f, the quantum query complexity is at most polynomially smaller than the classical randomized query complexity, more precisely that R(f) = O~(Q^7(f)). In this paper, we improve this result and show that R(f) = O(Q^3(f)) for a more general class of symmetric functions. Our proof is constructive and relies largely on the quantum hardness of distinguishing a random permutation from a random function with small range from Zhandry [Zhandry, 2015].

André Chailloux. A Note on the Quantum Query Complexity of Permutation Symmetric Functions. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 19:1-19:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chailloux:LIPIcs.ITCS.2019.19, author = {Chailloux, Andr\'{e}}, title = {{A Note on the Quantum Query Complexity of Permutation Symmetric Functions}}, booktitle = {10th Innovations in Theoretical Computer Science Conference (ITCS 2019)}, pages = {19:1--19:7}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-095-8}, ISSN = {1868-8969}, year = {2019}, volume = {124}, editor = {Blum, Avrim}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.19}, URN = {urn:nbn:de:0030-drops-101126}, doi = {10.4230/LIPIcs.ITCS.2019.19}, annote = {Keywords: quantum query complexity, permutation symmetric functions} }

Document

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

We introduce a novel technique to give bounds to the entangled value of non-local games. The technique is based on a class of graphs used by Cabello, Severini and Winter in 2010. The upper bound uses the famous Lovàsz theta number and is efficiently computable; the lower one is based on the quantum independence number, which is a quantity used in the study of entanglement-assisted channel capacities and graph homomorphism games.

André Chailloux, Laura Mancinska, Giannicola Scarpa, and Simone Severini. Graph-theoretical Bounds on the Entangled Value of Non-local Games. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 67-75, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{chailloux_et_al:LIPIcs.TQC.2014.67, author = {Chailloux, Andr\'{e} and Mancinska, Laura and Scarpa, Giannicola and Severini, Simone}, title = {{Graph-theoretical Bounds on the Entangled Value of Non-local Games}}, booktitle = {9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)}, pages = {67--75}, 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.2014.67}, URN = {urn:nbn:de:0030-drops-48074}, doi = {10.4230/LIPIcs.TQC.2014.67}, annote = {Keywords: Graph theory, non-locality, entangled games} }

Document

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

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].

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)

Copy BibTex To Clipboard

@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

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

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.

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)

Copy BibTex To Clipboard

@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} }

Document

**Published in:** LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)

In quantum zero knowledge, the assumption was made that the
verifier is only using unitary operations. Under this assumption,
many nice properties have been shown about quantum zero
knowledge, including the fact that Honest-Verifier Quantum
Statistical Zero Knowledge ($HVQSZK$) is equal to
Cheating-Verifier Quantum Statistical Zero Knowledge ($QSZK$)
(see ~\cite{Wat02,Wat06}).
In this paper, we study what happens when we allow an honest
verifier to flip some coins in addition to using unitary
operations. Flipping a coin is a non-unitary operation but
doesn\'t seem at first to enhance the cheating possibilities of
the verifier since a classical honest verifier can flip coins. In
this setting, we show an unexpected result: any classical
Interactive Proof has an Honest-Verifier Quantum Statistical Zero
Knowledge proof with coins. Note that in the classical case,
honest verifier $SZK$ is no more powerful than $SZK$ and hence it
is not believed to contain even $NP$. On the other hand, in the
case of cheating verifiers, we show that Quantum Statistical Zero
Knowledge where the verifier applies any non-unitary operation is
equal to Quantum Zero-Knowledge where the verifier uses only
unitaries.
One can think of our results in two complementary ways. If we
would like to use the honest verifier model as a means to study
the general model by taking advantage of their equivalence, then
it is imperative to use the unitary definition without coins,
since with the general one this equivalence is most probably not
true. On the other hand, if we would like to use quantum zero
knowledge protocols in a cryptographic scenario where the
honest-but-curious model is sufficient, then adding the unitary
constraint severely decreases the power of quantum zero knowledge
protocols.

Andre Chailloux and Iordanis Kerenidis. Increasing the power of the verifier in Quantum Zero Knowledge. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 95-106, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{chailloux_et_al:LIPIcs.FSTTCS.2008.1744, author = {Chailloux, Andre and Kerenidis, Iordanis}, title = {{Increasing the power of the verifier in Quantum Zero Knowledge}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {95--106}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-08-8}, ISSN = {1868-8969}, year = {2008}, volume = {2}, editor = {Hariharan, Ramesh and Mukund, Madhavan and Vinay, V}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1744}, URN = {urn:nbn:de:0030-drops-17446}, doi = {10.4230/LIPIcs.FSTTCS.2008.1744}, annote = {Keywords: Quantum cryptography, zero-knowledge protocols, honest-verifier, quantum semi-honest model, hiddenquantum cryptography, zero-knowledge protocols, honest-verifier, quantum semi-honest model, hidden-bits} }

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