arXiv subjects

André Chailloux

Publications and source records attributed to André Chailloux.

At least 37 records · Page 2Linked to original sources

arXiv2019

Ternary Syndrome Decoding with Large Weight

The Syndrome Decoding problem is at the core of many code-based cryptosystems. In this paper, we study ternary Syndrome Decoding in large weight. This problem has been introduced in the Wave signature scheme but has never been thoroughly studied. We perform an algorithmic study of this problem which results in an update of the Wave parameters. On a more fundamental level, we show that ternary Syndrome Decoding with large weight is a really harder problem than the binary Syndrome Decoding problem, which could have several applications for the design of code-based cryptosystems.

cs.CR↗

arXiv2018

A note on the quantum query complexity of permutation symmetric functions

It is known since the work of [AA14] 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 $R(f) = \widetilde{O}\left(Q^7(f)\right)$. In this paper, we improve this result and show that $R(f) = {O}\left(Q^3(f)\right)$ 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 [Zha15].

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arXiv2017

A tight security reduction in the quantum random oracle model for code-based signature schemes

Quantum secure signature schemes have a lot of attention recently, in particular because of the NIST call to standardize quantum safe cryptography. However, only few signature schemes can have concrete quantum security because of technical difficulties associated with the Quantum Random Oracle Model (QROM). In this paper, we show that code-based signature schemes based on the full domain hash paradigm can behave very well in the QROM i.e. that we can have tight security reductions. We also study quantum algorithms related to the underlying code-based assumption. Finally, we apply our reduction to a concrete example: the SURF signature scheme. We provide parameters for 128 bits of quantum security in the QROM and show that the obtained parameters are competitive compared to other similar quantum secure signature schemes.

quant-ph↗

arXiv2017

Relativistic (or $2$-prover $1$-round) zero-knowledge protocol for $\mathsf{NP}$ secure against quantum adversaries

In this paper, we show that the zero-knowledge construction for Hamiltonian cycle remains secure against quantum adversaries in the relativistic setting. Our main technical contribution is a tool for studying the action of consecutive measurements on a quantum state which in turn gives upper bounds on the value of some entangled games. This allows us to prove the security of our protocol against quantum adversaries. We also prove security bounds for the (single-round) relativistic string commitment and bit commitment in parallel against quantum adversaries. As an additional consequence of our result, we answer an open question from [Unr12] and show tight bounds on the quantum knowledge error of some $Σ$-protocols.

quant-ph↗

arXiv2017

The information cost of quantum memoryless protocols

We consider memoryless quantum communication protocols, where the two parties do not possess any memory besides their classical input and they take turns performing unitary operations on a pure quantum state that they exchange between them. Most known quantum protocols are of this type and recently a deep connection between memoryless protocols and Bell inequality violations has been explored recently by Buhrman et al. We study the information cost of memoryless quantum protocols by looking at a canonical problem: bounded-round quantum communication protocols for the one-bit AND function. We prove directly a tight lower bound of $Θ(\log(k) / k)$ for the information cost of AND for $k$-round memoryless quantum protocols and for the input distribution needed for the Disjointness function. It is not clear if memoryless protocols allow for a reduction between AND and Disjointness, due to the absence of private workspaces. We enhance the model by allowing the players to keep in their private classical workspace apart from their input also some classical private coins. Surprisingly, we show that every quantum protocol can be transformed into an equivalent quantum protocol with private coins that is perfectly private, i.e. the players only learn the value of the function and nothing more. Last, we consider the model where the players are allowed to use one-shot coins, i.e. private coins that can be used only once during the protocol. While in the classical case, private coins and one-shot coins are equivalent, in the quantum case, we prove that they are not. More precisely, we show that every quantum memoryless protocol with one-bit inputs that uses one-shot coins can be transformed into a memoryless quantum protocol without private coins and without increasing too much its information cost. Hence, while private coins always allow for private quantum protocols, one-shot coins do not.

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arXiv2016

Optimal bounds for semi-honest quantum oblivious transfer

Oblivious transfer is a fundamental cryptographic primitive in which Bob transfers one of two bits to Alice in such a way that Bob cannot know which of the two bits Alice has learned. We present an optimal security bound for quantum oblivious transfer protocols under a natural and demanding definition of what it means for Alice to cheat. Our lower bound is a smooth tradeoff between the probability B with which Bob can guess Alice's bit choice and the probability A with which Alice can guess both of Bob's bits given that she learns one of the bits with certainty. We prove that 2B + A is greater than or equal to 2 in any quantum protocol for oblivious transfer, from which it follows that one of the two parties must be able to cheat with probability at least 2/3. We prove that this bound is optimal by exhibiting a family of protocols whose cheating probabilities can be made arbitrarily close to any point on the tradeoff curve.

quant-ph↗

arXiv2016

Recursive cheating strategies for the relativistic $F_Q$ bit commitment protocol

In this paper, we study relativistic bit commitment, which uses timing and location constraints to achieve information theoretic security. We consider the $F_Q$ multi-round bit commitment scheme introduced by Lunghi et al. [LKB+15]. This protocol was shown secure against classical adversaries as long as the number of rounds $m$ is small compared to $\sqrt{Q}$ where $Q$ is the size of the used field in the protocol [CCL15,FF16]. In this work, we study classical attacks on this scheme. We use classical strategies for the $CHSH_Q$ game described in [BS15] to derive cheating strategies for this protocol. In particular, our cheating strategy shows that if $Q$ is an even power of any prime, then the protocol is not secure when the number of rounds $m$ is of the order of $\sqrt{Q}$. For those values of $Q$, this means that the upper bound of [CCL15,FF16] is essentially optimal.

quant-ph↗

arXiv2016

Robust Relativistic Bit Commitment

Relativistic cryptography exploits the fact that no information can travel faster than the speed of light in order to obtain security guarantees that cannot be achieved from the laws of quantum mechanics alone. Recently, Lunghi et al [Phys. Rev. Lett. 2015] presented a bit commitment scheme where each party uses two agents that exchange classical information in a synchronized fashion, and that is both hiding and binding. A caveat is that the commitment time is intrinsically limited by the spatial configuration of the players, and increasing this time requires the agents to exchange messages during the whole duration of the protocol. While such a solution remains computationally attractive, its practicality is severely limited in realistic settings since all communication must remain perfectly synchronized at all times. In this work, we introduce a robust protocol for relativistic bit commitment that tolerates failures of the classical communication network. This is done by adding a third agent to both parties. Our scheme provides a quadratic improvement in terms of expected sustain time compared to the original protocol, while retaining the same level of security.

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arXiv2016

Optimal bounds for parity-oblivious random access codes

Random access coding 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 $ρ_x$, such that Bob, when receiving the state $ρ_x$, can choose any bit $i \in [n]$ and recover the input bit $x_i$ with high probability. Here we study two variants: parity-oblivious random access 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 from the single bits $x_i$; and even-parity-oblivious random access codes, where Bob cannot infer any information about the parity of any even-size subset of bits of the input. In this paper, we provide the optimal bounds for parity-oblivious quantum random access codes and show that they are asymptotically better than the optimal classical ones. Our results provide a large non-contextuality inequality violation and resolve the main open problem in a work of Spekkens, Buzacott, Keehn, Toner, and Pryde (2009). Second, we provide the optimal bounds for even-parity-oblivious random access codes by proving their equivalence to a non-local game and by providing tight bounds for the success probability of the non-local game via semidefinite programming. In the case of even-parity-oblivious random access codes, the cryptographic property holds also in the device-independent model.

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arXiv2015

Arbitrarily long relativistic bit commitment

We consider the recent relativistic bit commitment protocol introduced by Lunghi et al. [Phys. Rev. Lett. 2015] and present a new security analysis against classical attacks. In particular, while the initial complexity of the protocol scaled double-exponentially with the commitment time, our analysis shows that the correct dependence is only linear. This has dramatic implications in terms of implementation: in particular, the commitment time can easily be made arbitrarily long, by only requiring both parties to communicate classically and perform efficient classical computation.

quant-ph↗

arXiv2015

Parallel Repetition of Free Entangled Games: Simplification and Improvements

In a two-player game, two cooperating but non communicating players, Alice and Bob, receive inputs taken from a probability distribution. Each of them produces an output and they win the game if they satisfy some predicate on their inputs/outputs. The entangled value $ω^*(G)$ of a game $G$ is the maximum probability that Alice and Bob can win the game if they are allowed to share an entangled state prior to receiving their inputs. The $n$-fold parallel repetition $G^n$ of $G$ consists of $n$ instances of $G$ where Alice and Bob receive all the inputs at the same time and must produce all the outputs at the same time. They win $G^n$ if they win each instance of $G$. Recently, there has been a series of works showing parallel repetition with exponential decay for projection games [DSV13], games on the uniform distribution [CS14] and for free games, i.e. games on a product distribution [JPY13]. This article is meant to be a follow up of [CS14], where we improve and simplify several parts of our previous paper. Our main result is that for any free game $G$ with value $ω^*(G)=1-\varepsilon$, we have $ω^*(G^n) \le (1 - \varepsilon^2)^{Ω(\frac{n}{\log(l)})}$ where $l$ is the size of the output set of the game. This result improves on both the results in [JPY13] and [CS14]. The framework we use can also be extended to free projection games. We show that for a free projection game $G$ with value $ω^*(G)=1-\varepsilon$, we have $ω^*(G^n) \le (1 - \varepsilon)^{Ω(n)}$.

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arXiv2015

Graph-theoretical Bounds on the Entangled Value of Non-local Games

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 Lovász 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.

quant-ph↗

arXiv2014

Parallel Repetition of Entangled Games with Exponential Decay via the Superposed Information Cost

In a two-player game, two cooperating but non communicating players, Alice and Bob, receive inputs taken from a probability distribution. Each of them produces an output and they win the game if they satisfy some predicate on their inputs/outputs. The entangled value $ω^*(G)$ of a game $G$ is the maximum probability that Alice and Bob can win the game if they are allowed to share an entangled state prior to receiving their inputs. The $n$-fold parallel repetition $G^n$ of $G$ consists of $n$ instances of $G$ where the players receive all the inputs at the same time and produce all the outputs at the same time. They win $G^n$ if they win each instance of $G$. In this paper we show that for any game $G$ such that $ω^*(G) = 1 - \varepsilon < 1$, $ω^*(G^n)$ decreases exponentially in $n$. First, for any game $G$ on the uniform distribution, we show that $ω^*(G^n) = (1 - \varepsilon^2)^{Ω\left(\frac{n}{\log(|I||O|)} - |\log(\varepsilon)|\right)}$, where $|I|$ and $|O|$ are the sizes of the input and output sets. From this result, we show that for any entangled game $G$, $ω^*(G^n) \le (1 - \varepsilon^2)^{Ω(\frac{n}{Q\log(|I||O|)} - \frac{|\log(\varepsilon)|}{Q})}$ where $p$ is the input distribution of $G$ and $Q= \frac{|I|^2 \max_{xy} p_{xy}^2 }{\min_{xy} p_{xy} }$. This implies parallel repetition with exponential decay as long as $\min_{xy} \{p_{xy}\} \neq 0$ for general games. To prove this parallel repetition, we introduce the concept of \emph{Superposed Information Cost} for entangled games which is inspired from the information cost used in communication complexity.

quant-ph↗

arXiv2014

Experimental plug&play quantum coin flipping

Performing complex cryptographic tasks will be an essential element in future quantum communication networks. These tasks are based on a handful of fundamental primitives, such as coin flipping, where two distrustful parties wish to agree on a randomly generated bit. Although it is known that quantum versions of these primitives can offer information-theoretic security advantages with respect to classical protocols, a demonstration of such an advantage in a practical communication scenario has remained elusive. Here, we experimentally implement a quantum coin flipping protocol that performs strictly better than classically possible over a distance suitable for communication over metropolitan area optical networks. The implementation is based on a practical plug&play system, designed for quantum key distribution. We also show how to combine our protocol with coin flipping protocols that are almost perfectly secure against bounded adversaries, hence enhancing them with a level of information-theoretic security. Our results offer a powerful toolbox for future secure quantum communications.

quant-ph↗

arXiv2014

Strong connections between quantum encodings, non-locality and quantum cryptography

Encoding information in quantum systems can offer surprising advantages but at the same time there are limitations that arise from the fact that measuring an observable may disturb the state of the quantum system. In our work, we provide an in-depth analysis of a simple question: What happens when we perform two measurements sequentially on the same quantum system? This question touches upon some fundamental properties of quantum mechanics, namely the uncertainty principle and the complementarity of quantum measurements. Our results have interesting consequences, for example they can provide a simple proof of the optimal quantum strategy in the famous Clauser-Horne-Shimony-Holt game. Moreover, we show that the way information is encoded in quantum systems can provide a different perspective in understanding other fundamental aspects of quantum information, like non-locality and quantum cryptography. We prove some strong equivalences between these notions and provide a number of applications in all areas.

quant-ph↗

arXiv2014

A simpler proof of existence of quantum weak coin flipping with arbitrarily small bias

Mochon's proof [Moc07] of existence of quantum weak coin flipping with arbitrarily small bias is a fundamental result in quantum cryptography, but at the same time one of the least understood. Though used several times as a black box in important follow-up results [Gan09, CK09, AS10, CK11, KZ13] the result has not been peer-reviewed, its novel techniques (and in particular Kitaev's point game formalism) have not been applied anywhere else, and an explicit protocol is missing. We believe that truly understanding the existence proof and the novel techniques it relies on would constitute a major step in quantum information theory, leading to deeper understanding of entanglement and of quantum protocols in general. In this work, we make a first step in this direction. We simplify parts of Mochon's construction considerably, making about 20 pages of analysis in the original proof superfluous, clarifying some other parts of the proof on the way, and presenting the proof in a way which is conceptually easier to grasp. We believe the resulting proof of existence is easier to understand, more readable, and certainly verifiable. Moreover, we analyze the resources needed to achieve a bias $ε$ and show that the number of qubits is $O(\log 1/ε)$, while the number of rounds is $(1/ε)^{O(1/ε)}$. A true understanding of the proof, including Kitaev's point game techniques and their applicability, as well as completing the task of constructing an explicit (and also simpler and more efficient) protocol, are left to future work.

quant-ph↗

arXiv2013

Lower Bounds for Quantum Oblivious Transfer

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.

quant-ph↗

arXiv2012

Multipartite entanglement verification resistant against dishonest parties

Future quantum information networks will likely consist of quantum and classical agents, who have the ability to communicate in a variety of ways with trusted and untrusted parties and securely delegate computational tasks to untrusted large-scale quantum computing servers. Multipartite quantum entanglement is a fundamental resource for such a network and hence it is imperative to study the possibility of verifying a multipartite entanglement source in a way that is efficient and provides strong guarantees even in the presence of multiple dishonest parties. In this work, we show how an agent of a quantum network can perform a distributed verification of a multipartite entangled source with minimal resources, which is, nevertheless, resistant against any number of dishonest parties. Moreover, we provide a tight tradeoff between the level of security and the distance between the state produced by the source and the ideal maximally entangled state. Last, by adding the resource of a trusted common random source, we can further provide security guarantees for all honest parties in the quantum network simultaneously.

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