arXiv subjects

Christian Schaffner

Publications and source records attributed to Christian Schaffner.

50 records · Page 3Linked to original sources

arXiv2011

Position-Based Quantum Cryptography: Impossibility and Constructions

In this work, we study position-based cryptography in the quantum setting. The aim is to use the geographical position of a party as its only credential. On the negative side, we show that if adversaries are allowed to share an arbitrarily large entangled quantum state, no secure position-verification is possible at all. We show a distributed protocol for computing any unitary operation on a state shared between the different users, using local operations and one round of classical communication. Using this surprising result, we break any position-verification scheme of a very general form. On the positive side, we show that if adversaries do not share any entangled quantum state but can compute arbitrary quantum operations, secure position-verification is achievable. Jointly, these results suggest the interesting question whether secure position-verification is possible in case of a bounded amount of entanglement. Our positive result can be interpreted as resolving this question in the simplest case, where the bound is set to zero. In models where secure positioning is achievable, it has a number of interesting applications. For example, it enables secure communication over an insecure channel without having any pre-shared key, with the guarantee that only a party at a specific location can learn the content of the conversation. More generally, we show that in settings where secure position-verification is achievable, other position-based cryptographic schemes are possible as well, such as secure position-based authentication and position-based key agreement.

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arXiv2011

Implementation of two-party protocols in the noisy-storage model

The noisy-storage model allows the implementation of secure two-party protocols under the sole assumption that no large-scale reliable quantum storage is available to the cheating party. No quantum storage is thereby required for the honest parties. Examples of such protocols include bit commitment, oblivious transfer and secure identification. Here, we provide a guideline for the practical implementation of such protocols. In particular, we analyze security in a practical setting where the honest parties themselves are unable to perform perfect operations and need to deal with practical problems such as errors during transmission and detector inefficiencies. We provide explicit security parameters for two different experimental setups using weak coherent, and parametric down conversion sources. In addition, we analyze a modification of the protocols based on decoy states.

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arXiv2010

Simple Protocols for Oblivious Transfer and Secure Identification in the Noisy-Quantum-Storage Model

We present simple protocols for oblivious transfer and password-based identification which are secure against general attacks in the noisy-quantum-storage model as defined in [KWW09]. We argue that a technical tool from [KWW09] suffices to prove security of the known protocols. Whereas the more involved protocol for oblivious transfer from [KWW09] requires less noise in storage to achieve security, our "canonical" protocols have the advantage of being simpler to implement and the security error is easier control. Therefore, our protocols yield higher OT-rates for many realistic noise parameters. Furthermore, the first proof of security of a direct protocol for password-based identification against general noisy-quantum-storage attacks is given.

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arXiv2010

Leftover Hashing Against Quantum Side Information

The Leftover Hash Lemma states that the output of a two-universal hash function applied to an input with sufficiently high entropy is almost uniformly random. In its standard formulation, the lemma refers to a notion of randomness that is (usually implicitly) defined with respect to classical side information. Here, we prove a (strictly) more general version of the Leftover Hash Lemma that is valid even if side information is represented by the state of a quantum system. Furthermore, our result applies to arbitrary delta-almost two-universal families of hash functions. The generalized Leftover Hash Lemma has applications in cryptography, e.g., for key agreement in the presence of an adversary who is not restricted to classical information processing.

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arXiv2009

On the Power of Two-Party Quantum Cryptography

We study quantum protocols among two distrustful parties. Under the sole assumption of correctness - guaranteeing that honest players obtain their correct outcomes - we show that every protocol implementing a non-trivial primitive necessarily leaks information to a dishonest player. This extends known impossibility results to all non-trivial primitives. We provide a framework for quantifying this leakage and argue that leakage is a good measure for the privacy provided to the players by a given protocol. Our framework also covers the case where the two players are helped by a trusted third party. We show that despite the help of a trusted third party, the players cannot amplify the cryptographic power of any primitive. All our results hold even against quantum honest-but-curious adversaries who honestly follow the protocol but purify their actions and apply a different measurement at the end of the protocol. As concrete examples, we establish lower bounds on the leakage of standard universal two-party primitives such as oblivious transfer.

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arXiv2009

Robust Cryptography in the Noisy-Quantum-Storage Model

It was shown in [WST08] that cryptographic primitives can be implemented based on the assumption that quantum storage of qubits is noisy. In this work we analyze a protocol for the universal task of oblivious transfer that can be implemented using quantum-key-distribution (QKD) hardware in the practical setting where honest participants are unable to perform noise-free operations. We derive trade-offs between the amount of storage noise, the amount of noise in the operations performed by the honest participants and the security of oblivious transfer which are greatly improved compared to the results in [WST08]. As an example, we show that for the case of depolarizing noise in storage we can obtain secure oblivious transfer as long as the quantum bit-error rate of the channel does not exceed 11% and the noise on the channel is strictly less than the quantum storage noise. This is optimal for the protocol considered. Finally, we show that our analysis easily carries over to quantum protocols for secure identification.

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arXiv2009

Improving the Security of Quantum Protocols via Commit-and-Open

We consider two-party quantum protocols starting with a transmission of some random BB84 qubits followed by classical messages. We show a general "compiler" improving the security of such protocols: if the original protocol is secure against an "almost honest" adversary, then the compiled protocol is secure against an arbitrary computationally bounded (quantum) adversary. The compilation preserves the number of qubits sent and the number of rounds up to a constant factor. The compiler also preserves security in the bounded-quantum-storage model (BQSM), so if the original protocol was BQSM-secure, the compiled protocol can only be broken by an adversary who has large quantum memory and large computing power. This is in contrast to known BQSM-secure protocols, where security breaks down completely if the adversary has larger quantum memory than expected. We show how our technique can be applied to quantum identification and oblivious transfer protocols.

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arXiv2009

Secure Identification and QKD in the Bounded-Quantum-Storage Model

We consider the problem of secure identification: user U proves to server S that he knows an agreed (possibly low-entropy) password w, while giving away as little information on w as possible, namely the adversary can exclude at most one possible password for each execution of the scheme. We propose a solution in the bounded-quantum-storage model, where U and S may exchange qubits, and a dishonest party is assumed to have limited quantum memory. No other restriction is posed upon the adversary. An improved version of the proposed identification scheme is also secure against a man-in-the-middle attack, but requires U and S to additionally share a high-entropy key k. However, security is still guaranteed if one party loses k to the attacker but notices the loss. In both versions of the scheme, the honest participants need no quantum memory, and noise and imperfect quantum sources can be tolerated. The schemes compose sequentially, and w and k can securely be re-used. A small modification to the identification scheme results in a quantum-key-distribution (QKD) scheme, secure in the bounded-quantum-storage model, with the same re-usability properties of the keys, and without assuming authenticated channels. This is in sharp contrast to known QKD schemes (with unbounded adversary) without authenticated channels, where authentication keys must be updated, and unsuccessful executions can cause the parties to run out of keys.

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arXiv2008

Composing Quantum Protocols in a Classical Environment

We propose a general security definition for cryptographic quantum protocols that implement classical non-reactive two-party tasks. The definition is expressed in terms of simple quantum-information-theoretic conditions which must be satisfied by the protocol to be secure. The conditions are uniquely determined by the ideal functionality F defining the cryptographic task to be implemented. We then show the following composition result. If quantum protocols pi_1,...,pi_k securely implement ideal functionalities F_1,...,F_k according to our security definition, then any purely classical two-party protocol, which makes sequential calls to F_1,...,F_k, is equally secure as the protocol obtained by replacing the calls to F_1,...,F_k with the respective quantum protocols pi_1,...,pi_k. Hence, our approach yields the minimal security requirements which are strong enough for the typical use of quantum protocols as subroutines within larger classical schemes. Finally, we show that recently proposed quantum protocols for oblivious transfer and secure identification in the bounded-quantum-storage model satisfy our security definition, and thus compose in the above sense.

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arXiv2008

Cryptography from Noisy Storage

We show how to implement cryptographic primitives based on the realistic assumption that quantum storage of qubits is noisy. We thereby consider individual-storage attacks, i.e. the dishonest party attempts to store each incoming qubit separately. Our model is similar to the model of bounded-quantum storage, however, we consider an explicit noise model inspired by present-day technology. To illustrate the power of this new model, we show that a protocol for oblivious transfer (OT) is secure for any amount of quantum-storage noise, as long as honest players can perform perfect quantum operations. Our model also allows the security of protocols that cope with noise in the operations of the honest players and achieve more advanced tasks such as secure identification.

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arXiv2007

Randomness Extraction via Delta-Biased Masking in the Presence of a Quantum Attacker

Randomness extraction is of fundamental importance for information-theoretic cryptography. It allows to transform a raw key about which an attacker has some limited knowledge into a fully secure random key, on which the attacker has essentially no information. Up to date, only very few randomness-extraction techniques are known to work against an attacker holding quantum information on the raw key. This is very much in contrast to the classical (non-quantum) setting, which is much better understood and for which a vast amount of different techniques are known and proven to work. We prove a new randomness-extraction technique, which is known to work in the classical setting, to be secure against a quantum attacker as well. Randomness extraction is done by XOR'ing a so-called delta-biased mask to the raw key. Our result allows to extend the classical applications of this extractor to the quantum setting. We discuss the following two applications. We show how to encrypt a long message with a short key, information-theoretically secure against a quantum attacker, provided that the attacker has enough quantum uncertainty on the message. This generalizes the concept of entropically-secure encryption to the case of a quantum attacker. As second application, we show how to do error-correction without leaking partial information to a quantum attacker. Such a technique is useful in settings where the raw key may contain errors, since standard error-correction techniques may provide the attacker with information on, say, a secret key that was used to obtain the raw key.

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arXiv2007

Cryptography in the Bounded-Quantum-Storage Model

This thesis initiates the study of cryptographic protocols in the bounded-quantum-storage model. On the practical side, simple protocols for Rabin Oblivious Transfer, 1-2 Oblivious Transfer and Bit Commitment are presented. No quantum memory is required for honest players, whereas the protocols can only be broken by an adversary controlling a large amount of quantum memory. The protocols are efficient, non-interactive and can be implemented with today's technology. On the theoretical side, new entropic uncertainty relations involving min-entropy are established and used to prove the security of protocols according to new strong security definitions. For instance, in the realistic setting of Quantum Key Distribution (QKD) against quantum-memory-bounded eavesdroppers, the uncertainty relation allows to prove the security of QKD protocols while tolerating considerably higher error rates compared to the standard model with unbounded adversaries.

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arXiv2007

A Tight High-Order Entropic Quantum Uncertainty Relation With Applications

We derive a new entropic quantum uncertainty relation involving min-entropy. The relation is tight and can be applied in various quantum-cryptographic settings. Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit Commitment are presented and the uncertainty relation is used to prove the security of these protocols in the bounded quantum-storage model according to new strong security definitions. As another application, we consider the realistic setting of Quantum Key Distribution (QKD) against quantum-memory-bounded eavesdroppers. The uncertainty relation allows to prove the security of QKD protocols in this setting while tolerating considerably higher error rates compared to the standard model with unbounded adversaries. For instance, for the six-state protocol with one-way communication, a bit-flip error rate of up to 17% can be tolerated (compared to 13% in the standard model). Our uncertainty relation also yields a lower bound on the min-entropy key uncertainty against known-plaintext attacks when quantum ciphers are composed. Previously, the key uncertainty of these ciphers was only known with respect to Shannon entropy.

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arXiv2006

Cryptography In the Bounded Quantum-Storage Model

We initiate the study of two-party cryptographic primitives with unconditional security, assuming that the adversary's quantum memory is of bounded size. We show that oblivious transfer and bit commitment can be implemented in this model using protocols where honest parties need no quantum memory, whereas an adversarial player needs quantum memory of size at least n/2 in order to break the protocol, where n is the number of qubits transmitted. This is in sharp contrast to the classical bounded-memory model, where we can only tolerate adversaries with memory of size quadratic in honest players' memory size. Our protocols are efficient, non-interactive and can be implemented using today's technology. On the technical side, a new entropic uncertainty relation involving min-entropy is established.

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