Composable security in relativistic quantum cryptography

Vilasini, V.; Portmann, Christopher; Rio, Lídia del

doi:10.1088/1367-2630/ab0e3b

Cited by 22 publications

(38 citation statements)

References 37 publications

(184 reference statements)

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“…The precise relationships between all these notions of causality, their operational meaning and implications for the physics of information processing remains open. In an upcoming work involving one the authors [53], further relationships between the interventionist notion of causation, indefinite causation and no superluminal signalling are derived by extending the approach initiated here. This suggests that indefinite causation can be explained through definite cyclic causation (as also implied by the results of [28]), which would mean that cyclic and non-classical causal models can have applications beyond scenarios with a definite spacetime structure.…”

Section: Open Questionsmentioning

confidence: 93%

“…f. Indefinite space-time locations: In the present work, we have embedded causal models in a space-time structure by assigning a single space-time location to each observed system. More generally, we can have, both in theory and practice, systems whose space-time locations are associated with some classical or quantum uncertainty or protocols involving quantum systems that are delocalised over space and in time [27,53,[69][70][71]. It would therefore be of interest to generalise our methods to allow for such superpositions.…”

Section: E Causal Discovery In the Presence Of Fine-tuningmentioning

confidence: 99%

“…It would therefore be of interest to generalise our methods to allow for such superpositions. In an upcoming work [53], a method to do this for finite dimensional quantum systems in a discrete space-time (i.e., a partially ordered set as considered here) is proposed, which has applications for physically characterising so-called indefinite causal order processes [26]. 7 and Corollary IV.1).…”

Section: E Causal Discovery In the Presence Of Fine-tuningmentioning

confidence: 99%

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Possibility of causal loops without superluminal signalling -- a general framework

Vilasini,

Colbeck

2021

Preprint

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Causality is fundamental to science, but it appears in several different forms. One is relativistic causality, which is tied to a space-time structure and forbids signalling outside the future. On the other hand, causality can be defined operationally using causal models by considering the flow of information within a network of physical systems and interventions on them. From both a foundational and practical viewpoint, it is useful to establish the class of causal models that can coexist with relativistic principles such as no superluminal signalling, noting that causation and signalling are not equivalent. Here we develop such a general framework that allows these different notions of causality to be independently defined and for connections between them to be established. The framework first gives an operational way to study causation that allows for cyclic, fine-tuned and non-classical causal influences. We then consider how a causal model can be embedded in a space-time structure (modelled as a partial order) and propose a mathematical condition for ensuring that the embedded causal model does not allow signalling outside the space-time future, which we call compatibility. We identify several distinct classes of causal loops that can arise in our framework, showing that compatibility with a space-time can rule out only some of them. In addition, we demonstrate the mathematical possibility of causal loops embedded in Minkowski space-time, whose existence can be operationally verified without leading to superluminal signalling. Within our framework we discuss conditions for preventing superluminal signalling within arbitrary (possibly cyclic) causal models. We also consider causation in post-quantum theories admitting so-called jamming correlations. By considering arbitrary interventions, this goes beyond previous works on jamming that focus on correlations. Finally, this work introduces a new causal modelling concept of "higher-order affects relations" and several technical results in this regard, which have applications for causal discovery in fined-tuned causal models. Contents I. Introduction II. Preliminaries: Acyclic and faithful causal models III. Motivation for analysing cyclic and fine-tuned causal models A. Friedman's thermostat and the one-time pad B. Jamming non-local correlations IV. The framework, Part 1: Causality A. Cyclic and fine-tuned causal models B. Interventions and affects relations C. Conditional and higher-order affects relations D. Relationships between concepts V. The framework, Part 2: Space-time A. Space-time structure B. Embedding of a causal model in a space-time structure C. Compatibility of a causal model with an embedding in space-time D. Necessary and sufficient conditions for compatibility VI. Causal loops and their space-time embeddings

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Section: Open Questionsmentioning

confidence: 93%

Section: E Causal Discovery In the Presence Of Fine-tuningmentioning

confidence: 99%

Section: E Causal Discovery In the Presence Of Fine-tuningmentioning

confidence: 99%

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Possibility of causal loops without superluminal signalling -- a general framework

Vilasini,

Colbeck

2021

Preprint

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“…The argument of Ref. [48] is that a condition for a coin-flipping protocol to have composable security is that the outcome o of the protocol must be independent of the outcome o′ of another arbitrary coin-flipping protocol that may take place in parallel, and that this condition cannot be guaranteed because a dishonest party may apply a man-in-the-middle attack and correlate the outcomes o and o′ of both protocols. We discuss below how this argument applies to our die-rolling protocols.…”

Section: Unconditionally Secure Relativistic Multi-party Biased Die Rollingmentioning

confidence: 99%

“…It follows from Ref. [48] and from the previous discussion that our die-rolling protocols cannot be composed securely in arbitrary ways. However, an honest party can participate in various die-rolling protocols in parallel and be guaranteed not only that each protocol is secure on its own but also that the outcomes of the protocols are independent, by choosing carefully the space–time regions where she communicates her messages to, and where she accepts messages from, the other parties in all the protocols where she is participating.…”

Section: Unconditionally Secure Relativistic Multi-party Biased Die Rollingmentioning

confidence: 99%

Unconditionally secure relativistic multi-party biased coin flipping and die rolling

Pitalúa-García

2021

Proc. R. Soc. A.

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We introduce relativistic multi-party biased die-rolling protocols, generalizing coin flipping to M ≥ 2 parties and to N ≥ 2 outcomes for any chosen outcome biases and show them unconditionally secure. Our results prove that the most general random secure multi-party computation, where all parties receive the output and there is no secret input by any party, can be implemented with unconditional security. Our protocols extend Kent’s (Kent A. 1999 Phys. Rev. Lett. 83 , 5382) two-party unbiased coin-flipping protocol, do not require any quantum communication, are practical to implement with current technology and to our knowledge are the first multi-party relativistic cryptographic protocols.

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Composable and Finite Computational Security of Quantum Message Transmission

Banfi

Maurer

Portmann

et al. 2019

Theory of Cryptography

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Recent research in quantum cryptography has led to the development of schemes that encrypt and authenticate quantum messages with computational security. The security definitions used so far in the literature are asymptotic, gamebased, and not known to be composable. We show how to define finite, composable, computational security for secure quantum message transmission. The new definitions do not involve any games or oracles, they are directly operational: a scheme is secure if it transforms an insecure channel and a shared key into an ideal secure channel from Alice to Bob, i.e., one which only allows Eve to block messages and learn their size, but not change them or read them. By modifying the ideal channel to provide Eve with more or less capabilities, one gets an array of different security notions. By design these transformations are composable, resulting in composable security. Crucially, the new definitions are finite. Security does not rely on the asymptotic hardness of a computational problem. Instead, one proves a finite reduction: if an adversary can distinguish the constructed (real) channel from the ideal one (for some fixed security parameters), then she can solve a finite instance of some computational problem. Such a finite statement is needed to make security claims about concrete implementations. We then prove that (slightly modified versions of) protocols proposed in the literature satisfy these composable definitions. And finally, we study the relations between some game-based definitions and our composable ones. In particular, we look at notions of quantum authenticated encryption and QCCA2, and show that they suffer from the same issues as their classical counterparts: they exclude certain protocols which are arguably secure.

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Composable security in relativistic quantum cryptography

Cited by 22 publications

References 37 publications

Possibility of causal loops without superluminal signalling -- a general framework

Possibility of causal loops without superluminal signalling -- a general framework

Unconditionally secure relativistic multi-party biased coin flipping and die rolling

Composable and Finite Computational Security of Quantum Message Transmission

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