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Composable security in relativistic quantum cryptography

V. Vilasini, Christopher Portmann, Lídia del Rio

Published Apr 1, 2019• 16 citations
Publisher

Abstract

Relativistic protocols have been proposed to overcome certain impossibility results in classical and \nquantum cryptography. In such a setting, one takes the location of honest players into account, and \nuses the signalling limit given by the speed of light to constraint the abilities of dishonest agents. \nHowever, composing such protocols with each other to construct new cryptographic resources is \nknown to be insecure in some cases. To make general statements about such constructions, a \ncomposable framework for modelling cryptographic security in Minkowski space is required. \nHere, we introduce a framework for performing such a modular security analysis of classical and \nquantum cryptographic schemes in Minkowski space. As an application, we show that (1) fair and \nunbiased coin flipping can be constructed from a simple resource called channel with delay; (2) \nbiased coin flipping, bit commitment and channel with delay through any classical, quantum or \npost-quantum relativistic protocols are all impossible without further setup assumptions; (3) it is \nimpossible to securely increase the delay of a channel, given several short-delay channels as \ningredients. Results(1) and (3) imply in particular the non-composability of existing relativistic bit \ncommitment and coin flipping protocols.

DOI
10.3929/ethz-b-000342946

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Relativistic protocols have been proposed to overcome certain impossibility results in classical and \nquantum cryptography. In such a setting, one takes the location of honest players into account, and \nuses the signalling limit given by the speed of light to constraint the abilities of dishonest agents. \nHowever, composing such protocols with each other to construct new cryptographic resources is \nknown to be insecure in some cases. To make general statements about such constructions, a \ncomposable framework for modelling cryptographic security in Minkowski space is required. \nHere, we introduce a framework for performing such a modular security analysis of classical and \nquantum cryptographic schemes in Minkowski space. As an application, we show that (1) fair and \nunbiased coin flipping can be constructed from a simple resource called channel with delay; (2) \nbiased coin flipping, bit commitment and channel with delay through any classical, quantum or \npost-quantum relativistic protocols are all impossible without further setup assumptions; (3) it is \nimpossible to securely increase the delay of a channel, given several short-delay channels as \ningredients. Results(1) and (3) imply in particular the non-composability of existing relativistic bit \ncommitment and coin flipping protocols.
Abstract Relativistic protocols have been proposed to overcome certain impossibility results in classical and quantum cryptography. In such a setting, one takes the location of honest players into account, and uses the signalling limit given by the speed of light to constraint the abilities of dishonest agents. However, composing such protocols with each other to construct new cryptographic resources is known to be insecure in some cases. To make general statements about such constructions, a composable framework for modelling cryptographic security in Minkowski space is required. Here, we introduce a framework for performing such a modular security analysis of classical and quantum cryptographic schemes in Minkowski space. As an application, we show that (1) fair and unbiased coin flipping can be constructed from a simple resource called channel with delay; (2) biased coin flipping, bit commitment and channel with delay through any classical, quantum or post-quantum relativistic protocols are all impossible without further setup assumptions; (3) it is impossible to securely increase the delay of a channel, given several short-delay channels as ingredients. Results (1) and (3) imply in particular the non-composability of existing relativistic bit commitment and coin flipping protocols.
We study the cryptographic primitive Oblivious Transfer; a composable construction of this resource would allow arbitrary multi-party computation to be carried out in a secure way, i.e. to compute functions in a distributed way while keeping inputs from different parties private. First we review a framework that allows us to analyze composability of classical and quantum cryptographic protocols in special relativity: Abstract Cryptography implemented with Causal Boxes. We then (1) explore and formalize different versions of oblivious transfer found in the literature, (2) prove that their equivalence holds also in relativistic quantum settings, (3) show that it is impossible to composably construct any of these versions of oblivious transfer from only classical or quantum communication among distrusting agents in relativistic settings, (4) prove that the impossibility also extends to multi-party computation, and (5) provide a mutual construction between oblivious transfer and bit commitment.
In this thesis we explore the benefits of relativistic constraints for cryptography. We first revisit non-communicating models and its applications in the context of interactive proofs and cryptography. We propose bit commitment protocols whose security hinges on communication constraints and investigate its limitations. We explain how some non-communicating models can be justified by special relativity and study the limitations of such models. In particular, we present a framework for analysing security of multiround relativistic protocols. The second part of the thesis is dedicated to analysing specific protocols. We start by considering a recently proposed two-round quantum bit commitment protocol. We propose a fault-tolerant variant of the protocol, present a complete security analysis and report on an experimental implementation performed in collaboration with an experimental group at the University of Geneva. We also propose a new, multiround classical bit commitment protocol and prove its security against classical adversaries. This demonstrates that in the classical world an arbitrarily long commitment can be achieved even if the agents are restricted to occupy a finite region of space. Moreover, the protocol is easy to implement and we report on an experiment performed in collaboration with the Geneva group.
In this thesis we have studied how to exploit relativistic constraints such as the non-superluminal signalling principle to design secure cryptographic primitives like position-verification and bit commitment. According to non-superluminal signalling principle, no physical carrier of information can travel faster than the speed of light. This put a constraint on the communication time between two distant stations. One can consider this delay in information transfer as a temporal non-communication constraint. Cryptographic primitives like bit-commitment, oblivious transfer can be implemented with perfect secrecy under such non-communication assumption between the agents. The first part of this thesis has studied how non-signalling constraints can be used for secure position verification. Here, we have discussed about a strategy which can attack any position verification scheme. In the next part of this thesis we have discussed about the nonlocal games, relevant for studying relativistic bit commitment protocols. We have established an upper bound on the classical value of such family of games. The last part of this thesis discusses about two relativistic bit commitment protocols and their security against classical adversaries. We conclude this thesis by giving a brief summary of the content of each chapter and mentioning interesting open problems. These open problems can be very useful for better understanding of the role of spacetime constraints such as non-superluminal signalling in designing perfectly secure cryptographic primitives.
Weak coin flipping is a cryptographic primitive in which two mutually distrustful parties generate a shared random bit to agree on a winner via remote communication. While a stand-alone secure weak coin flipping protocol can be constructed from noiseless quantum communication channels, its composability remains unexplored. In this work, we demonstrate that no weak coin flipping protocol can be abstracted as a simple black-box resource with composable security. Despite this, we also establish the overall stand-alone security of quantum weak coin flipping protocols under composition in sequential order.
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. 115, 030502 (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 with the original protocol, while retaining the same level of security.