Weak Coin Flipping in a Device-Independent Setting
A protocol is said to be device-independent when the level of its performance can be inferred without making any assumptions regarding the inner workings of the apparatus used to implement it. In this paper we introduce a device-independent weak coin flip
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School of Physics and Astronomy, Tel-Aviv University, 69978 Tel-Aviv, Israel [email protected] 2 LIAFA, University of Paris 7, 75205 Paris, France 3 University of Paris-Sud, 91405 Orsay, France 4 Computer Science Division, UC Berkeley, Berkeley 94720, CA, USA 5 LIAFA, University of Paris 7 – CNRS, 75205 Paris, France 6 Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore 7 Laboratoire d’Information Quantique, Universit´e Libre de Bruxelles, 1050 Bruxelles, Belgium [email protected]
Abstract. A protocol is said to be device-independent when the level of its performance can be inferred without making any assumptions regarding the inner workings of the apparatus used to implement it. In this paper we introduce a device-independent weak coin flipping protocol based on a single GHZ test. Interestingly, the protocol calls for the exchange of (quantum) systems between participants; a feature which is not trivial to incorporate in a device-independent setting where a system’s behavior may depend on the time, location, and its history. Alice’s and Bob’s maximal cheating probabilities are given by 0.974 and cos2 ( π8 ) 0.854.
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Introduction
Cryptographic protocols, whether quantum or classical are always formulated under a certain set of assumptions. In particular, quantum protocols rely on the validity of quantum mechanics, but also on the security of each participant’s lab and his having a trusted source of randomness to carry out random choices called for by the protocol. The list, however, usually does not end here. Most protocols, also make, for instance, assumptions as to the Hilbert space dimension of the quantum information carriers, the measurements that are carried out, etc. Such protocols are said to be device-dependent. Clearly, it is desirable to base security N. Aharon— Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel A. Chailloux— SECRET Project Team, INRIA Paris-Recquencourt, 78153 Le Chesnay Cedex, France D. Bacon et al. (Eds.): TQC 2011, LNCS 6745, pp. 1–12, 2014. c Springer-Verlag Berlin Heidelberg 2014 DOI: 10.1007/978-3-642-54429-3 1,
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on a minimum number of assumptions, as this facilitates checking the reliability of the protocol’s implementation. The aim of the device-independent approach to quantum cryptography is to do just that by doing away with a maximal number of assumptions regarding the apparatus used to implement the protocol. More specifically, a quantum protocol is said to be device-independent if the reliability of its implementation can be guaranteed without making any assumptions about the internal workings of the underlying apparatus. Remarkably, this can be achieved by certifying a sufficient amount of nonlocality (quantified by the degree of violation of a suitable Bell inequality) [1]. For example, in quantum key-distribution a high violation of the CHSH inequality guarantees that an eavesdropper will have no information about the (post-processed) key [2–6]. This shoul
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