Quantum Cryptography

11 Feb 2016

Quantum Cryptography

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The security of cryptographic quantum protocols can be based only on the validity of quantum theory. Nevertheless, to harness this validity, most protocols also make additional assumptions regarding the im- plementation, e.g., specifying the Hilbert space dimension of the quantum systems used, the bases of the measurements performed, etc. This type of protocols are said to be device-dependent, and their security may be vulnerable due to imperfect implementations of the quantum devices. Clearly, it is desirable to base security on a minimal number of assumptions, as this facilitates evaluating security. The aim of the device-independent approach to quantum cryptography is to do just that by doing away with a maximum number of assumptions regarding the implementation. More specifically, a cryptographic protocol is said to be device-independent if its security can be guaranteed without making any assumptions about the internal workings of the devices used in its implementation. This can be achieved by certifying a sufficient amount of nonlocality (quantified by the degree of violation of a suitable Bell inequality).
     In a previous work we showed for the first time that the device-independent approach also covers protocols belonging to the distrustful cryptography class by presenting device-independent quantum bit commitment and coin flipping protocols, which are based on the Greenberger- Horne-Zeilinger (GHZ) paradox. In view of the unique nature of distrustful cryptography, in particular, the difficulties arising from the fact that the different parties have conflicting goals, it is not obvious that a secure protocol can be based on the Clauser-Horne-Shimony-Holt (CHSH) correlations. These difficulties were overcome using the pseudo- telepathic property of the GHZ correlations, but this property is lacking in the CHSH setting. In addition, a real-life implementation of the GHZ-based protocols would require a reliable source of particles in a GHZ state and the ability to store, manipulate, and transmit these particles while maintaining their coherence, and with current state-of-the-art technology this is still impossible. Nevertheless, the situation is markedly different when it comes to EPR states.
     In this project we show that a device-independent bit commitment protocol can be based also on the CHSH inequality. We present a CHSH-based device-independent bit commitment protocol and analyze its security for any degree of a CHSH violation and for an arbitrary number of CHSH tests.
     This work is done in collaboration with Prof. Serge Massar, Dr. Stefano Pironio, and Dr. Jonathan
Silman.

 

https://doi.org/10.1088/1367-2630/18/2/025014