Individual attack analysis of device independent counterfactual quantum key distribution

Abstract

The study of quantum key distribution (QKD) which began in the early 80's has seen much fruition and development for almost three decades now. Ranging from security proofs and new protocols, quantum cryptography takes the limit of security definition to the most extreme especially in the context of device independent QKD. This is the scenario where even the equipment used by the legitimate parties cannot be trusted and is considered as black boxes i.e. the parties are assumed to have no knowledge of the device's full function. Further extreme is explored when the adversary, Eve is even seen to have access to physics beyond that of quantum mechanics; or commonly known as `supra-quantum' and violations of Bell inequalities become a necessary condition for security. Moving on to a recent development in a new type of protocol, namely counterfactual QKD (CQKD), quantum physics allows for the establishment of secure keys without a net transmission of signals between the legitimate parties; exploiting the single photon entanglement phenomena. We consider taking this new type of protocol to the extreme security requirements of device independence against a supra quantum Eve. We begin by exploring binary measurement based QKD with binary output within a device independent context in which we present the security analysis of the protocol against an individual attack by a supra-quantum adversary considering two different scenarios. The two scenarios involved in determining the maximal key rate are between the measurement that would maximizes the legitimate parties' correlations and those that would achieve maximal violation of Bell-type inequality. We show that higher correlation between shared raw keys at the expense of maximal Bell violation provide for better key rate for low channel disturbance. This naturally allows us to apply to the single photon entanglement QKD where we show that a non zero key rate is indeed possible. Finally, we show how, the counterfactual QKD protocol, as described in the original papers are not secure given a device independent scenario, let alone a supra-quantum adversary. Capitalizing on the results of the earlier chapters, we propose a possible framework for device independent CQKD against an individual attack by a supra-quantum Eve. We show how, at least, as an example of an equivalent protocol could provide for a secure key given a heuristic analysis within the device independent framework and how this can be used in a CQKD picture with a Bell check. We conclude the thesis with future outlooks on how the work could be developed for understanding not only in the field of quantum cryptography but also more fundamental issues in physics.