Dang, Minh-Dung (2008) Quantum Primitives for Secure Two-party Computations and Entanglement Attacks. PhD thesis Informatique et Réseaux, Département Informatique et Réseaux, ENST p.143.

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Abstract

In this thesis, we are interested in the theory of unconditional secure two-party computations of which Oblivious Transfer (OT) and Bit Commitment (BC) are the central primitives.

On one hand, my works are inspired from Crépeau's et al.'s framework of building of OT protocol from noisy communication channels. The principle of this framework is to conceive, from noisy channels, an intermediate erasure model which is a variant of OT. We contributed to this framework by proposing a more general intermediate model, the Binary Symmetric Multi-Error-Rate Channel, which also can be built from noisy channels. With this intermediate model, we can build OT protocol from the noisy channels more effectively.

In addition, we expose some case studies on emulating noisy models by a quantum nonorthogonal coding (QNOC) scheme which

uses two non-orthogonal pure states for encoding two values of the classical bit.

On the other hand, we revise the quantum model for general two-party protocols concerning classical and quantum computations and communications. We state that in the general model, a classical channel is inevitably macroscopic and its decoherence is so strong that quantum information is not accepted to be transfered on it. Thus, the quantum model for two-party protocols becomes three-party, including an environment of the channel.

Indeed, with the faithful interpretation of general quantum two-party protocols in this three-party model, we reaffirm the no-go theorems of Mayers and Lo & Chau on the impossibilities of quantum OT, BC. In addion, we can go further to apply these negative results to protocols using some quantum trusted oracles, such as Coin-Flipping.

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