Security Proof of Device-Independent Quantum Key Distribution

Nilesh, Kumar (2022) Security Proof of Device-Independent Quantum Key Distribution. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Kumar Nilesh (16MS155)) 16MS155_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

Quantum key distribution (QKD) resolves the most important issues concerning secure and authenticated communication. This is performed by establishing a secret key between two remote users using quantum principles, the security of which is guaranteed by the laws of physics. The main point to remember is that QKD protocols have been proven to be secure against any attack that even the most powerful eavesdropper could launch The thesis begins with a simple security proof of BB84 QKD based on Shor and Presskill’s work [1]. The BB84’s security is proved by employing well-known quantum error correction and entanglement purification techniques. We start by ensuring the security of the entangled-based version and work our way down to our analogous original BB84 version. By integrating FTQC with classical statistics on the Bell basis, we show that the entanglement version of BB84 is secure. The equivalency was then used to demonstrate the conditional security of the original BB84. The second part of the thesis proves that Fully Device-Independent QKD (DIQKD) is secure [2]. DIQKD provides the ultimate security, where even the untrusted device can be used to establish secure key. One just needs to perform classical statistics on the Bell violation observed during the key distribution. For the security proof of DI-QKD, we resort to tools like randomness extractor, privacy amplification, guessing game, etc. We first use contradiction in the guessing game to prove the security of single-round key distribution. This only requires no-signaling formalism. Then we use the full quantum formalism to prove the case of multi-round key distribution, where devices can have internal memory. Then, using the strong randomness extractor, we show that if any third party is able to differentiate the key after privacy amplification from random, then one can use the classical approach to reconstruct the original key with some probability. This allows us to use the classical tools to again show contradiction to the guessing lemma.

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