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Fully Device Independent Quantum Key Distribution


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Quantum cryptography promises levels of security that are impossible to attain in a classical world. Can this security be guaranteed to classical users of a quantum protocol, who may not even trust the quantum devices used to implement the protocol?

This central question dates back to the early 1990s when the challenge of achieving Device-Independent Quantum Key Distribution (DIQKD) was first formulated. We answer the challenge by rigorously proving the device-independent security of an entanglement-based protocol building on Ekert's original proposal for quantum key distribution. The proof of security builds on techniques from the classical theory of pseudo-randomness to achieve a new quantitative understanding of the non-local nature of quantum correlations.

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1. Introduction

The gold standard in classical cryptography is semantic security16—given an encoded message (ciphertext), any polynomial time adversary should have a negligible chance of obtaining any information whatsoever about the plaintext (the message that was encoded). Classical cryptographers have developed encryption schemes that are able to provide this guarantee by relying on un-proven assumptions about the computational difficulty of number-theoretic problems, such as factoring large numbers,28 or other more general complexity-theoretic assumptions. Such cryptographic assumptions are stronger than PNP, and considered unlikely to be proven in the foreseeable future, so one may ask whether any cryptosystems can have security guarantees that do not rely on unproven computational assumptions.

Bennett and Brassard's seminal discovery7 of a Quantum Protocol for Key Distribution (QKD) in 1984 opened up the possibility for a different kind of security—"unconditional security," or security based solely on the validity of universally accepted physical laws. QKD is a protocol that allows two distant parties to collaboratively and privately generate a perfectly random string, called the users' key. Once the users have generated a private shared key they can use it to communicate with perfect security as follows. To send a message securely, the sender uses the shared key as one time pad: the encoded message is simply the bit-wise XOR (parity) of the key with the message. The semantic security of this scheme is easy to verify, provided the one-time pad (the key) is completely random and unpredictable to any adversary.


 

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