## Cryptology ePrint Archive: Report 2017/830

Security proof for Round Robin Differential Phase Shift QKD

Daan Leermakers and Boris Skoric

Abstract: We give a security proof of the `Round Robin Differential Phase Shift' Quantum Key Distribution scheme, and we give a tight bound on the required amount of privacy amplification. Our proof consists of the following steps. We construct an EPR variant of the scheme. We identify Eve's optimal way of coupling an ancilla to an EPR qudit pair under the constraint that the bit error rate between Alice and Bob should not exceed a value $beta$. As a function of $beta$ we derive, for finite key size, the trace distance between the real state and a state in which no leakage exists. For asymptotic key size we obtain a bound on the trace distance by computing the von Neumann entropy. Our asymptotic result for the privacy amplification is sharper than existing bounds.

Category / Keywords: quantum key distribution

Date: received 30 Aug 2017, last revised 8 Feb 2018

Contact author: b skoric at tue nl

Available format(s): PDF | BibTeX Citation

Note: Added a discussion of symmetrisation.

Short URL: ia.cr/2017/830

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