Paper 2017/830

Security proof for Round Robin Differential Phase Shift QKD

Daan Leermakers and Boris Skoric


We give a security proof of the Round Robin Differential Phase Shift (RRDPS) 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 show that the RRDPS protocol is equivalent to RRDPS with basis permutation and phase flips performed by Alice and Bob; this causes a symmetrisation of Eve's state. 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 non-asymptotic key size, the trace distance between the real state and a state in which no leakage exists. We invoke post-selection in order to go from qudit-wise attacks to general attacks. For asymptotic key size we obtain a bound on the trace distance based on the von Neumann entropy. Our asymptotic result for the privacy amplification is sharper than existing bounds. At low qudit dimension, even our non-asymptotic result is sharper than existing asymptotic bounds.

Note: Added a discussion of symmetrisation.

Available format(s)
Publication info
Preprint. MINOR revision.
quantum key distribution
Contact author(s)
b skoric @ tue nl
2018-09-07: last of 4 revisions
2017-08-31: received
See all versions
Short URL
Creative Commons Attribution


      author = {Daan Leermakers and Boris Skoric},
      title = {Security proof for Round Robin Differential Phase Shift QKD},
      howpublished = {Cryptology ePrint Archive, Paper 2017/830},
      year = {2017},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.