Novel quantum key distribution with shift operations based on Fibonacci and Lucas valued orbital angular momentum entangled states

Abstract

There have been many proposals for round-robin-differential-phase-shift (RRDPS) quantum key distribution (QKD) protocols due to their unique security foundation and many advantages over the existing QKD protocols. Inspired by such QKD protocols, we propose a novel QKD protocol with k-right or k-left shifts (where k=1,2) based on the Fibonacci- and Lucas-valued orbital angular momentum (OAM) entangled states. That is, we firmly establish the link by the shift operation to Fibonacci or Lucas numbers using the Fibonacci-valued or Lucas-valued OAM entangled states. There are three critical aspects of our proposal highlighted as follows. First, we randomly use a certain number of k-right or k-left shifts to resist the side channel attack. Second, we add the shifted Fibonacci numbers to the original Fibonacci numbers to obtain the Fibonacci or Lucas sequences, which are then used for a constructing a diagonal matrix for the key. Third, we greatly improve the key rate while reducing the complexity of the implementation of the protocol.