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.

由于其独特的安全基础和相对于现有QKD协议的许多优势，已经提出了许多建议用于循环差分相移（RRDPS）量子密钥分发（QKD）协议。受此类QKD协议的启发，我们提出了一种新颖的QKD协议$ķ$-对或 $ķ$-左移（其中 $ķ=\mathrm{1个}，2$）基于斐波那契值和卢卡斯值的轨道角动量（OAM）纠缠态。也就是说，我们通过使用Fibonacci值或Lucas值的OAM纠缠态通过对Fibonacci或Lucas数的移位操作来牢固地建立链接。我们的提案的三个关键方面突出如下。首先，我们随机使用一定数量的$ķ$-对或 $ķ$-向左移动可抵抗侧通道攻击。其次，我们将移位后的斐波那契数与原始斐波那契数相加以获得斐波那契或卢卡斯序列，然后将其用于构建密钥的对角矩阵。第三，我们大大提高了密钥率，同时降低了协议实现的复杂性。