Quantum key distribution (QKD) is a popular protocol that provides information theoretically secure keys to multiple parties. Two important post-processing steps of QKD are 1) the information reconciliation (IR) step, where parties reconcile mismatches in generated keys through classical communication, and 2) the privacy amplification (PA) step, where parties distill their common key into a new secure key that the adversary has little to no information about. In general, these two steps have been abstracted as two distinct problems. In this work, we consider a new technique of performing the IR and PA steps jointly through sampling that relaxes the requirement on the IR step, allowing for more success in key creation. We provide a novel LDPC code construction known as Block-MDS QC-LDPC codes that can utilize the relaxed requirement by creating LDPC codes with pre-defined sub-matrices of full-rank. We demonstrate through simulations that our technique of sampling can provide notable gains in successfully creating secret keys.

翻译：量子密钥分发（QKD）是一种流行的协议，旨在为多方提供信息理论上安全的密钥。QKD的两个重要后处理步骤包括：1）信息协调（IR）步骤，其中各方通过经典通信协调生成密钥中的不匹配；2）隐私放大（PA）步骤，其中各方将公共密钥提炼为新的安全密钥，使对手几乎无法获知其信息。通常，这两个步骤被抽象为两个不同的问题。本文考虑一种通过采样联合执行IR和PA步骤的新技术，该技术放宽了对IR步骤的要求，从而提高了密钥生成的成功率。我们提出一种称为块-MDS QC-LDPC码的新型LDPC码构造，其通过创建具有预定义满秩子矩阵的LDPC码来利用这种放宽的要求。仿真结果表明，我们的采样技术在成功生成密钥方面能够带来显著增益。