Information Reconciliation Techniques for Quantum Key Distribution Using Short to Medium Length Codes

Abstract

Quantum Key Distribution (QKD) is a cryptographic communication protocol that utilizes quantum mechanical properties for provable absolute security against an eavesdropper. Researchers consider QKD as the merely strictly protected key distribution technology since the QKD system is safe from the inherent laws of quantum physics. Real devices used by QKD and fiber do not have the ideal characteristics predicted by the preliminary QKD concept, and they can have a threat of quantum hacking. Trusting a photon device and QKD optical components along with hacking measurement can be done through their overall metrological characterization. This characterization will, in turn, influence the system-level plan and design issues, such as the selection of reconciliation techniques. It is recognized that the most key contributor to the delay of reconciliation protocols is considered as channel coding scheme. The problem of delay-constrained reconciliation protocols must be addressed in order to increase the quantum data rates and to tackle the latency acute QKD applications. To achieve minimum delays with less complexity short/medium length codes need to be addressed, but for these codes, iterative decoding is sub-optimal (due to the presence of short loops in their graphical structure). Short block codes need innovative soft decoding algorithms and the related reconciliation protocols to accomplish the target requirement in terms of delay and error rates for the QKD appli cation. In this research, a novel reconciliation system is proposed that investigates and imple ments soft decoding techniques for QKD using short to medium-length codes and its associated reconciliation protocols that ensure low error rates with very low complexity for QKD applications. The core idea of the research is employing Forward Error Cor rection (FEC) coding in QKD schemes for information reconciliation and its associatedoptimal decoding algorithms. Bose-Chaudhuri-Hochquenghem (BCH) code is used at the transmitter side with short to medium block lengths with its own state-of-the-art decod ing algorithm Berlakamp Massey (BM) and Ordered Statistic Decoding (OSD). OSD is the promising class of soft decoding technique that works on the reliability values of the received data at the receiving end. The decoding complexity and the accuracy of the al gorithm rely on the order of the decoder. The functionality of the algorithm is based on the required error order. This also creates a trade-off between optimality and complexity. Thus it was investigated and checked that the order of the decoding algorithm depends purely on the code length. The results are compared with Low density Parity Check Codes (LDPC) with the Bose Chaudhuri Hocquenghem-Berlekamp–Massey (BCH-BM) decoding method. Polar codes are linear block error-correcting codes that are known to have provable achieve channel capacity on certain channels. Their coding and decoding algorithms function with an asymptotic complexity of the logarithmic scale. This thesis also investigates its appli cation towards various types of classical and classical-quantum channels. Transmission systems utilizing these channels are based on photons of different polarization states and are able to process both classical as well as quantum information. This thesis also debates on a channel that works with the photon counting detector. For this, we have suggested a time-varying Binary Input Multiple Output (BIMO) channel model and explored its performance in the presence of soft-metric-based capacity ap proaching iteratively decoded error-correcting codes, such as soft-metric-based BCH and polar codes. The capacity of the proposed BIMO model is higher than that of the Binary Symetric Channe (BSC) model, and using the BIMO model allows soft information, in the form of reliabilities values, to be sent into the channel decoder, resulting in a significant reduction in Bit Error Rate (BER) and Frame Error Rate (FER). The practical implementation of the long-range QKD system has been done by attaining possible safe and secure key generation within system level and security constraints. The transmission of the physical states of a photon is carried out using a standard communication waveguide. Furthermore, we investigated and checked the problem related to the Free Space Optics (FSO) links if the optical link is not available for communication.