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arXiv:1302.1701

Blind post-processing for the unbalanced BB84

Satoshi Sunohara, Kiyoshi Tamaki, Nobuyuki Imoto

Published Feb 7, 2013• 1 citation
arXivHTMLPDF

Abstract

For the realization of quantum key distribution, it is important to investigate its security based on a mathematical model that captures properties of the actual devices used by the legitimate users. Recently, Ferenczi, et. al. (Phys. Rev. A 86 042327 (2012)) pointed out potential influences that the losses in phase modulators and/or the unbalance in the transmission rate of beam splitters may have on the security of the phase-encoded BB84 and analyzed the security of this scheme, which is called the unbalanced BB84. In this paper, we ask whether blindly applying the post-processing of the balanced BB84 to the unbalanced BB84 would lead to an insecure key or not, and we conclude that we can safely distill a secure key even with this post-processing. It follows from our proof that as long as the unbalances are basis-independent, our conclusion holds even if the unbalances are unknown and fluctuate in time.

DOI
10.48550/arxiv.1302.1701

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For the realization of quantum key distribution, it is important to investigate its security based on a mathematical model that captures properties of the actual devices used by the legitimate users. Recently, Ferenczi, et. al. (Phys. Rev. A 86 042327 (2012)) pointed out potential influences that the losses in phase modulators and/or the unbalance in the transmission rate of beam splitters may have on the security of the phase-encoded BB84 and analyzed the security of this scheme, which is called the unbalanced BB84. In this paper, we ask whether blindly applying the post-processing of the balanced BB84 to the unbalanced BB84 would lead to an insecure key or not, and we conclude that we can safely distill a secure key even with this post-processing. It follows from our proof that as long as the unbalances are basis-independent, our conclusion holds even if the unbalances are unknown and fluctuate in time.
In optical implementations of the phase-encoded BB84 protocol, the bit information is usually encoded in the phase of two consecutive photon pulses generated in a Mach-Zehnder interferometer. In the actual experimental realization, the loss in the arms of the Mach-Zehnder interferometer is not balanced, for example because only one arm contains a lossy phase modulator. Therefore, the amplitudes of the pulses are not balanced, and the structure of the signals and measurements no longer corresponds to the (balanced) ideal BB84 protocol. Hence, the BB84 security analysis no longer applies in this scenario. We provide a security proof of the unbalanced phase-encoded BB84. The resulting key rate turns out to be lower than the key rate of the ideal BB84 protocol. Therefore, in order to guarantee security, the loss due to the phase modulator cannot be ignored.
Security proof of practical quantum key distribution (QKD) has attracted a lot of attentions in recent years. Most of real-life QKD implementations are based on phase-coding BB84 protocol, which usually use Unbalanced Mach-Zehnder Interferometer (UMZI) as the information encoder and decoder. However, the long arm and short arm of UMZI will introduce different loss in practical experimental realizations, the state emitted by Alice's side is nolonger perfect BB84 states correspondingly. In this paper, we will give the security analysis in this situation. Counterintuitively, active compensation for this different loss will only lower the secret key bit rate.
Key distillation, also referred to as classical post-processing, plays a pivotal role in Quantum Key Distribution (QKD) protocols. Key distillation encompasses numerous subroutines, making the analysis of its overall security implications potentially challenging for those outside the research community. In this paper, we elucidate the role of the key distillation phase in QKD from a security standpoint. We begin by analyzing the different components of the key distillation phase individually, followed by an examination of the process as a whole. We then calculate the bit strength of the produced key, assuming that an attacker is executing an intercept and resend attack. For our analysis, we employ a practical key distillation implementation linked to a decoy state BB84 protocol as a case study. Our findings suggest that the security of the final key, post the key distillation phase, hinges on several factors. These include the theoretical security of the implemented subroutines, the total information leakage throughout the process, and the choices of subroutine parameters. Given these assumptions, we can distill 287 secure bits for every 1000 bits that undergo the key distillation procedure.
This paper demonstrates ways to improve the post-processing phase of BB84-based Quantum Key Distribution (QKD) while maintaining Information-Theoretic security. Maximum entropy in the distilled bits can be achieved provided that we follow certain rules on which bits are sacrificed based on the properties of the generator matrix. We use standard decoder techniques to distill bits and establish Information-Theoretic security and provide insights into how those techniques can be adapted to provide greater bit throughput. Finally, we compare popular coding schemes in BB84 post-processing as a basis for code selection and discover at low initial Bit Error Rates (BER), a Polar 4/5 or Hamming* give the best performance and for higher initial BER, the LDPC 3/4 and Hamming* (a modified Hamming code) give the best performance [1] [2] [9] [10].
All phase-encoded BB84 implementations have signal states with unbalanced amplitudes in practice.Thus the original security analyses a priori do not apply to them.Previous security proofs use signal tagging of multiphoton pulses to recover the behavior of regular BB84.This is overly conservative as for unbalanced signals the photon number splitting attack does not leak full information to Eve.In this work we exploit the flag-state squashing model to preserve some parts of the multiphoton-generated private information in our analysis.Using a numerical proof technique we obtain significantly higher key rates compared with previously published results in the low-loss regime.It turns out that the usual scenario of untrusted dark counts runs into conceptual difficulties in some parameter regimes.Thus we discuss the trusted dark-count scenario in this paper as well.We also report a gain in key rates when part of the total loss is known to be induced by a trusted device.We highlight that all these key rate improvements can be achieved without modification of the experimental setup.
Abstract Considering the rapid development of quantum technology, it has become inevitable to use this technology to develop an ultimately secured key exchange system. Quantum key distribution (QKD) technology has become more sophisticated, is expected to provide secure key distribution mechanism for the actual information security systems. The unique advantage of quantum cryptography is precisely its ability to guarantee absolute security. Previous works have demonstrated unconditional security of the ideal BB84 QKD system. However, on a typical QKD system, many practical situations often cannot satisfy the requirements of the ideal condition. This problem causes some security issues for practical QKD system. Therefore, it is necessary to analyze the security of QKD system under practical conditions, and identify the security implications on the practical physical systems and equipment, in order to find a method that guarantees the security of QKD system. The security of QKD system based on BB84 involves many aspects; this paper mainly focuses on how to resolve security issues that may exist, especially in the BB84 protocol post-processing. We introduce ways to tackle these issues and make vital key information leakage very small. Their impact on the security of entire QKD system is analyzed, and the interaction and security optimization between the various parts is researched. Finally, the thesis briefly introduces five sub-modules of post-processing of QKD system: the base comparison, error estimation, information correction, data check and privacy amplification; the existent security factors of each module is given, for error estimation and information correction is provided the secure model with those issues. Thus, the security model of post-processing is further optimized.