Quantum Keyless Privacy vs. Quantum Key Distribution for Space Links

We study information theoretical security for space links between a satellite and a ground-station. Quantum key distribution (QKD) is a well established method for information theoretical secure communication, giving the eavesdropper unlimited access to the channel and technological resources only limited by the laws of quantum physics. But QKD for space links is extremely challenging, the achieved key rates are extremely low, and day-time operating impossible. However, eavesdropping on a channel in free-space without being noticed seems complicated, given the constraints imposed by orbital mechanics. If we also exclude eavesdropper's presence in a given area around the emitter and receiver, we can guarantee that he has only access to a fraction of the optical signal. In this setting, quantum keyless private (direct) communication based on the wiretap channel model is a valid alternative to provide information theoretical security. Like for QKD, we assume the legitimate users to be limited by state-of-the-art technology, while the potential eavesdropper is only limited by physical laws: physical measurement (Helstrom detector) and quantum electrodynamics (Holevo bound). Nevertheless, we demonstrate information theoretical secure communication rates (positive keyless private capacity) over a classical-quantum wiretap channel using on-off-keying of coherent states. We present numerical results for a setting equivalent to the recent experiments with the Micius satellite and compare them to the fundamental limit for the secret key rate of QKD. We obtain much higher rates compared with QKD with exclusion area of less than 13 meters for Low Earth Orbit (LEO) satellites. Moreover, we show that the wiretap channel quantum keyless privacy is much less sensitive to noise and signal dynamics and daytime operation is possible.

[1]  Dominic Mayers,et al.  Unconditional security in quantum cryptography , 1998, JACM.

[2]  A. D. Wyner,et al.  Capacity and error exponent for the direct detection photon channel. II , 1988 .

[3]  Alexander S. Holevo,et al.  The Capacity of the Quantum Channel with General Signal States , 1996, IEEE Trans. Inf. Theory.

[4]  G. Guo,et al.  Background noise of satellite-to-ground quantum key distribution , 2005 .

[5]  Hoi-Kwong Lo,et al.  Simple security proof of twin-field type quantum key distribution protocol , 2018, npj Quantum Information.

[6]  Shor,et al.  Simple proof of security of the BB84 quantum key distribution protocol , 2000, Physical review letters.

[7]  Ueli Maurer,et al.  Secret key agreement by public discussion from common information , 1993, IEEE Trans. Inf. Theory.

[8]  Aaron D. Wyner,et al.  Capacity and error exponent for the direct detection photon channel-Part I , 1988, IEEE Trans. Inf. Theory.

[9]  H. Yuen.  Quantum detection and estimation theory , 1978, Proceedings of the IEEE.

[10]  A. S. Kholevo.  On Asymptotically Optimal Hypothesis Testing in Quantum Statistics , 1979 .

[11]  Liuguo Yin,et al.  Implementation and security analysis of practical quantum secure direct communication , 2018, Light: Science & Applications.

[12]  Lei Deng,et al.  Entanglement-based secure quantum cryptography over 1,120 kilometres , 2020, Nature.

[13]  Aaron D. Wyner,et al.  Capacity and error-exponent for the direct detection photon channel-Part II , 1988, IEEE Trans. Inf. Theory.

[14]  A. Robert Calderbank,et al.  Applications of LDPC Codes to the Wiretap Channel , 2004, IEEE Transactions on Information Theory.

[15]  V. Scarani,et al.  The security of practical quantum key distribution , 2008, 0802.4155.

[16]  Byung-Jae Kwak,et al.  LDPC Codes for the Gaussian Wiretap Channel , 2009, IEEE Transactions on Information Forensics and Security.

[17]  Gilles Brassard,et al.  Quantum cryptography: Public key distribution and coin tossing , 2014, Theor. Comput. Sci..

[18]  Ivan B. Djordjevic,et al.  Secret key distillation over a pure loss quantum wiretap channel under restricted eavesdropping , 2019, 2019 IEEE International Symposium on Information Theory (ISIT).

[19]  F. Bussières,et al.  Operation of parallel SNSPDs at high detection rates , 2021, 2109.03126.

[20]  Ivan B. Djordjevic,et al.  Secret key distillation across a quantum wiretap channel under restricted eavesdropping , 2019, Physical Review Applied.

[21]  U. Maurer.  The Strong Secret Key Rate of Discrete Random Triples , 1994 .

[22]  Graeme Smith.  Private classical capacity with a symmetric side channel and its application to quantum cryptography , 2007, 0705.3838.

[23]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[24]  Masahito Hayashi,et al.  Quantum Wiretap Channel With Non-Uniform Random Number and Its Exponent and Equivocation Rate of Leaked Information , 2012, IEEE Transactions on Information Theory.

[25]  P. Shor,et al.  The Capacity of a Quantum Channel for Simultaneous Transmission of Classical and Quantum Information , 2003, quant-ph/0311131.

[26]  A. D. Wyner,et al.  The wire-tap channel , 1975, The Bell System Technical Journal.

[27]  A. Winter,et al.  Distillation of secret key and entanglement from quantum states , 2003, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[28]  Paolo Villoresi,et al.  Free-space optical channel estimation for physical layer security , 2016, Optics express.

[29]  M. Nussbaum,et al.  Asymptotic Error Rates in Quantum Hypothesis Testing , 2007, Communications in Mathematical Physics.

[30]  Go Kato,et al.  Security of six-state quantum key distribution protocol with threshold detectors , 2010, Scientific Reports.

[31]  Imre Csiszár,et al.  Broadcast channels with confidential messages , 1978, IEEE Trans. Inf. Theory.

[32]  Masahide Sasaki,et al.  Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receivers , 2007, 0706.1038.

[33]  Masahide Sasaki,et al.  Quantum receiver beyond the standard quantum limit of coherent optical communication. , 2011, Physical review letters.

[34]  Xiongfeng Ma,et al.  Implementation of quantum key distribution surpassing the linear rate-transmittance bound , 2020, Nature Photonics.

[35]  Himanshu Tyagi,et al.  Universal Hashing for Information-Theoretic Security , 2014, Proceedings of the IEEE.

[36]  Mark M. Wilde,et al.  Energy-Constrained Private and Quantum Capacities of Quantum Channels , 2016, IEEE Transactions on Information Theory.

[37]  K. Audenaert,et al.  Discriminating States: the quantum Chernoff bound. , 2006, Physical review letters.

[38]  Yongmei Huang,et al.  Satellite-to-ground quantum key distribution , 2017, Nature.

[39]  Masahito Hayashi,et al.  Two-Way Physical Layer Security Protocol for Gaussian Channels , 2019, IEEE Transactions on Communications.

[40]  F. Bussières,et al.  Secure Quantum Key Distribution over 421 km of Optical Fiber. , 2018, Physical review letters.

[41]  Masahide Sasaki,et al.  Numerical Study on Secrecy Capacity and Code Length Dependence of the Performances in Optical Wiretap Channels , 2015, IEEE Photonics Journal.

[42]  A. Winter,et al.  Quantum privacy and quantum wiretap channels , 2004 .

[43]  Tom Vergoossen,et al.  Satellite Quantum Communications When Man-in-the-Middle Attacks Are Excluded , 2019, Entropy.

[44]  Alexander Vardy,et al.  Semantic Security for the Wiretap Channel , 2012, CRYPTO.

[45]  Masahide Sasaki,et al.  Free-space optical wiretap channel and experimental secret key agreement in 7.8 km terrestrial link. , 2018, Optics express.

[46]  Igor Devetak.  The private classical capacity and quantum capacity of a quantum channel , 2005, IEEE Transactions on Information Theory.

[47]  S. Pirandola,et al.  General Benchmarks for Quantum Repeaters , 2015, 1512.04945.

[48]  Masahito Hayashi,et al.  Physical Layer Security Protocol for Poisson Channels for Passive Man-in-the-Middle Attack , 2019, IEEE Transactions on Information Forensics and Security.