Two-Way Physical Layer Security Protocol for Gaussian Channels

In this paper we propose a two-way protocol of physical layer security using the method of privacy amplification against eavesdroppers. First we justify our proposed protocol by analyzing the physical layer security provided by the classic wiretap channel model (i.e. one-way protocol). In the Gaussian channels, the classic one-way protocol requires Eve’s channel to be degraded w.r.t. Bob’s channel. However, this channel degradation condition depends on Eve’s location and whether Eve’s receiving antenna is more powerful than Bob’s. To overcome this limitation, we introduce a two-way protocol inspired in IEEE TIT (1993) that eliminates the channel degradation condition. In the proposed two-way protocol, on a first phase, via Gaussian channel, Bob sends randomness to Alice, which is partially leaked to Eve. Then, on a second phase, Alice transmits information to Bob over a public noiseless channel. We derive the secrecy capacity of the two-way protocol when the channel to Eve is also Gaussian. We show that the capacity of the two-way protocol is always positive. We present numerical values of the capacities illustrating the gains obtained by our proposed protocol. We apply our result to simple yet realistic models of satellite communication channels.

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

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

[3]  Massimo Franceschetti,et al.  Wiretap Channel With Secure Rate-Limited Feedback , 2009, IEEE Transactions on Information Theory.

[4]  Hugo Krawczyk,et al.  LFSR-based Hashing and Authentication , 1994, CRYPTO.

[5]  Xiqi Gao,et al.  A Survey of Physical Layer Security Techniques for 5G Wireless Networks and Challenges Ahead , 2018, IEEE Journal on Selected Areas in Communications.

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

[7]  Shlomo Shamai,et al.  The wiretap channel with generalized feedback: Secure communication and key generation , 2015, 2015 IEEE Information Theory Workshop - Fall (ITW).

[8]  Masahito Hayashi,et al.  Non-asymptotic analysis of privacy amplification via Rényi entropy and inf-spectral entropy , 2012, 2013 IEEE International Symposium on Information Theory.

[9]  Mauro Conti,et al.  A Survey of Man In The Middle Attacks , 2016, IEEE Communications Surveys & Tutorials.

[10]  Shlomo Shamai,et al.  Secure Communication Over Fading Channels , 2007, IEEE Transactions on Information Theory.

[11]  Hong Wen,et al.  Build-in wiretap channel I with feedback and LDPC codes , 2009, Journal of Communications and Networks.

[12]  Hiroki Koga,et al.  Information-Spectrum Methods in Information Theory , 2002 .

[13]  Masahito Hayashi,et al.  Tight Exponential Analysis of Universally Composable Privacy Amplification and Its Applications , 2010, IEEE Transactions on Information Theory.

[14]  Ivan Martinovic,et al.  A Practical Man-In-The-Middle Attack on Signal-Based Key Generation Protocols , 2012, ESORICS.

[15]  Ueli Maurer,et al.  Generalized privacy amplification , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[16]  Masahito Hayashi,et al.  Secure uniform random number extraction via incoherent strategies , 2017, ArXiv.

[17]  Xiongfeng Ma,et al.  Practical issues in quantum-key-distribution postprocessing , 2009, 0910.0312.

[18]  Matthieu R. Bloch,et al.  Physical-Layer Security: From Information Theory to Security Engineering , 2011 .

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

[20]  Himanshu Tyagi,et al.  Strong converse for a degraded wiretap channel via active hypothesis testing , 2014, 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[21]  Masahito Hayashi,et al.  Semi-Finite Length Analysis for Information Theoretic Tasks , 2018, ArXiv.

[22]  Masahito Hayashi,et al.  General non-asymptotic and asymptotic formulas in channel resolvability and identification capacity and their application to wire-tap channel , 2005, ArXiv.

[23]  Leonid A. Levin,et al.  A Pseudorandom Generator from any One-way Function , 1999, SIAM J. Comput..

[24]  Andrew Thangaraj,et al.  Error-Control Coding for Physical-Layer Secrecy , 2015, Proceedings of the IEEE.

[25]  Richard Moulds,et al.  Quantum Random Number Generators , 2016 .

[26]  Masahito Hayashi,et al.  Secure wireless communication under spatial and local Gaussian noise assumptions , 2016, 2017 IEEE International Symposium on Information Theory (ISIT).

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

[28]  Zhu Cao,et al.  Quantum random number generation , 2015, npj Quantum Information.

[29]  Sennur Ulukus,et al.  The Secrecy Capacity Region of the Gaussian MIMO Multi-Receiver Wiretap Channel , 2009, IEEE Transactions on Information Theory.

[30]  Masahito Hayashi,et al.  Exponential Decreasing Rate of Leaked Information in Universal Random Privacy Amplification , 2009, IEEE Transactions on Information Theory.

[31]  Masahito Hayashi,et al.  Physical Layer Security for RF Satellite Channels in the Finite-Length Regime , 2018, IEEE Transactions on Information Forensics and Security.

[32]  Hong Wen,et al.  Build-in wiretap channel I with feedback and LDPC codes by soft decision decoding , 2017, IET Commun..

[33]  Maria Angeles Vázquez-Castro,et al.  Information-theoretic physical layer security for satellite channels , 2016, 2017 IEEE Aerospace Conference.

[34]  Ender Tekin,et al.  The General Gaussian Multiple-Access and Two-Way Wiretap Channels: Achievable Rates and Cooperative Jamming , 2007, IEEE Transactions on Information Theory.

[35]  Maria Angeles Vázquez-Castro,et al.  Statistical modeling of the LMS channel , 2001, IEEE Trans. Veh. Technol..

[36]  Martin E. Hellman,et al.  The Gaussian wire-tap channel , 1978, IEEE Trans. Inf. Theory.

[37]  Larry Carter,et al.  New Hash Functions and Their Use in Authentication and Set Equality , 1981, J. Comput. Syst. Sci..

[38]  Masahito Hayashi,et al.  General nonasymptotic and asymptotic formulas in channel resolvability and identification capacity and their application to the wiretap channel , 2006, IEEE Transactions on Information Theory.

[39]  Hesham El Gamal,et al.  On the Secrecy Capacity of Fading Channels , 2006, 2007 IEEE International Symposium on Information Theory.

[40]  Masahito Hayashi,et al.  One-Way and Two-Way Physical Layer Security Protocols for the Gaussian Satellite Channel , 2019, ICC 2019 - 2019 IEEE International Conference on Communications (ICC).

[41]  Himanshu Tyagi,et al.  Secret Key Agreement: General Capacity and Second-Order Asymptotics , 2014, IEEE Transactions on Information Theory.

[42]  H. Vincent Poor,et al.  Wiretap Channels: Nonasymptotic Fundamental Limits , 2017, IEEE Transactions on Information Theory.

[43]  Yi Yang,et al.  An Efficient Advantage Distillation Scheme for Bidirectional Secret-Key Agreement , 2017, Entropy.

[44]  Masahito Hayashi.  Quantum-Inspired Secure Wireless Communication Protocol Under Spatial and Local Gaussian Noise Assumptions , 2016, IEEE Access.