research-article

Wiretap Channels: Nonasymptotic Fundamental Limits

Authors:

Rafael F. Schaefer,

H. Vincent PoorAuthors Info & Claims

IEEE Transactions on Information Theory, Volume 65, Issue 7

Pages 4069 - 4093

https://doi.org/10.1109/TIT.2019.2904500

Published: 01 July 2019 Publication History

Abstract

This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are uniformly tighter than existing bounds, and lead to the tightest bounds on the second-order coding rate for discrete memoryless and Gaussian wiretap channels. The exact second-order coding rate is established for semi-deterministic wiretap channels, which characterizes the optimal tradeoff between reliability and secrecy in the finite-blocklength regime. Underlying our achievability bounds are two new privacy amplification results, which not only refine the classic privacy amplification results, but also achieve secrecy under the stronger semantic-security metric.

References

[1]

A. D. Wyner, “The wire-tap channel,” Bell Syst. Tech. J., vol. 54, no. 8, pp. 1355–1387, Oct. 1975.

[2]

I. Csiszar and J. Korner, “Broadcast channels with confidential messages,” IEEE Trans. Inf. Theory, vol. 24, no. 3, pp. 339–348, May 1978.

Digital Library

[3]

Y. Liang, H. V. Poor, and S. Shamai (Shitz), “Information theoretic security,” Found. Trends Commun. Inf. Theory, vol. 5, nos. 4–5, pp. 355–580, 2008.

[4]

M. Bloch and J. Barros, Physical-Layer Security: From Information Theory to Security Engineering. Cambridge, U.K.: Cambridge Univ. Press, 2011.

[5]

H. V. Poor and R. F. Schaefer, “Wireless physical layer security,” Proc. Nat. Acad. Sci. USA, vol. 114, no. 1, pp. 19–26, Jan. 2017.

[6]

H. V. Poor, M. Goldenbaum, and W. Yang, “Fundamentals for IoT networks: Secure and low-latency communications,” in Proc. Int. Conf. Dist. Comput. Network. (ICDCN), Bengaluru, India, Jan. 2019, pp. 362–364.

[7]

Y. Polyanskiy, H. V. Poor, and S. Verdú, “Channel coding rate in the finite blocklength regime,” IEEE Trans. Inf. Theory, vol. 56, no. 5, pp. 2307–2359, May 2010.

Digital Library

[8]

M. Hayashi, “Information spectrum approach to second-order coding rate in channel coding,” IEEE Trans. Inf. Theory, vol. 55, no. 11, pp. 4947–4966, Nov. 2009.

Digital Library

[9]

V. Y. F. Tan, “Asymptotic estimates in information theory with non-vanishing error probabilities,” Found. Trends Commun. Inf. Theory, vol. 11, nos. 1–2, pp. 1–184, 2014.

Digital Library

[10]

M. Bellare, S. Tessaro, and A. Vardy, “Semantic security for the wiretap channel,” in Advances in Cryptology (Lecture Notes Comput. Science), vol. 7417. Berlin, Germany: Springer, 2012, pp. 311–2940.

[11]

M. Bellare and S. Tessaro. (Jan. 2012). “Polynomial-time, semantic-secure encryption achieving the secrecy capacity.” [Online]. Available: https://arxiv.org/abs/1201.3160

[12]

I. Tal and A. Vardy, “Channel upgrading for semantically-secure encryption on wiretap channels,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Istanbul, Turkey, Jul. 2013, pp. 1561–1565.

[13]

S. Goldwasser and S. Micali, “Probabilistic encryption,” J. Comput. Syst. Sci., vol. 28, no. 2, pp. 270–299, Apr. 1984.

[14]

M. Hayashi, “General nonasymptotic and asymptotic formulas in channel resolvability and identification capacity and their application to the wiretap channel,” IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1562–1575, Apr. 2006.

Digital Library

[15]

T. S. Han and S. Verdu, “Approximation theory of output statistics,” IEEE Trans. Inf. Theory, vol. 39, no. 3, pp. 752–772, May 1993.

Digital Library

[16]

A. Wyner, “The common information of two dependent random variables,” IEEE Trans. Inf. Theory, vol. 21, no. 2, pp. 163–179, Mar. 1975.

Digital Library

[17]

M. Hayashi, “Tight exponential analysis of universally composable privacy amplification and its applications,” IEEE Trans. Inf. Theory, vol. 59, no. 11, pp. 7728–7746, Nov. 2013.

Digital Library

[18]

M. H. Yassaee, M. R. Aref, and A. Gohari, “Non-asymptotic output statistics of Random Binning and its applications,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Istanbul, Turkey, Jul. 2013, pp. 1849–1853.

[19]

V. Y. F. Tan, “Achievable second-order coding rates for the wiretap channel,” in Proc. IEEE Int. Conf. Commun. Syst., Singapore, Nov. 2012, pp. 65–69.

[20]

M. Hayashi, “Exponential decreasing rate of leaked information in universal random privacy amplification,” IEEE Trans. Inf. Theory, vol. 57, no. 6, pp. 3989–4001, Jun. 2011.

Digital Library

[21]

M. H. Yassaee, “One-shot achievability via fidelity,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Hong Kong, Jun. 2015, pp. 301–305.

[22]

M. Tahmasbi and M. R. Bloch, “Second order asymptotics for degraded wiretap channels: How good are existing codes?” in Proc. 54th Allerton Conf. Commun., Control, Comput., Monticello, IL, USA, Sep. 2016, pp. 830–837.

[23]

M. B. Parizi, E. Telatar, and N. Merhav, “Exact random coding secrecy exponents for the wiretap channel,” IEEE Trans. Inf. Theory, vol. 63, no. 1, pp. 509–531, Jan. 2017.

[24]

H. Tyagi and S. Watanabe, “Converses For Secret Key Agreement and Secure Computing,” IEEE Trans. Inf. Theory, vol. 61, no. 9, pp. 4809–4827, Sep. 2015.

Digital Library

[25]

M. Hayashi, H. Tyagi, and S. Watanabe, “Strong converse for a degraded wiretap channel via active hypothesis testing,” in Proc. Allerton Conf. Commun., Control, Comput., Monticello, IL, USA, Oct. 2014, pp. 148–151.

[26]

V. Y. F. Tan and M. Bloch, “Information spectrum approach to strong converse theorems for degraded wiretap channels,” IEEE Trans. Inf. Forensics Security, vol. 10, no. 9, pp. 1891–1904, Sep. 1904, Sep. 2015.

[27]

J. Liu, P. Cuff, and S. Verdú, “ $E_\gamma$ -resolvability,” IEEE Trans. Inf. Theory, vol. 63, no. 5, pp. 2629–2658, May 2017.

Digital Library

[28]

I. Csiszar and P. Narayan, “Secrecy capacities for multiple terminals,” IEEE Trans. Inf. Theory, vol. 50, no. 12, pp. 3047–3061, Dec. 2004.

Digital Library

[29]

I. Csiszár and J. Körner, Information Theory: Coding Theorems for Discrete Memoryless Systems, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 2011.

[30]

M. Hayashi, “Upper bounds of eavesdropper’s performances in finite-length code with the decoy method,” Phys. Rev. A, Gen. Phys., vol. 76, no. 1, Jul. 2007, Art no.

[31]

M. Iwamoto and K. Ohta, “Security notions for information theoretically secure encryptions,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Saint Petersburg, Russia, Jul./Aug. 2011, pp. 1743–1747.

[32]

C. H. Bennett, G. Brassard, C. Crépeau, and U. M. Maurer, “Generalized privacy amplification,” IEEE Trans. Inf. Theory, vol. 41, no. 6, pp. 1915–1923, Nov. 1995.

Digital Library

[33]

R. Renner, “Security of quantum key distribution,” Ph.D. dissertation, ETH Zurich, Zürich, Switzerland, Sep. 2005.

[34]

M. Hayashi, “Security analysis of $\varepsilon$ -almost dual universal₂hash functions: Smoothing of min entropy versus smoothing of Rényi entropy of order 2,” IEEE Trans. Inf. Theory, vol. 62, no. 6, pp. 3451–3476, Jun. 2016.

[35]

S. Watanabe and M. Hayashi, “Non-asymptotic analysis of privacy amplification via Rényi entropy and inf-spectral entropy,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Istanbul, Turkey, Jul. 2013, pp. 2715–2719.

[36]

J. M. Renes, “On privacy amplification, lossy compression, and their duality to channel coding,” IEEE Trans. Inf. Theory, vol. 64, no. 12, pp. 7792–7801, Dec. 2018.

Digital Library

[37]

W. Yang, R. F. Schaefer, and H. V. Poor, “Privacy amplification: Recent developments and applications,” in Proc. IEEE Int. Symp. Inf. Theory Appl. (ISITA), Singapore, Oct. 2018, pp. 120–124.

[38]

W. Hoeffding, “Probability inequalities for sums of bounded random variables,” J. Amer. Statist. Assoc, vol. 58, no. 301, pp. 13–30, Mar. 1963.

[39]

C. McDiarmid, “On the method of bounded differences,” in Surveys in Combinatorics, vol. 141. Cambridge, UK: Cambridge Univ. Press, Aug. 1989, pp. 148–188.

[40]

R. Ahlswede and I. Csiszár, “Common randomness in information theory and cryptography. II. CR capacity,” IEEE Trans. Inf. Theory, vol. 44, no. 1, pp. 225–240, Jan. 1998.

Digital Library

[41]

P. Cuff, “A stronger soft-covering lemma and applications,” in Proc. IEEE Commun. Netw. Secur. (CNS), Florence, Italy, Sep. 2015, pp. 40–43.

[42]

P. Cuff, “Soft covering with high probability,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Barcelona, Spain, Jul. 2016, pp. 2963–2967.

[43]

R. Ahlswede and A. Winter, “Strong converse for identification via quantum channels,” in IEEE Trans. Inf. Theory, vol. 48, no. 3, pp. 569–579, Aug. 2002.

Digital Library

[44]

G. Vazquez-Vilar, A. T. Campo, A. Guillén i Fàbregas, and A. Martinez, “Bayesian M-ary hypothesis testing: The meta-converse and Verdú-Han bounds are tight,” IEEE Trans. Inf. Theory, vol. 62, no. 5, pp. 2324–2333, May 2016.

Digital Library

[45]

Z. Goldfeld, P. Cuff, and H. H. Permuter, “Semantic-security capacity for wiretap channels of type II,” IEEE Trans. Inf. Theory, vol. 62, no. 7, pp. 3863–3879, Jul. 2016.

Digital Library

[46]

S. Watanabe and M. Hayashi, “Strong converse and second-order asymptotics of channel resolvability,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Honolulu, HI, USA, Jun. 2014, pp. 1882–1886.

[47]

S. Leung-Yan-Cheong and M. Hellman, “The Gaussian wire-tap channel,” IEEE Trans. Inf. Theory, vol. IT-24, no. 4, pp. 451–456, Jul. 1978.

[48]

M. Hayashi and R. Matsumoto, “Secure multiplex coding with dependent and non-uniform multiple messages,” IEEE Trans. Inf. Theory, vol. 62, no. 5, pp. 2355–2409, May 2016.

Digital Library

[49]

C. E. Shannon, “Probability of error for optimal codes in a Gaussian channe,” Bell Syst. Tech. J., vol. 38, no. 3, pp. 611–656, May 1959.

[50]

A. Collinset al. SPECTRE: Short-Packet Communication Toolbox. [Online]. Available: https://github.com/yp-mit/spectre

[51]

W. Yang, G. Durisi, T. Koch, and Y. Polyanskiy, “Quasi-static multiple-antenna fading channels at finite blocklength,” IEEE Trans. Inf. Theory, vol. 60, no. 7, pp. 4232–4265, Jul. 2014.

[52]

D. Wang, A. Ingber, and Y. Kochman, “The dispersion of joint source-channel coding,” in Proc. 49th Allerton Conf. Commun., Control, Comput., Monticello, IL, USA, Sep. 2011, pp. 180–187.

[53]

V. Kostina and S. Verdú, “Lossy joint source-channel coding in the finite blocklength regime,” IEEE Trans. Inf. Theory, vol. 59, no. 5, pp. 2545–2575, May 2013.

Digital Library

[54]

R. Yaguchi and M. Hayashi, “Second order analysis for joint source-channel coding with Markovian source,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Aachen, Germany, Jun. 2017, pp. 918–922.

[55]

J. Grubb, S. Vishwanath, Y. Liang, and H. V. Poor, “Secrecy capacity of semi-deterministic wire-tap channels,” in Proc. IEEE Inf. Theory Workshop Inf. Theory Wireless Netw., Solstrand, Norway, Jul. 2007, pp. 1–4.

[56]

M. Hayashi, H. Tyagi, and S. Watanabe, “Secret key agreement: General capacity and second-order asymptotics,” IEEE Trans. Inf. Theory, vol. 62, no. 7, pp. 3796–3810, Jul. 2016.

Digital Library

[57]

W. Yang, R. F. Schaefer, and H. V. Poor, “Secrecy-reliability tradeoff for semi-deterministic wiretap channels at finite blocklength,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Aachen, Germany, Jun. 2017, pp. 2133–2137.

[58]

L. Carter and M. Wegman, “Universal classes of hash functions,” J. Comput. Syst. Sci., vol. 18, no. 2, pp. 143–154, Apr. 1979.

[59]

S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.

[60]

M. Raginsky and I. Sason, “Concentration of measure inequalities in information theory, communications and coding,” Found. Trends Commun. Inf. Theory, vol. 10, nos. 1–2, pp. 1–246, 2013.

Digital Library

[61]

W. Feller, An Introduction to Probability Theory and Its Applications, vol. 1. New York, NY, USA: Wiley, 1970.

[62]

C. E. Shannon, R. G. Gallager, and E. R. Berlekamp, “Lower bounds to error probability for coding on discrete memoryless channels I,” Inf. Contr., vol. 10, pp. 65–103, Jan. 1967.

[63]

V. Y. F. Tan and M. Tomamichel, “The third-order term in the normal approximation for the AWGN channel,” IEEE Trans. Inf. Theory, vol. 61, no. 5, pp. 2430–2438, May 2015.

Digital Library

[64]

I. Csiszár and P. C. Shields, “Information theory and statistics: A tutorial,” Found. Trends Commun. Inf. Theory, vol. 1, no. 4, pp. 417–528, Dec. 2004.

Digital Library

Cited By

Chen DLi JHu JZhang XZhang SWang D(2024)Secure short-packet communications in power beacon-assisted IoT networks over Nakagami-m fading channelsEURASIP Journal on Wireless Communications and Networking10.1186/s13638-024-02409-w2024:1Online publication date: 10-Oct-2024
https://dl.acm.org/doi/10.1186/s13638-024-02409-w
Tatar Mamaghani MZhou XYang NLee Swindlehurst AVincent Poor H(2024)Performance Analysis of Finite Blocklength Transmissions Over Wiretap Fading Channels: An Average Information Leakage PerspectiveIEEE Transactions on Wireless Communications10.1109/TWC.2024.340060123:10_Part_1(13252-13266)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1109/TWC.2024.3400601
Tatar Mamaghani MZhou XYang NSwindlehurst A(2024)Secure Short-Packet Communications via UAV-Enabled Mobile Relaying: Joint Resource Optimization and 3D Trajectory DesignIEEE Transactions on Wireless Communications10.1109/TWC.2023.334480223:7(7802-7815)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1109/TWC.2023.3344802
Show More Cited By

Index Terms

Wiretap Channels: Nonasymptotic Fundamental Limits
1. Hardware

Index terms have been assigned to the content through auto-classification.

Recommendations

Compound wiretap channels
Special issue on wireless physical layer security

This paper considers the compound wiretap channel, which generalizes Wyner's wiretap model to allow the channels to the (legitimate) receiver and to the eavesdropper to take a number of possible states. No matter which states occur, the transmitter ...
Capacity results for arbitrarily varying wiretap channels
Information Theory, Combinatorics, and Search Theory

In this work the arbitrarily varying wiretap channel AVWC is studied. We derive a lower bound on the random code secrecy capacity for the average error criterion and the strong secrecy criterion in the case of a best channel to the eavesdropper by using ...
Semantic-Security Capacity for Wiretap Channels of Type II

The secrecy capacity of the type II wiretap channel (WTC II) with a noisy main channel is currently an open problem. Herein its secrecy-capacity is derived and shown to be equal to its semantic-security (SS) capacity. In this setting, the legitimate ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image IEEE Transactions on Information Theory

IEEE Transactions on Information Theory Volume 65, Issue 7

July 2019

642 pages

ISSN:0018-9448

Issue’s Table of Contents

0018-9448 © 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Publisher

IEEE Press

Publication History

Published: 01 July 2019

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

19
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 13 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

Chen DLi JHu JZhang XZhang SWang D(2024)Secure short-packet communications in power beacon-assisted IoT networks over Nakagami-m fading channelsEURASIP Journal on Wireless Communications and Networking10.1186/s13638-024-02409-w2024:1Online publication date: 10-Oct-2024
https://dl.acm.org/doi/10.1186/s13638-024-02409-w
Tatar Mamaghani MZhou XYang NLee Swindlehurst AVincent Poor H(2024)Performance Analysis of Finite Blocklength Transmissions Over Wiretap Fading Channels: An Average Information Leakage PerspectiveIEEE Transactions on Wireless Communications10.1109/TWC.2024.340060123:10_Part_1(13252-13266)Online publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1109/TWC.2024.3400601
Tatar Mamaghani MZhou XYang NSwindlehurst A(2024)Secure Short-Packet Communications via UAV-Enabled Mobile Relaying: Joint Resource Optimization and 3D Trajectory DesignIEEE Transactions on Wireless Communications10.1109/TWC.2023.334480223:7(7802-7815)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1109/TWC.2023.3344802
Loyka SMerhav N(2024)The Secrecy Capacity of the Wiretap Channel With Additive Noise and Rate-Limited HelpIEEE Transactions on Information Theory10.1109/TIT.2023.332211670:1(189-205)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/TIT.2023.3322116
Qian SZhou X(2023)Physical Layer Security in Air-To-Underwater Untrusted Relay NetworksProceedings of the 17th International Conference on Underwater Networks & Systems10.1145/3631726.3631741(1-5)Online publication date: 24-Nov-2023
https://dl.acm.org/doi/10.1145/3631726.3631741
Oh MPark JChoi J(2023)Joint Optimization for Secure and Reliable Communications in Finite Blocklength RegimeIEEE Transactions on Wireless Communications10.1109/TWC.2023.327092522:12(9457-9472)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1109/TWC.2023.3270925
Zhang JXu XHan SZhang KZhang PRen S(2023)Intelligent Ultra-Reliable and Low Latency Communications: Security and FlexibilityIEEE Transactions on Wireless Communications10.1109/TWC.2023.326279122:11(8392-8406)Online publication date: 1-Nov-2023
https://dl.acm.org/doi/10.1109/TWC.2023.3262791
Hayashi MChen Y(2023)Non-Adaptive Coding for Two-Way Wiretap Channel With or Without Cost ConstraintsIEEE Transactions on Information Theory10.1109/TIT.2023.334336270:7(4611-4633)Online publication date: 15-Dec-2023
https://dl.acm.org/doi/10.1109/TIT.2023.3343362
Zhu YYuan XHu YSchaefer RSchmeink A(2023)Trade Reliability for Security: Leakage-Failure Probability Minimization for Machine-Type Communications in URLLCIEEE Journal on Selected Areas in Communications10.1109/JSAC.2023.328096041:7(2123-2137)Online publication date: 1-Jul-2023
https://dl.acm.org/doi/10.1109/JSAC.2023.3280960
Wang YZhou FWang R(2022)Transmission Design in Secure URLLC Network Assisted by Reconfigurable Intelligent SurfacesWireless Communications & Mobile Computing10.1155/2022/87182792022Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1155/2022/8718279
Show More Cited By

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Issue’s Table of Contents