Noncoherent Capacity of Secret-Key Agreement With Public Discussion

We study the noncoherent capacity of secret-key agreement with public discussion over independent identically distributed (i.i.d.) Rayleigh fading wireless channels, where neither the sender nor the receivers have access to instantaneous channel state information (CSI). We present two results. At high signal-to-noise ratio (SNR), the secret-key capacity is bounded in SNR, regardless of the number of antennas at each terminal. Second, for a system with a single antenna at both the legitimate and the eavesdropper terminals and an arbitrary number of transmit antennas, the secret-key capacity-achieving input distribution is discrete, with a finite number of mass points. Numerically we observe that at low SNR, the capacity achieving distribution has two mass points with one of them at the origin.

[1]  Abbas El Gamal,et al.  Lecture Notes on Network Information Theory , 2010, ArXiv.

[2]  T.D. Abhayapala,et al.  Upper bound on non-coherent MIMO channel capacity in Rayleigh fading , 2005, 2005 Asia-Pacific Conference on Communications.

[3]  Max H. M. Costa,et al.  Writing on dirty paper , 1983, IEEE Trans. Inf. Theory.

[4]  Brian Davies,et al.  Integral transforms and their applications , 1978 .

[5]  Venkat Anantharam,et al.  Information-Theoretic Key Agreement of Multiple Terminals—Part I , 2010, IEEE Transactions on Information Theory.

[6]  Alex Reznik,et al.  Extracting Secrecy from Jointly Gaussian Random Variables , 2006, 2006 IEEE International Symposium on Information Theory.

[7]  Abbas El Gamal,et al.  Wiretap Channel With Causal State Information , 2012, IEEE Transactions on Information Theory.

[8]  Venkat Anantharam,et al.  Information-Theoretic Key Agreement of Multiple Terminals—Part II: Channel Model , 2010, IEEE Transactions on Information Theory.

[9]  Ahmed Ali Mohammed,et al.  Integral transforms and their applications , 2009 .

[10]  Thomas L. Marzetta,et al.  Capacity of a Mobile Multiple-Antenna Communication Link in Rayleigh Flat Fading , 1999, IEEE Trans. Inf. Theory.

[11]  G. Taricco,et al.  Capacity of fading channel with no side information , 1997 .

[12]  Larry J. Greenstein,et al.  Fingerprints in the Ether: Using the Physical Layer for Wireless Authentication , 2007, 2007 IEEE International Conference on Communications.

[13]  T. Broadbent.  Complex Variables , 1970, Nature.

[14]  Gregory W. Wornell,et al.  Secure Broadcasting Over Fading Channels , 2008, IEEE Transactions on Information Theory.

[15]  Aaron D. Wyner,et al.  Channels with Side Information at the Transmitter , 1993 .

[16]  T.D. Abhayapala,et al.  Performance of Gaussian Distributed Input in Non-Coherent Rayleigh Fading MIMO Channels , 2005, 2005 5th International Conference on Information Communications & Signal Processing.

[17]  Gregory W. Wornell,et al.  Secure Transmission With Multiple Antennas I: The MISOME Wiretap Channel , 2010, IEEE Transactions on Information Theory.

[18]  Venkat Anantharam,et al.  Information-theoretic key agreement of multiple terminal: part II: channel model , 2010, IEEE Trans. Inf. Theory.

[19]  Mohamed-Slim Alouini,et al.  Non-Coherent Capacity of Secret-Key Agreement with Public Discussion , 2011, 2011 IEEE International Conference on Communications Workshops (ICC).

[20]  Rudolf Ahlswede,et al.  Common randomness in information theory and cryptography - I: Secret sharing , 1993, IEEE Trans. Inf. Theory.

[21]  David Tse,et al.  Channel Identification: Secret Sharing using Reciprocity in Ultrawideband Channels , 2007 .

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

[23]  Shlomo Shamai,et al.  The capacity of average and peak-power-limited quadrature Gaussian channels , 1995, IEEE Trans. Inf. Theory.

[24]  Matthieu Bloch,et al.  Secret Sharing over Fast-Fading MIMO Wiretap Channels , 2009, EURASIP J. Wirel. Commun. Netw..

[25]  Alfred O. Hero,et al.  Secure space-time communication , 2003, IEEE Trans. Inf. Theory.

[26]  Vinod M. Prabhakaran,et al.  Secrecy via sources and channels — A secret key - Secret message rate tradeoff region , 2008, 2008 IEEE International Symposium on Information Theory.

[27]  Wade Trappe,et al.  Radio-telepathy: extracting a secret key from an unauthenticated wireless channel , 2008, MobiCom '08.

[28]  Ibrahim C. Abou-Faycal,et al.  The capacity of discrete-time memoryless Rayleigh-fading channels , 2001, IEEE Trans. Inf. Theory.

[29]  Matthieu R. Bloch,et al.  Wireless Information-Theoretic Security , 2008, IEEE Transactions on Information Theory.

[30]  Shlomo Shamai,et al.  Secrecy Capacity Region of Fading Broadcast Channels , 2007, 2007 IEEE International Symposium on Information Theory.

[31]  T. Aono,et al.  Wireless secret key generation exploiting reactance-domain scalar response of multipath fading channels , 2005, IEEE Transactions on Antennas and Propagation.

[32]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .