The Wiretap Channel With Generalized Feedback: Secure Communication and Key Generation

It is a well-known fact that feedback does not increase the capacity of point-to-point memoryless channels, however, its effect in secure communications is not fully understood yet. In this paper, an achievable scheme for the wiretap channel with generalized feedback is presented. This scheme, which uses the feedback signal to generate a shared secret key between the legitimate users, encrypts the message to be sent at the bit level. New capacity results for a class of channels are provided, as well as some new insights into the secret key agreement problem. Moreover, this scheme recovers previously reported rate regions from the literature, and thus it can be seen as a generalization that unifies several results in the field.

[1]  H. Vincent Poor,et al.  Secure Communications With Insecure Feedback: Breaking the High-SNR Ceiling , 2010, IEEE Transactions on Information Theory.

[2]  Imre Csiszár,et al.  Secrecy capacities for multiterminal channel models , 2005, ISIT.

[3]  I. Csiszár,et al.  Common randomness and secret key generation with a helper , 1997, Proceedings of the 1999 IEEE Information Theory and Communications Workshop (Cat. No. 99EX253).

[4]  Ueli Maurer,et al.  Information-Theoretic Key Agreement: From Weak to Strong Secrecy for Free , 2000, EUROCRYPT.

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

[6]  A. J. Han Vinck,et al.  Wiretap Channel With Side Information , 2006, IEEE Transactions on Information Theory.

[7]  Haim H. Permuter,et al.  Wiretap channels with random states non-causally available at the encoder , 2016, 2016 IEEE International Conference on the Science of Electrical Engineering (ICSEE).

[8]  Mikael Skoglund,et al.  Key Agreement over a Generalized Multiple Access Channel Using Noiseless and Noisy Feedback , 2013, IEEE Journal on Selected Areas in Communications.

[9]  Gunter Dueck,et al.  Partial Feedback for Two-Way and Broadcast Channels , 1980, Inf. Control..

[10]  Shlomo Shamai,et al.  On the capacity of the wiretap channel with generalized feedback , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[11]  H. Vincent Poor,et al.  Multiple Access Channels with Generalized Feedback and Confidential Messages , 2007, 2007 IEEE Information Theory Workshop.

[12]  Yuan Luo,et al.  Capacity region of non-degraded wiretap channel with noiseless feedback , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

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

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

[15]  Mahtab Mirmohseni,et al.  On the achievable rate region of a new Gaussian wiretap channel with side information , 2012, 2012 IEEE Information Theory Workshop.

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

[17]  H. Vincent Poor,et al.  Secret communication with feedback , 2008, 2008 International Symposium on Information Theory and Its Applications.

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

[19]  Raef Bassily,et al.  Cooperative Security at the Physical Layer: A Summary of Recent Advances , 2013, IEEE Signal Processing Magazine.

[20]  V. Prabhakaran.  A Separation Result for Secure Communication , 2007 .

[21]  Sennur Ulukus,et al.  Effects of cooperation on the secrecy of multiple access channels with generalized feedback , 2008, 2008 42nd Annual Conference on Information Sciences and Systems.

[22]  Rudolf Ahlswede,et al.  Transmission, Identification and Common Randomness Capacities for Wire-Tape Channels with Secure Feedback from the Decoder , 2005, GTIT-C.

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

[24]  Shlomo Shamai,et al.  On multi-user MISO wiretap channels with delayed CSIT , 2014, 2014 IEEE International Symposium on Information Theory.

[25]  H. Vincent Poor,et al.  The Wiretap Channel With Feedback: Encryption Over the Channel , 2007, IEEE Transactions on Information Theory.

[26]  Wei Liu,et al.  Wiretap Channel With Two-Sided Channel State Information , 2007, 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers.

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

[28]  Shlomo Shamai,et al.  Secrecy Degrees of Freedom of MIMO Broadcast Channels With Delayed CSIT , 2011, IEEE Transactions on Information Theory.

[29]  Cyril Leung,et al.  An achievable rate region for the multiple-access channel with feedback , 1981, IEEE Trans. Inf. Theory.

[30]  Shlomo Shamai,et al.  Information Theoretic Security , 2009, Found. Trends Commun. Inf. Theory.

[31]  Vinod M. Prabhakaran,et al.  Secrecy via Sources and Channels , 2008, IEEE Transactions on Information Theory.

[32]  Suhas N. Diggavi,et al.  Secret Communication Over Broadcast Erasure Channels With State-Feedback , 2014, IEEE Transactions on Information Theory.

[33]  Aylin Yener,et al.  The Role of Feedback in Two-Way Secure Communications , 2009, IEEE Transactions on Information Theory.

[34]  Suhas N. Diggavi,et al.  Secret-Key Generation Using Correlated Sources and Channels , 2009, IEEE Transactions on Information Theory.

[35]  Thomas Kailath,et al.  A coding scheme for additive noise channels with feedback-I: No bandwidth constraint , 1966, IEEE Trans. Inf. Theory.