Perfect secrecy via compressed sensing

In this paper we consider the compressive sensing based encryption and proposed the conditions in which the perfect secrecy is achievable. We prove that when the measurement matrix holds the Restricted Isometry Property (RIP) and the number of measurements is more than two times of the sparsity level, i.e., M ≥ 2k, the Shannon perfect secrecy condition is achievable either i) the cardinality of the message set tends to infinity or ii) the message set does not include the zero message. As an implicit assumption, we suppose that the eavesdropper has not access to the secret key during the transmission.

[1]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[2]  Tang Ming . Wei Lian. Si Tuo Lin Si,et al.  Cryptography and Network Security - Principles and Practice , 2015 .

[3]  Sheng Chen,et al.  Orthogonal least squares methods and their application to non-linear system identification , 1989 .

[4]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[5]  Hyun Sung Chang,et al.  Learning Compressed Sensing , 2007 .

[6]  William Stallings,et al.  Cryptography and Network Security: Principles and Practice , 1998 .

[7]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[8]  G. Sharma,et al.  On the security and robustness of encryption via compressed sensing , 2008, MILCOM 2008 - 2008 IEEE Military Communications Conference.

[9]  J. Romberg.  Imaging via Compressive Sampling [Introduction to compressive sampling and recovery via convex programming] , 2008 .

[10]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[11]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

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

[13]  J. Romberg,et al.  Imaging via Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[14]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[15]  R. DeVore,et al.  A Simple Proof of the Restricted Isometry Property for Random Matrices , 2008 .

[16]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[17]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[18]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[19]  Michael Elad,et al.  From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images , 2009, SIAM Rev..

[20]  Richard G. Baraniuk,et al.  Sparse Signal Detection from Incoherent Projections , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

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

[22]  Y. Rachlin,et al.  The secrecy of compressed sensing measurements , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

[23]  R. Baraniuk,et al.  Compressive Radar Imaging , 2007, 2007 IEEE Radar Conference.