Source coding with side information for error free perfect secrecy systems

This paper considers source coding problems with the requirements of perfect secrecy and zero error at receivers. In the problems considered in this paper, there is always one transmitter but there can be one or two receivers. Two different scenarios depending on whether the receivers' side information are present at the transmitter or not are considered. By deriving bounds on the probability masses of the cipher-text and the key, the minimum transmission rate and key rate are characterized. Although zero-error capacities are typically difficult to characterize, the perfect secrecy constraint turns out to be the key that simplifies the problems considered in this paper and makes them analytically tractable.

[1]  Alon Orlitsky,et al.  Communication with secrecy constraints , 1984, STOC '84.

[2]  Sennur Ulukus,et al.  Secure Lossy Transmission of Vector Gaussian Sources , 2011, IEEE Transactions on Information Theory.

[3]  Kenneth Rose,et al.  On zero-error source coding with decoder side information , 2003, IEEE Trans. Inf. Theory.

[4]  Pablo Piantanida,et al.  Secure lossy source coding with side information at the decoders , 2010, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[5]  H. S. WITSENHAUSEN,et al.  The zero-error side information problem and chromatic numbers (Corresp.) , 1976, IEEE Trans. Inf. Theory.

[6]  H.V. Poor,et al.  Privacy-security tradeoffs in biometric security systems , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

[7]  Himanshu Tyagi,et al.  When Is a Function Securely Computable? , 2010, IEEE Transactions on Information Theory.

[8]  Frans M. J. Willems,et al.  Biometric Systems: Privacy and Secrecy Aspects , 2009, IEEE Transactions on Information Forensics and Security.

[9]  Giuseppe Longo,et al.  Two-step encoding for finite sources , 1973, IEEE Trans. Inf. Theory.

[10]  Sennur Ulukus,et al.  Secure Lossy Transmission of Vector Gaussian Sources , 2013, IEEE Trans. Inf. Theory.

[11]  Alon Orlitsky,et al.  Coding for computing , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[12]  R. Balakrishnan,et al.  A textbook of graph theory , 1999 .

[13]  H. Vincent Poor,et al.  Lossless compression with security constraints , 2008, 2008 IEEE International Symposium on Information Theory.

[14]  V. Prabhakaran,et al.  On Secure Distributed Source Coding , 2007, 2007 IEEE Information Theory Workshop.

[15]  Noga Alon,et al.  Source coding and graph entropies , 1996, IEEE Trans. Inf. Theory.

[16]  H. Vincent Poor,et al.  Privacy–Security Trade-Offs in Biometric Security Systems—Part I: Single Use Case , 2011, IEEE Transactions on Information Forensics and Security.

[17]  Alon Orlitsky,et al.  Zero-Error Information Theory , 1998, IEEE Trans. Inf. Theory.

[18]  Sergio Verdú,et al.  On the Interplay Between Conditional Entropy and Error Probability , 2010, IEEE Transactions on Information Theory.