Secret Key and Private Key Constructions for Simple Multiterminal Source Models

We propose an approach for constructing secret and private keys based on the long-known Slepian-Wolf code, due to Wyner, for correlated sources connected by a virtual additive noise channel. Our work is motivated by results of Csiszár and Narayan which highlight innate connections between secrecy generation by multiple terminals that observe correlated source signals and Slepian-Wolf near-lossless data compression. Explicit procedures for such constructions and their substantiation are provided. The performance of low-density parity check channel codes in devising a new class of secret keys is examined.

[1]  Muriel Médard,et al.  On some new approaches to practical Slepian-Wolf compression inspired by channel coding , 2004, Data Compression Conference, 2004. Proceedings. DCC 2004.

[2]  Ueli Maurer,et al.  Generalized privacy amplification , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[3]  Bernd Girod,et al.  Compression with side information using turbo codes , 2002, Proceedings DCC 2002. Data Compression Conference.

[4]  Patrick Mitran,et al.  Turbo source coding: a noise-robust approach to data compression , 2002, Proceedings DCC 2002. Data Compression Conference.

[5]  Prakash Narayan,et al.  Secret Key Constructions for Simple Multiterminal Source Models , 2004 .

[6]  A. Robert Calderbank,et al.  Applications of LDPC Codes to the Wiretap Channel , 2004, IEEE Transactions on Information Theory.

[7]  Steven Roman Introduction to coding and information theory , 1997, Undergraduate texts in mathematics.

[8]  Jun Muramatsu,et al.  Secret Key Agreement from Correlated Source Outputs Using Low Density Parity Check Matrices , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

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

[10]  A. Robert Calderbank,et al.  Capacity Achieving Codes for the Wire Tap Channel with Applications to Quantum Key Distribution , 2004, ArXiv.

[11]  Zixiang Xiong,et al.  Compression of binary sources with side information at the decoder using LDPC codes , 2002, IEEE Communications Letters.

[12]  Ying Zhao,et al.  Compression of correlated binary sources using turbo codes , 2001, IEEE Communications Letters.

[13]  J. Muramatu Secret key agreement from correlated source outputs using LDPC matrices , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[14]  Imre Csiszár,et al.  Common randomness and secret key generation with a helper , 2000, IEEE Trans. Inf. Theory.

[15]  Imre Csiszár Linear codes for sources and source networks: Error exponents, universal coding , 1982, IEEE Trans. Inf. Theory.

[16]  F. Lemmermeyer Error-correcting Codes , 2005 .

[17]  Zixiang Xiong,et al.  Slepian-Wolf Coding of Three Binary Sources Using LDPC Codes , 2003 .

[18]  En-Hui Yang,et al.  On the Duality between Slepian-Wolf Coding and Channel Coding , 2006, ISIT.

[19]  Rüdiger L. Urbanke,et al.  The capacity of low-density parity-check codes under message-passing decoding , 2001, IEEE Trans. Inf. Theory.

[20]  Imre Csiszár,et al.  Secrecy Capacities for Multiterminal Channel Models , 2005, IEEE Transactions on Information Theory.

[21]  Kannan Ramchandran,et al.  Distributed code constructions for the entire Slepian-Wolf rate region for arbitrarily correlated sources , 2004, Data Compression Conference, 2004. Proceedings. DCC 2004.

[22]  Imre Csiszár,et al.  Secrecy capacities for multiple terminals , 2004, IEEE Transactions on Information Theory.

[23]  Zixiang Xiong,et al.  Slepian-Wolf coding of multiple M-ary sources using LDPC codes , 2004, Data Compression Conference, 2004. Proceedings. DCC 2004.

[24]  Kannan Ramchandran,et al.  Distributed source coding using syndromes (DISCUS): design and construction , 2003, IEEE Trans. Inf. Theory.

[25]  Aaron D. Wyner,et al.  Recent results in the Shannon theory , 1974, IEEE Trans. Inf. Theory.

[26]  Ron M. Roth,et al.  Introduction to Coding Theory , 2019, Discrete Mathematics.

[27]  David Tse,et al.  Channel Identification: Secret Sharing Using Reciprocity in Ultrawideband Channels , 2007, IEEE Transactions on Information Forensics and Security.

[28]  Jing Li,et al.  A new coding scheme for the noisy-channel Slepian-Wolf problem: separate design and joint decoding , 2004, IEEE Global Telecommunications Conference, 2004. GLOBECOM '04..

[29]  Hans-Otto Georgii,et al.  Gibbs Measures and Phase Transitions , 1988 .

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

[31]  David J. C. MacKay,et al.  Good Error-Correcting Codes Based on Very Sparse Matrices , 1997, IEEE Trans. Inf. Theory.

[32]  Robert Michael Tanner,et al.  A recursive approach to low complexity codes , 1981, IEEE Trans. Inf. Theory.

[33]  Renato Renner,et al.  New Bounds in Secret-Key Agreement: The Gap between Formation and Secrecy Extraction , 2003, EUROCRYPT.

[34]  Kannan Ramchandran,et al.  Distributed code constructions for the entire Slepian-Wolf rate region for arbitrarily correlated sources , 2003, The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003.

[35]  Rick S. Blum,et al.  Slepian-Wolf coding for nonuniform sources using turbo codes , 2004, Data Compression Conference, 2004. Proceedings. DCC 2004.

[36]  Prakash Narayan,et al.  Secret key and private key constructions for simple multiterminal source models , 2005, ISIT.

[37]  Wei Zhong,et al.  LDPC codes for compression of multi-terminal sources with hidden Markov correlation , 2003, IEEE Communications Letters.

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