Optimal Coding for Streaming Authentication and Interactive Communication

We consider the task of communicating a data stream-a long, possibly infinite message not known in advance to the sender-over a channel with adversarial noise. For any given noise rate c <; 1, we show an efficient, constant-rate scheme that correctly decodes a (1 - c) fraction of the stream sent so far with high probability, or aborts if the noise rate exceeds c. In addition, we prove that no constant-rate scheme can recover more than a (1 - c) fraction of the stream sent so far with non-negligible probability, which makes our scheme optimal in that aspect. The parties are assumed to preshare a random string unknown to the channel. Our techniques can also be applied to the task of interactive communication (two-way communication) over a noisy channel. In a recent paper (Braverman and Rao, STOC11), the possibility of two-party interactive communication as long as the noise level is <; 1/4 was shown. By allowing the parties to preshare some private random string, we extend this result and construct a (nonefficient) constant-rate interactive protocol that succeeds with overwhelming probability against noise rates up to 1/2. We complete this result by proving that no constant-rate protocol can withstand noise rates > 1/2.

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

[2]  Amit Sahai,et al.  Efficient and Explicit Coding for Interactive Communication , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[3]  Michael Langberg,et al.  Private codes or succinct random codes that are (almost) perfect , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[4]  Ran Canetti,et al.  Efficient authentication and signing of multicast streams over lossy channels , 2000, Proceeding 2000 IEEE Symposium on Security and Privacy. S&P 2000.

[5]  Mark Braverman,et al.  Towards deterministic tree code constructions , 2012, ITCS '12.

[6]  Cristopher Moore,et al.  Tree codes and a conjecture on exponential sums , 2013, ITCS.

[7]  Claude E. Shannon,et al.  A Note on a Partial Ordering for Communication Channels , 1958, Information and Control.

[8]  Crosby Newell Bonsall,et al.  The Case of the Hungry Stranger , 1963 .

[9]  Amit Sahai,et al.  Efficient Coding for Interactive Communication , 2014, IEEE Transactions on Information Theory.

[10]  Leonard J. Schulman.  Coding for interactive communication , 1996, IEEE Trans. Inf. Theory.

[11]  Rosario Gennaro,et al.  How to Sign Digital Streams , 1997, CRYPTO.

[12]  Madhu Sudan,et al.  Optimal error rates for interactive coding I: adaptivity and other settings , 2013, STOC.

[13]  Rafail Ostrovsky,et al.  Optimal Coding for Streaming Authentication and Interactive Communication , 2015, IEEE Trans. Inf. Theory.

[14]  Moni Naor,et al.  Fast Algorithms for Interactive Coding , 2013, SODA.

[15]  Rafail Ostrovsky,et al.  Public Key Locally Decodable Codes with Short Keys , 2011, APPROX-RANDOM.

[16]  Marcin Peczarski.  An improvement of the tree code construction , 2006, Inf. Process. Lett..

[17]  Rafail Ostrovsky,et al.  Public-Key Locally-Decodable Codes , 2008, CRYPTO.

[18]  Mark Braverman,et al.  List and Unique Coding for Interactive Communication in the Presence of Adversarial Noise , 2014, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[19]  Silvio Micali,et al.  Optimal Error Correction Against Computationally Bounded Noise , 2005, TCC.

[20]  Philippe Golle,et al.  Authenticating Streamed Data in the Presence of Random Packet Loss , 2001, NDSS.

[21]  Mark Braverman,et al.  Toward Coding for Maximum Errors in Interactive Communication , 2011, IEEE Transactions on Information Theory.

[22]  Silvio Micali,et al.  On-line/off-line digital signatures , 1996, Journal of Cryptology.

[23]  Bernhard Haeupler,et al.  Optimal Error Rates for Interactive Coding II: Efficiency and List Decoding , 2013, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[24]  Leonard J. Schulman,et al.  Deterministic coding for interactive communication , 1993, STOC.

[25]  Adam D. Smith.  Scrambling adversarial errors using few random bits, optimal information reconciliation, and better private codes , 2007, SODA '07.

[26]  Leonard J. Schulman,et al.  Communication on noisy channels: a coding theorem for computation , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[27]  Rafail Ostrovsky,et al.  Efficient Error-Correcting Codes for Sliding Windows , 2014, SOFSEM.

[28]  Amit Sahai,et al.  Adaptive protocols for interactive communication , 2013, 2016 IEEE International Symposium on Information Theory (ISIT).

[29]  Venkatesan Guruswami,et al.  Codes for Computationally Simple Channels: Explicit Constructions with Optimal Rate , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[30]  Jessica Staddon,et al.  Graph-based authentication of digital streams , 2001, Proceedings 2001 IEEE Symposium on Security and Privacy. S&P 2001.

[31]  F. MacWilliams,et al.  Codes which detect deception , 1974 .

[32]  Klim Efremenko,et al.  Maximal Noise in Interactive Communication Over Erasure Channels and Channels With Feedback , 2015, IEEE Transactions on Information Theory.

[33]  Richard J. Lipton,et al.  A New Approach To Information Theory , 1994, STACS.

[34]  S. Rajsbaum.  Foundations of Cryptography , 2014 .

[35]  Yael Tauman Kalai,et al.  Efficient Interactive Coding against Adversarial Noise , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.

[36]  Gilles Brassard,et al.  Noisy Interactive Quantum Communication , 2013, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[37]  Klaus Jansen,et al.  Approximation, Randomization and Combinatorial Optimization. , 2008 .