Non-Malleable Extractors and Codes in the Interleaved Split-State Model and More

We present explicit constructions of non-malleable codes with respect to the following tampering classes. (i) Linear functions composed with split-state adversaries: In this model, the codeword is first tampered by a split-state adversary, and then the whole tampered codeword is further tampered by a linear function. (ii) Interleaved split-state adversary: Here the codeword is partitioned in an unknown (but fixed) way, and then tampered by a split-state adversary. (iii) Bounded communication split-state model: In this model, the split-state adversaries are allowed to participate in a communication protocol (with bounded communication budget) to tamper the codeword. Our results are the first explicit constructions of non-malleable codes in any of these tampering models. We derive all our non-malleable codes from explicit constructions of seedless non-malleable extractors. We believe that our results on seedless non-malleable extractors and the techniques developed are of independent interest. Using our techniques, we also give an improved extractor for an unknown interleaving of two independent sources.

[1]  Luca Trevisan,et al.  Extractors and pseudorandom generators , 2001, JACM.

[2]  Stefan Dziembowski,et al.  Non-Malleable Codes from Two-Source Extractors , 2013, IACR Cryptol. ePrint Arch..

[3]  Silas Richelson,et al.  Textbook non-malleable commitments , 2016, STOC.

[4]  Venkatesan Guruswami,et al.  Non-malleable Coding against Bit-Wise and Split-State Tampering , 2014, TCC.

[5]  Manoj Prabhakaran,et al.  A Rate-Optimizing Compiler for Non-malleable Codes Against Bit-Wise Tampering and Permutations , 2015, TCC.

[6]  Anup Rao,et al.  Extractors for Low-Weight Affine Sources , 2009, 2009 24th Annual IEEE Conference on Computational Complexity.

[7]  Bhavana Kanukurthi,et al.  Four-State Non-malleable Codes with Explicit Constant Rate , 2017, Journal of Cryptology.

[8]  Jiapeng Zhang,et al.  A Tight Lower Bound for Entropy Flattening , 2018, Computational Complexity Conference.

[9]  Divya Gupta,et al.  Constant-rate Non-malleable Codes in the Split-state Model , 2017, IACR Cryptol. ePrint Arch..

[10]  Li-Yang Tan,et al.  Non-Malleable Codes for Small-Depth Circuits , 2018, 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS).

[11]  Eshan Chattopadhyay,et al.  Non-malleable codes and extractors for small-depth circuits, and affine functions , 2017, STOC.

[12]  Gil Cohen.  Local Correlation Breakers and Applications to Three-Source Extractors and Mergers , 2015, FOCS.

[13]  Xin Li,et al.  Improved Two-Source Extractors, and Affine Extractors for Polylogarithmic Entropy , 2016, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS).

[14]  Vipul Goyal,et al.  Non-malleable extractors and codes, with their many tampered extensions , 2015, IACR Cryptol. ePrint Arch..

[15]  David Zuckerman.  Randomness-optimal oblivious sampling , 1997, Random Struct. Algorithms.

[16]  Xin Li,et al.  Improved non-malleable extractors, non-malleable codes and independent source extractors , 2016, Electron. Colloquium Comput. Complex..

[17]  Avi Wigderson,et al.  2-source dispersers for $n^{o(1)}$ entropy, and Ramsey graphs beating the Frankl-Wilson construction , 2012 .

[18]  Gil Cohen,et al.  Two-source dispersers for polylogarithmic entropy and improved ramsey graphs , 2015, Electron. Colloquium Comput. Complex..

[19]  D. Zuckerman,et al.  Explicit two-source extractors and resilient functions , 2016, Electron. Colloquium Comput. Complex..

[20]  David Zuckerman,et al.  Electronic Colloquium on Computational Complexity, Report No. 100 (2005) Linear Degree Extractors and the Inapproximability of MAX CLIQUE and CHROMATIC NUMBER , 2005 .

[21]  Eshan Chattopadhyay,et al.  Extractors for sumset sources , 2016, STOC.

[22]  Suela Kodra.  Fuzzy extractors : How to generate strong keys from biometrics and other noisy data , 2015 .

[23]  Ueli Maurer,et al.  Privacy Amplification Secure Against Active Adversaries , 1997, CRYPTO.

[24]  Xin Li,et al.  Pseudorandom Correlation Breakers, Independence Preserving Mergers and their Applications , 2018, Electron. Colloquium Comput. Complex..

[25]  Yevgeniy Dodis,et al.  Non-malleable Reductions and Applications , 2015, Electron. Colloquium Comput. Complex..

[26]  David Zuckerman,et al.  New Extractors for Interleaved Sources , 2016, Electron. Colloquium Comput. Complex..

[27]  David Zuckerman,et al.  Non-malleable Codes against Constant Split-State Tampering , 2014, 2014 IEEE 55th Annual Symposium on Foundations of Computer Science.

[28]  Ueli Maurer,et al.  From Single-Bit to Multi-bit Public-Key Encryption via Non-malleable Codes , 2015, TCC.

[29]  Tal Malkin,et al.  Non-malleable Codes for Bounded Depth, Bounded Fan-In Circuits , 2016, EUROCRYPT.

[30]  Oded Goldreich,et al.  Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Complexity , 1988, SIAM J. Comput..

[31]  Ran Raz,et al.  Multilinear formulas, maximal-partition discrepancy and mixed-sources extractors , 2011, J. Comput. Syst. Sci..

[32]  Luca Trevisan,et al.  Extracting randomness from samplable distributions , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[33]  Ran Raz,et al.  Extracting all the randomness and reducing the error in Trevisan's extractors , 1999, STOC '99.

[34]  Stefan Dziembowski,et al.  Non-Malleable Codes , 2018, ICS.

[35]  Enkatesan G Uruswami.  Unbalanced expanders and randomness extractors from Parvaresh-Vardy codes , 2008 .

[36]  Yevgeniy Dodis,et al.  Non-malleable extractors and symmetric key cryptography from weak secrets , 2009, STOC '09.