Low Error Efficient Computational Extractors in the CRS Model

In recent years, there has been exciting progress on building two-source extractors for sources with low min-entropy. Unfortunately, all known explicit constructions of two-source extractors in the low entropy regime suffer from non-negligible error, and building such extractors with negligible error remains an open problem. We investigate this problem in the computational setting, and obtain the following results.

[1]  Gil Cohen,et al.  Non-Malleable Extractors - New Tools and Improved Constructions , 2016, Electron. Colloquium Comput. Complex..

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

[3]  Tanja Lange,et al.  Factoring RSA keys from certified smart cards: Coppersmith in the wild , 2013, IACR Cryptol. ePrint Arch..

[4]  Brent Waters,et al.  Lossy trapdoor functions and their applications , 2008, SIAM J. Comput..

[5]  Venkatesan Guruswami,et al.  Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes , 2009, JACM.

[6]  Yael Tauman Kalai,et al.  2-Source Extractors under Computational Assumptions and Cryptography with Defective Randomness , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.

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

[8]  Yael Tauman Kalai,et al.  Network Extractor Protocols , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[9]  Xin Li,et al.  Explicit Non-malleable Extractors, Multi-source Extractors, and Almost Optimal Privacy Amplification Protocols , 2016, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS).

[10]  Craig Gentry,et al.  Separating succinct non-interactive arguments from all falsifiable assumptions , 2011, STOC '11.

[11]  J. Bourgain,et al.  MORE ON THE SUM-PRODUCT PHENOMENON IN PRIME FIELDS AND ITS APPLICATIONS , 2005 .

[12]  Amit Sahai,et al.  On the (im)possibility of cryptography with imperfect randomness , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[13]  Krzysztof Pietrzak,et al.  How to Fake Auxiliary Input , 2014, IACR Cryptol. ePrint Arch..

[14]  Gil Cohen,et al.  Making the Most of Advice: New Correlation Breakers and Their Applications , 2016, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS).

[15]  Amnon Ta-Shma,et al.  Explicit two-source extractors for near-logarithmic min-entropy , 2016, Electron. Colloquium Comput. Complex..

[16]  Amnon Ta-Shma,et al.  A reduction from efficient non-malleable extractors to low-error two-source extractors with arbitrary constant rate , 2017, Electron. Colloquium Comput. Complex..

[17]  Gil Cohen,et al.  Two-Source Extractors for Quasi-Logarithmic Min-Entropy and Improved Privacy Amplification Protocols , 2016, Electron. Colloquium Comput. Complex..

[18]  Nadia Heninger,et al.  Biased Nonce Sense: Lattice Attacks against Weak ECDSA Signatures in Cryptocurrencies , 2019, IACR Cryptol. ePrint Arch..

[19]  Ran Raz,et al.  Extractors with weak random seeds , 2005, STOC '05.

[20]  Rafail Ostrovsky,et al.  Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data , 2004, SIAM J. Comput..

[21]  Gil Cohen,et al.  Local Correlation Breakers and Applications to Three-Source Extractors and Mergers , 2015, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science.

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

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

[24]  Kai-Min Chung,et al.  From Weak to Strong Zero-Knowledge and Applications , 2015, TCC.

[25]  Yael Tauman Kalai,et al.  Leaky Pseudo-Entropy Functions , 2011, ICS.