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Extractors and Lower Bounds for Locally Samplable Sources

Anindya De, Thomas Watson
2012 ACM Transactions on Computation Theory  
Using our result, we also improve a result of Viola (FOCS 2010), who proved a 1/2 − O(1/ log n) statistical distance lower bound for o(log n)-local samplers trying to sample inputoutput pairs of an explicit  ...  Using a different function, we simultaneously improve the lower bound to 1/2 − 2 −n Ω(1) and eliminate the restriction on the number of random bits.  ...  In particular, A.D. would like to thank Omer and Salil for answering his innumerable queries about extractors and Salil for suggesting the use of GUV condensers.  ... 
doi:10.1145/2141938.2141941 fatcat:ulymhsj7ongm7iuvcnjnlhfi4q

Extractors and Lower Bounds for Locally Samplable Sources [chapter]

Anindya De, Thomas Watson
2011 Lecture Notes in Computer Science  
Using our result, we also improve a result of Viola (FOCS 2010), who proved a 1/2 − O(1/ log n) statistical distance lower bound for o(log n)-local samplers trying to sample inputoutput pairs of an explicit  ...  Using a different function, we simultaneously improve the lower bound to 1/2 − 2 −n Ω(1) and eliminate the restriction on the number of random bits.  ...  In particular, A.D. would like to thank Omer and Salil for answering his innumerable queries about extractors and Salil for suggesting the use of GUV condensers.  ... 
doi:10.1007/978-3-642-22935-0_41 fatcat:2ttsascuvvbspncebf4aovltbi

Two-Source Non-Malleable Extractors and Applications to Privacy Amplification with Tamperable Memory [article]

Divesh Aggarwal, Maciej Obremski, João L. Ribeiro, Mark Simkin, Luisa Siniscalchi
2020 IACR Cryptology ePrint Archive  
This suggests that obtaining (information-theoretically secure) explicit non-malleable two-source extractors for (1) might be hard; (3) We present explicit constructions of low-error, low min-entropy non-malleable  ...  We extend the classical problem of privacy amplification to a setting where the active adversary, Eve, is also allowed to fully corrupt the internal memory (which includes the shared randomness, and local  ...  Then, they exploit this extractor and results of [BACD + 18] to construct an extractor of the same type for unbalanced sources with lower min-entropy.  ... 
dblp:journals/iacr/AggarwalORSS20a fatcat:hjmxjryji5bv7gtoiehw4htboy

Extractors for Circuit Sources

Emanuele Viola
2014 SIAM journal on computing (Print)  
As our starting point, we revisit the connection by Trevisan and Vadhan (FOCS 2000) between circuit lower bounds and extractors for sources generated by circuits.  ...  Introduced here, such sources are a special case of affine ones. As extractors for (1) and (2) one can use the extractor for low-weight affine sources by Rao (CCC 2009).  ...  We also thank Anup Rao for a discussion on [Rao09] which resulted in §2.3, and the organizers of the 2011 Dagstuhl seminar on complexity theory for the opportunity to present these results in March 2011  ... 
doi:10.1137/11085983x fatcat:xwk7rnflirbcxiavpdvwo5ppqe

Extractors for Circuit Sources

Emanuele Viola
2011 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science  
As our starting point, we revisit the connection by Trevisan and Vadhan (FOCS 2000) between circuit lower bounds and extractors for sources generated by circuits.  ...  Introduced here, such sources are a special case of affine ones. As extractors for (1) and (2) one can use the extractor for low-weight affine sources by Rao (CCC 2009).  ...  We also thank Anup Rao for a discussion on [Rao09] which resulted in §2.3, and the organizers of the 2011 Dagstuhl seminar on complexity theory for the opportunity to present these results in March 2011  ... 
doi:10.1109/focs.2011.20 dblp:conf/focs/Viola11 fatcat:lpg6me5m6vgr7hcsx2vxjkrkqq

Extractors for Turing-Machine Sources [chapter]

Emanuele Viola
2012 Lecture Notes in Computer Science  
We obtain the first deterministic randomness extractors for n-bit sources with minentropy ≥ n 1−α generated (or sampled) by single-tape Turing machines running in time n 2−16α , for all sufficiently small  ...  We now restate and prove our sampling lower bound for inner product. Theorem 1.2 (Sampling lower bound for Turing machines).  ...  Theorem 1.2 (Sampling lower bound for Turing machines).  ... 
doi:10.1007/978-3-642-32512-0_56 fatcat:62jaxqohr5h2bepkuxgparxhae

The complexity of estimating min-entropy

Thomas Watson
2014 Computational Complexity  
We consider the analogous problem for estimating the min-entropy and prove that it is SBPcomplete, even when restricted to 3-local samplers.  ...  Goldreich, Sahai, and Vadhan (CRYPTO 1999) proved that the promise problem for estimating the Shannon entropy of a distribution sampled by a given circuit is NISZK-complete.  ...  Acknowledgments I thank anonymous reviewers for their comments.  ... 
doi:10.1007/s00037-014-0091-2 fatcat:bex5nwb47nhrhojju3s4fs27py

Low-Degree Polynomials Extract from Local Sources [article]

Omar Alrabiah, Eshan Chattopadhyay, Jesse Goodman, Xin Li, João Ribeiro
2022 arXiv   pre-print
In particular, extractors for local sources also work for sources generated by these classical computational models.  ...  We answer this question in the positive, and fully characterize the power of low-degree polynomials as extractors for local sources.  ...  Extractors for local sources, AC 0 sources, and small-space sources.  ... 
arXiv:2205.13725v1 fatcat:exij5jebl5bmrb3h2g5hfcvp64

Circuit Lower Bounds for MCSP from Local Pseudorandom Generators

Mahdi Cheraghchi, Valentine Kabanets, Zhenjian Lu, Dimitrios Myrisiotis
2020 ACM Transactions on Computation Theory  
We get new and improved lower bounds for MCSP that almost match the best-known lower bounds against several circuit models.  ...  We improve several circuit lower bounds for MCSP, using pseudorandom generators (PRGs) that are local; a PRG is called local if its output bit strings, when viewed as the truth table of a Boolean function  ...  I C A L P 2 0 1 939:12 Circuit Lower Bounds for MCSP from Local PRGsThen, by the definition of the extractor, we have Lemma 24 . 24 For any s ≥ n, there exists a N, s, s 1/2 · 2 O √ log s -local PRG  ... 
doi:10.1145/3404860 fatcat:eeqmy7heabbsxcosw7yb7kjq6u

Non-malleable Coding against Bit-Wise and Split-State Tampering [chapter]

Mahdi Cheraghchi, Venkatesan Guruswami
2014 Lecture Notes in Computer Science  
In particular, Dziembowski et al. show that such codes exist and may achieve positive rates for any class of tampering functions of size at most 2 2 αn , for any constant α ∈ [0, 1).  ...  Non-malleable coding is possible against any class of adversaries of bounded size.  ...  In general, when the random permutation is -wise δ-dependent for δ 0, the above lower bound can only be affected by δ.  ... 
doi:10.1007/978-3-642-54242-8_19 fatcat:xw5awuv5bvenzbznxahcbak6tq

Pseudorandomness

Salil P. Vadhan
2012 Foundations and Trends® in Theoretical Computer Science  
This theory has significance for a number of areas in computer science and mathematics, including computational complexity, algorithms, cryptography, combinatorics, communications, and additive number  ...  , list-decodable error-correcting codes, samplers, and pseudorandom generators.  ...  I am indebted to Oded, Shafi, Madhu, Avi, Luca, and Omer for all the insights and research experiences they have shared with me.  ... 
doi:10.1561/0400000010 fatcat:2xv2ssm7lbhnjktg6l3u5o5kfu

Leftover Hash Lemma, Revisited [chapter]

Boaz Barak, Yevgeniy Dodis, Hugo Krawczyk, Olivier Pereira, Krzysztof Pietrzak, François-Xavier Standaert, Yu Yu
2011 Lecture Notes in Computer Science  
O(1), where u is the length of the source, and must grow with the number of extracted bits. * Microsoft Research New England.  ...  The famous Leftover Hash Lemma (LHL) states that (almost) universal hash functions are good randomness extractors.  ...  Acknowledgements: We would like to thank Russell Impagliazzo, Ronen Shaltiel and Daniel Wichs for useful discussions, and Gil Segev for pointing out the our construction in Section 4.3 also implies oblivious  ... 
doi:10.1007/978-3-642-22792-9_1 fatcat:2jrzqq3kvzaihidnv23tvze7de

Non-Malleable Coding Against Bit-wise and Split-State Tampering [article]

Mahdi Cheraghchi, Venkatesan Guruswami
2014 arXiv   pre-print
We show that construction of non-malleable codes for the split-state model reduces to construction of non-malleable two-source extractors.  ...  Dziembowski et al. show existence of non-malleable codes for any class of tampering functions of bounded size.  ...  and ordinary two-source extractors.  ... 
arXiv:1309.1151v2 fatcat:ulpnpz6sljbc5jrugxrtfvem2y

Rate one-third non-malleable codes

Divesh Aggarwal, Bhavana Kanukurthi, Sai Lakshmi Bhavana Obbattu, Maciej Obremski, Sruthi Sekar
2022 Symposium on the Theory of Computing  
This nearly matches the rate 1/2 lower bound for this model due to Cheraghchi and Guruswami (ITCS 2014).  ...  Our construction is simple, requiring just an inner-product extractor, a seeded extractor, and an affine-evasive function. CCS CONCEPTS • Theory of computation → Pseudorandomness and derandomization.  ...  The authors would also like to thank the anonymous referees for their valuable comments and helpful suggestions. The third author's work is supported by Microsoft Research Grant.  ... 
doi:10.1145/3519935.3519972 dblp:conf/stoc/AggarwalKOOS22 fatcat:2mnjyu7ywrfjtmrqwxmxsedtte

Non-malleable Coding Against Bit-Wise and Split-State Tampering

Mahdi Cheraghchi, Venkatesan Guruswami
2015 Journal of Cryptology  
In particular, Dziembowski et al. show that such codes exist and may achieve positive rates for any class of tampering functions of size at most 2 2 αn , for any constant α ∈ [0, 1).  ...  Non-malleable coding is possible against any class of adversaries of bounded size.  ...  and ordinary two-source extractors.  ... 
doi:10.1007/s00145-015-9219-z fatcat:ksl4mu35kffw7lvffmqqe6azr4
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