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Deterministic Extractors for Affine Sources over Large Fields
[chapter]

2010
*
Monographs in Theoretical Computer Science. An EATCS Series
*

We show how to (

doi:10.1007/978-3-642-14903-0_3
fatcat:vhndowpghrhq3inel3dquoif5u
*deterministically*) extract practically all the randomness from*affine**sources*,*for*any*field*of size larger than n c (where c is a*large*enough constant). ... An (n, k)-*affine**source**over*a finite*field*F is a random variable X = (X 1 , ..., X n ) ∈ F n , which is uniformly distributed*over*an (unknown) k-dimensional*affine*subspace of F n . ... Finally, a big big thanks to Asaf Nussboim*for*introducing the first author to Weil's theorems. ...##
###
Deterministic extractors for affine sources over large fields

2008
*
Combinatorica
*

We show how to (

doi:10.1007/s00493-008-2259-3
fatcat:dgm4unne35c4dbnyam53pad4cu
*deterministically*) extract practically all the randomness from*affine**sources*,*for*any*field*of size larger than n c (where c is a*large*enough constant). ... An (n, k)-*affine**source**over*a finite*field*F is a random variable X = (X 1 , ..., X n ) ∈ F n , which is uniformly distributed*over*an (unknown) k-dimensional*affine*subspace of F n . ... Finally, a big big thanks to Asaf Nussboim*for*introducing the first author to Weil's theorems. ...##
###
Deterministic Extractors for Affine Sources over Large Fields

*
46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)
*

We show how to (

doi:10.1109/sfcs.2005.31
dblp:conf/focs/GabizonR05
fatcat:ffqm5xlns5b67bum5iwb2jivie
*deterministically*) extract practically all the randomness from*affine**sources*,*for*any*field*of size larger than n c (where c is a*large*enough constant). ... An (n, k)-*affine**source**over*a finite*field*F is a random variable X = (X 1 , ..., X n ) ∈ F n , which is uniformly distributed*over*an (unknown) k-dimensional*affine*subspace of F n . ... Finally, a big big thanks to Asaf Nussboim*for*introducing the first author to Weil's theorems. ...##
###
An Introduction to Randomness Extractors
[chapter]

2011
*
Lecture Notes in Computer Science
*

Goal: Design

doi:10.1007/978-3-642-22012-8_2
fatcat:ldxe2dhplfdhvcdepfval6cxne
*extractors**for*"*large*" families of "interesting"*sources*. ... Existence of*deterministic**extractors*: Let m ≤ n be integers, let ϵ > 0 and let C be a class with at most 2 poly(n/ϵ) distributions*over*{0, 1} n . ...*Affine**sources*: Let F q be the finite*field*with q elements.*Affine**sources*are distributions that are uniform*over*some*affine*subspace of the vector space F n q . ...##
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Extractors and Rank Extractors for Polynomial Sources
[chapter]

2010
*
Monographs in Theoretical Computer Science. An EATCS Series
*

A direct consequence is a

doi:10.1007/978-3-642-14903-0_4
fatcat:vzv5tremgnhfhcahi7brcmmr7q
*deterministic**extractor**for*distributions sampled by polynomial size arithmetic circuits*over*exponentially*large**fields*. ... It also shows that a rank*extractor*is already a high quality condenser*for*polynomial*sources**over*polynomially*large**fields*. ... We thank Andrej Bogdanov and Gil Alon*for*helpful conversations. ...##
###
Extractors and Rank Extractors for Polynomial Sources

2007
*
Foundations of Computer Science (FOCS), IEEE Annual Symposium on
*

A direct consequence is a

doi:10.1109/focs.2007.4389479
fatcat:yqz4gbohmjcbzkzo3634tdwmua
*deterministic**extractor**for*distributions sampled by polynomial size arithmetic circuits*over*exponentially*large**fields*. ... It also shows that a rank*extractor*is already a high quality condenser*for*polynomial*sources**over*polynomially*large**fields*. ... We thank Andrej Bogdanov and Gil Alon*for*helpful conversations. ...##
###
Extractors and Rank Extractors for Polynomial Sources

2007
*
48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)
*

A direct consequence is a

doi:10.1109/focs.2007.9
dblp:conf/focs/EzraS07
fatcat:xofqsysjanb6xbgxsyegvetgca
*deterministic**extractor**for*distributions sampled by polynomial size arithmetic circuits*over*exponentially*large**fields*. ... It also shows that a rank*extractor*is already a high quality condenser*for*polynomial*sources**over*polynomially*large**fields*. ... We thank Andrej Bogdanov and Gil Alon*for*helpful conversations. ...##
###
Extractors And Rank Extractors For Polynomial Sources

2009
*
Computational Complexity
*

*deterministic*

*extractor*

*for*distributions sampled by polynomial size arithmetic circuits

*over*exponentially

*large*

*fields*. ... It also shows that a rank

*extractor*is already a high quality condenser

*for*polynomial

*sources*

*over*polynomially

*large*

*fields*. ... We thank Andrej Bogdanov and Gil Alon

*for*helpful conversations. ...

##
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Improved Extractors for Affine Lines
[article]

2013
*
arXiv
*
pre-print

We say that a function D:F^n0,1 is a 1 if

arXiv:1311.5622v2
fatcat:i24dtl7mrbbjjjw5ndzuvujfxe
*for*every*affine*line l⊆^n, D(X) is -close to uniform when X is uniformly distributed*over*l. ... Let F be the*field*of q elements. ... Acknowledgements I would like to thank Dana Moshkovitz and Ran Raz*for*helpful comments and discussions. ...##
###
Leakage-Resilient Secret Sharing in Non-Compartmentalized Models

2020
*
Conference on Information-Theoretic Cryptography
*

*For*

*affine*leakage functions, we obtain schemes with threshold access structure that are leakage-resilient as long as there is a substantial difference between the total amount of information obtained ... Specifically, we have a threshold scheme with parameters similar to Shamir's scheme and is leakage-resilient against

*affine*leakage. ...

*For*structured entropy

*source*,

*for*example, the

*source*is a flat distribution

*over*an

*affine*subspace of the universal space {0, 1} n , there exists a single function that turns any such

*source*distribution ...

##
###
Extractors for Low-Weight Affine Sources

2009
*
2009 24th Annual IEEE Conference on Computational Complexity
*

This gives new

doi:10.1109/ccc.2009.36
dblp:conf/coco/Rao09
fatcat:e6ml6i7uivdbhfln7fnsyushqq
*extractors**for*low entropy bit-fixing*sources*with exponentially small error, a parameter that is important*for*the application of these*extractors*to cryptography. ... We give polynomial time computable*extractors**for*low-weight affince*sources*. A distribution is*affine*if it samples a random points from some unknown low dimensional subspace of F n 2 . ...*sources**over*GF (2) (0.5 + α)n,*for*positive constant α 2 −Ω(n) Ω(n) [KZ]*Extractor**for**affine**sources**over*a*large**field*, |F| > n 20*Extractor**for*low-weight*affine**sources**over*GF (2) k > log c (n) ...##
###
Two-sources Randomness Extractors for Elliptic Curves
[article]

2014
*
arXiv
*
pre-print

This paper studies the task of two-

arXiv:1404.2226v2
fatcat:t5a5bi3hhrh6pkulzj6zu2qfne
*sources*randomness*extractors**for*elliptic curves defined*over*finite*fields*K, where K can be a prime or a binary*field*. ... In other words,*for*a ginven elliptic curve E defined*over*a finite*field*F_q and two random points P ∈P and Q∈Q, where P and Q are two subgroups of E(F_q), our function extracts the least significant ... Section 3 introduces our first contribution, ie. a new construction of a two-*source**deterministic*randomness*extractor**for*elliptic curves defined*over*prime*fields*. ...##
###
Simulating independence

2010
*
Journal of the ACM
*

We give the following new explicit constructions (namely, poly(n)-time computable functions) of

doi:10.1145/1734213.1734214
fatcat:odaxswxlvrbyjlusmoynqadyci
*deterministic**extractors*, dispersers and related objects. All work*for*any fixed rate δ > 0. ... A distribution X*over*binary strings of length n has minentropy k if every string has probability at most 2 −k in X. 1 We say that X is a δ-*source*if its rate k/n is at least δ. ... Temporary unrealistic assumption: We'll assume a*deterministic*1-*source**extractor*(called ext * )*for*any linear entropy*sources*. ...##
###
Simulating independence

2005
*
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing - STOC '05
*

We give the following new explicit constructions (namely, poly(n)-time computable functions) of

doi:10.1145/1060590.1060592
dblp:conf/stoc/BarakKSSW05
fatcat:6lziswiaf5fpbd33eydzexvtwi
*deterministic**extractors*, dispersers and related objects. All work*for*any fixed rate δ > 0. ... A distribution X*over*binary strings of length n has minentropy k if every string has probability at most 2 −k in X. 1 We say that X is a δ-*source*if its rate k/n is at least δ. ... Temporary unrealistic assumption: We'll assume a*deterministic*1-*source**extractor*(called ext * )*for*any linear entropy*sources*. ...##
###
How to get more mileage from randomness extractors

2008
*
Random structures & algorithms (Print)
*

A

doi:10.1002/rsa.20207
fatcat:ekydvlvjzfbuthkgi6kzvoqe6a
*deterministic*randomness*extractor**for*C is a function E : {0, 1} n → {0, 1} m such that*for*any X in C the distribution E(X) is statistically close to the uniform distribution. ... Using our transformation we give an explicit construction of a two-*source**extractor*E : {0, 1} n × {0, 1} n → {0, 1} m such that*for*every two independent distributions X 1 and X 2*over*{0, 1} n with min-entropy ... many discussions on various aspects of randomness*extractors*. ...
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