Gil Cohen Weizmann Institute Joint work with Ran Raz and Gil Segev Seeded Extractors 1 0 Seeded Extractor Seeded Extractors 00 01 11 10 Seeded Extractor ID: 278669
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Slide1
Non-Malleable Extractors
Gil CohenWeizmann InstituteJoint work withRan Raz and Gil SegevSlide2
Seeded Extractors
1
0
Seeded ExtractorSlide3
Seeded Extractors
00
01
11
10
Seeded Extractor
Strong Seeded
Extractor
00
01
10
11Slide4
Seeded Extractors
00
01
11
Seeded Extractor
000
101
100
111
…
…
No limitation
Small-Bias Set
10Slide5
Non-Malleable Extractors [DodisWichs09]
Seeded Extractor
Strong Seeded
Extractor
Non-Malleable
Extractor
0
1
0
0
1
Slide6
The Explicit Construction of [DodisLiWooleyZuckerman11]
Conditional efficiency
Slide7
The Explicit Construction of [DodisLiWooleyZuckerman11]
Conditional
efficiency
Slide8
The Explicit Construction of [DodisLiWooleyZuckerman11]
Conditional
efficiency
Slide9
The Explicit Construction of [DodisLiWooleyZuckerman11]
Conditional
efficiency
Slide10
Main Result
Unconditionally
efficient
Slide11
Main Result
Unconditionally
efficient
Slide12
Main Result
Unconditionally
efficient
Slide13
Main Result
Unconditionally
efficient
Slide14
Explicit Constructions [Li12]
Moreover,
Bourgain’s
extractor is non-malleable.Slide15
The ConstructionSlide16
Raz’s Theorem
[Raz05]
is aSlide17
Proof SketchSlide18
Proof Idea
Slide19
Proof Idea
is typically biased (say towards 0).
Slide20
Proof Idea
is typically biased (say towards 0
).
Slide21
Proof Idea
Slide22
Proof Idea
Acyclic
Many vertices
Average edge weight is largeSlide23
Proof Idea
is typically biased
Acyclic
Many vertices
Average edge weight is largeSlide24
Proof Idea
Small-Bias Set
[Raz05]
implies that this is also an extractor
stands in contradiction!
Slide25
Open QuestionsSlide26
?
Construct a non-malleable extractor for smaller
min-entropies, or prove this is hard.
? Waiting for applications to complexity (as apposed to cryptography).
Open QuestionsSlide27
Thank You!