Post on 23-Feb-2016
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Seeded Extractors
2π
2π
000111 10 2π
Seeded Extractor
2π
Strong SeededExtractor
2π00
0110
11
Seeded Extractors
2π
2π
000111
2π
Seeded Extractor
2π
000
101
100
111
β¦β¦ No limitation
Small-Bias Set
10
Non-Malleable Extractors [DodisWichs09]
Seeded Extractor Strong SeededExtractor
2π
2π
Non-MalleableExtractor
0
1
0
0
1
π΄ (π ) π
Proof Idea
π
π π΄ (π )
πΈπ₯π‘ (π ;π )πΈπ₯π‘ (π ; π΄ (π ) )
is typically biased (say towards 0).
Proof Idea
π
π π΄ (π )
πΈπ₯π‘ (π ;π )πΈπ₯π‘ (π ; π΄ (π ) )
is typically biased (say towards 0).
Proof Idea
π π΄ (π )
π π΄ (π )
ππππ (ππ )Acyclic
Many verticesAverage edge weight is large
Proof Idea
π π΄ (π )
π π΄ (π )
ππππ (ππ )Acyclic
Many verticesAverage edge weight is large
Proof Idea
β― π π β ππ΄ (π )β―
Small-Bias Set
[Raz05] implies that this is also an
extractorπ
stands in contradiction!
π π =E π₯π‘ (π ; π )βπΈπ₯π‘ (π ; π΄ (π ) )
? Construct a non-malleable extractor for smaller min-entropies, or prove this is hard.
? Waiting for applications to complexity (as apposed to cryptography).
Open Questions