non-malleable extractors
DESCRIPTION
Non-Malleable Extractors. Gil Cohen Weizmann Institute Joint work with Ran Raz and Gil Segev. Seeded Extractors. 0. 1. Seeded Extractor. Seeded Extractors. 11. 00. 10. 01. 01. 00. 10. 11. Seeded Extractor. Strong Seeded Extractor. Seeded Extractors. 11. 10. 101. 100. - PowerPoint PPT PresentationTRANSCRIPT
Seeded Extractors
2𝑛
2𝑑
000111
2𝑘
Seeded Extractor
2𝑑
000
101
100
111
…… No limitation
Small-Bias Set
10
Non-Malleable Extractors [DodisWichs09]
Seeded Extractor Strong SeededExtractor
2𝑑
2𝑘
Non-MalleableExtractor
0
1
0
0
1
𝐴 (𝑠 ) 𝑠
Proof Idea
⋯ 𝑍 𝑠⊕ 𝑍𝐴 (𝑠 )⋯
Small-Bias Set
[Raz05] implies that this is also an
extractor𝑊
stands in contradiction!
𝑌 𝑠=E 𝑥𝑡 (𝑊 ; 𝑠 )⊕𝐸𝑥𝑡 (𝑊 ; 𝐴 (𝑠) )
? 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