eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-02-01
66:1
66:18
10.4230/LIPIcs.ITCS.2023.66
article
Incompressiblity and Next-Block Pseudoentropy
Haitner, Iftach
1
Mazor, Noam
1
Silbak, Jad
1
The Blavatnik School of Computer Science at Tel-Aviv University, Israel
A distribution is k-incompressible, Yao [FOCS '82], if no efficient compression scheme compresses it to less than k bits. While being a natural measure, its relation to other computational analogs of entropy such as pseudoentropy, Hastad, Impagliazzo, Levin, and Luby [SICOMP '99], and to other cryptographic hardness assumptions, was unclear.
We advance towards a better understating of this notion, showing that a k-incompressible distribution has (k-2) bits of next-block pseudoentropy, a refinement of pseudoentropy introduced by Haitner, Reingold, and Vadhan [SICOMP '13]. We deduce that a samplable distribution X that is (H(X)+2)-incompressible, implies the existence of one-way functions.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol251-itcs2023/LIPIcs.ITCS.2023.66/LIPIcs.ITCS.2023.66.pdf
incompressibility
next-block pseudoentropy
sparse languages