Incompressiblity and Next-Block Pseudoentropy
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.
incompressibility
next-block pseudoentropy
sparse languages
Theory of computation~Computational complexity and cryptography
66:1-66:18
Regular Paper
Research supported by Israel Science Foundation grant 666/19.
https://eccc.weizmann.ac.il/report/2022/032/
We thank Geoffroy Couteau, Ronen Shaltiel and Ofer Shayevitz for many useful discussions.
Iftach
Haitner
Iftach Haitner
The Blavatnik School of Computer Science at Tel-Aviv University, Israel
Member of the Check Point Institute for Information Security.
Noam
Mazor
Noam Mazor
The Blavatnik School of Computer Science at Tel-Aviv University, Israel
Jad
Silbak
Jad Silbak
The Blavatnik School of Computer Science at Tel-Aviv University, Israel
Research supported by Israel Science Foundation grant 1628/17.
10.4230/LIPIcs.ITCS.2023.66
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https://eccc.weizmann.ac.il/report/2022/032/
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Iftach Haitner, Noam Mazor, and Jad Silbak
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