Incompressiblity and Next-Block Pseudoentropy

Iftach Haitner, Noam Mazor, Jad Silbak

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publication14th Innovations in Theoretical Computer Science Conference, ITCS 2023
EditorsYael Tauman Kalai
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772631
StatePublished - 1 Jan 2023
Event14th Innovations in Theoretical Computer Science Conference, ITCS 2023 - Cambridge, United States
Duration: 10 Jan 202313 Jan 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference14th Innovations in Theoretical Computer Science Conference, ITCS 2023
Country/TerritoryUnited States


  • incompressibility
  • next-block pseudoentropy
  • sparse languages


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