Incompressiblity and Next-Block Pseudoentropy

Authors Iftach Haitner, Noam Mazor, Jad Silbak

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Author Details

Iftach Haitner
  • The Blavatnik School of Computer Science at Tel-Aviv University, Israel
Noam Mazor
  • The Blavatnik School of Computer Science at Tel-Aviv University, Israel
Jad Silbak
  • The Blavatnik School of Computer Science at Tel-Aviv University, Israel


We thank Geoffroy Couteau, Ronen Shaltiel and Ofer Shayevitz for many useful discussions.

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Iftach Haitner, Noam Mazor, and Jad Silbak. Incompressiblity and Next-Block Pseudoentropy. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 66:1-66:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
  • incompressibility
  • next-block pseudoentropy
  • sparse languages


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