Incompressiblity and Next-Block Pseudoentropy

Iftach Haitner; Noam Mazor; Jad Silbak

doi:10.4230/LIPIcs.ITCS.2023.66

Incompressiblity and Next-Block Pseudoentropy

Iftach Haitner, Noam Mazor, Jad Silbak

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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 language	English
Title of host publication	14th Innovations in Theoretical Computer Science Conference, ITCS 2023
Editors	Yael Tauman Kalai
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959772631
DOIs	https://doi.org/10.4230/LIPIcs.ITCS.2023.66
State	Published - 1 Jan 2023
Event	14th Innovations in Theoretical Computer Science Conference, ITCS 2023 - Cambridge, United States Duration: 10 Jan 2023 → 13 Jan 2023

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	251
ISSN (Print)	1868-8969

Conference

Conference	14th Innovations in Theoretical Computer Science Conference, ITCS 2023
Country/Territory	United States
City	Cambridge
Period	10/01/23 → 13/01/23

Funding

Funders	Funder number
Israel Science Foundation	666/19
Check Point Institute for Information Security, Tel Aviv University	1628/17

Keywords

incompressibility
next-block pseudoentropy
sparse languages

Access to Document

10.4230/LIPIcs.ITCS.2023.66

Cite this

Haitner, I., Mazor, N., & Silbak, J. (2023). Incompressiblity and Next-Block Pseudoentropy. In Y. T. Kalai (Ed.), 14th Innovations in Theoretical Computer Science Conference, ITCS 2023 Article 66 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 251). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ITCS.2023.66

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abstract = "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.",

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Haitner, I, Mazor, N & Silbak, J 2023, Incompressiblity and Next-Block Pseudoentropy. in YT Kalai (ed.), 14th Innovations in Theoretical Computer Science Conference, ITCS 2023., 66, Leibniz International Proceedings in Informatics, LIPIcs, vol. 251, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 14th Innovations in Theoretical Computer Science Conference, ITCS 2023, Cambridge, United States, 10/01/23. https://doi.org/10.4230/LIPIcs.ITCS.2023.66

Incompressiblity and Next-Block Pseudoentropy. / Haitner, Iftach; Mazor, Noam; Silbak, Jad.
14th Innovations in Theoretical Computer Science Conference, ITCS 2023. ed. / Yael Tauman Kalai. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2023. 66 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 251).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Haitner, Iftach

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N2 - 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.

AB - 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.

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Incompressiblity and Next-Block Pseudoentropy

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