Document Open Access Logo

Incompressiblity and Next-Block Pseudoentropy

Authors Iftach Haitner, Noam Mazor, Jad Silbak

PDF
Thumbnail PDF

File

LIPIcs.ITCS.2023.66.pdf
  • Filesize: 0.72 MB
  • 18 pages

Document Identifiers

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

Funding

Research supported by Israel Science Foundation grant 666/19.
  • Haitner, Iftach: Member of the Check Point Institute for Information Security.
  • Silbak, Jad: Research supported by Israel Science Foundation grant 1628/17.

Acknowledgements

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

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.ITCS.2023.66

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.

Subject Classification

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

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Boaz Barak, Ronen Shaltiel, and Avi Wigderson. Computational analogues of entropy. In Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques (APPROX), pages 200-215. Springer, 2003. Google Scholar
  2. Manuel Blum and Silvio Micali. How to generate cryptographically strong sequences of pseudo random bits. In Annual Symposium on Foundations of Computer Science (FOCS), pages 112-117, 1982. Google Scholar
  3. Robert M Fano. The transmission of information. Massachusetts Institute of Technology, Research Laboratory of Electronics, 1949. Google Scholar
  4. Andrew Goldberg and Michael Sipser. Compression and ranking. In Annual ACM Symposium on Theory of Computing (STOC), pages 440-448, 1985. Google Scholar
  5. Shafi Goldwasser and Silvio Micali. Probabilistic encryption. Journal of Computer and System Sciences, pages 270-299, 1984. Google Scholar
  6. Iftach Haitner, Thomas Holenstein, Omer Reingold, Salil P. Vadhan, and Hoeteck Wee. Inaccessible entropy II: IE functions and universal one-way hashing. Theory of Computing, 2020. Preliminary version in Eurocrypt '10. Google Scholar
  7. Iftach Haitner, Noam Mazor, and Jad Silbak. Incompressiblity and next-block pseudoentropy. Electronic Colloquium on Computational Complexity, TR22-032, 2022. URL: https://eccc.weizmann.ac.il/report/2022/032/.
  8. Iftach Haitner, Omer Reingold, and Salil Vadhan. Efficiency improvements in constructing pseudorandom generators from one-way functions. SIAM Journal on Computing, 42(3):1405-1430, 2013. Google Scholar
  9. Iftach Haitner, Omer Reingold, Salil Vadhan, and Hoeteck Wee. Inaccessible entropy i: Inaccessible entropy generators and statistically hiding commitments from one-way functions. Technical Report 2010.05586, arXiv, 2019. Preliminary version in STOC '09. Google Scholar
  10. Johan Hastad, Russell Impagliazzo, Leonid A. Levin, and Michael Luby. A pseudorandom generator from any one-way function. SIAM Journal on Computing, pages 1364-1396, 1999. Google Scholar
  11. Chun-Yuan Hsiao, Chi-Jen Lu, and Leonid Reyzin. Conditional computational entropy, or toward separating pseudoentropy from compressibility. In Annual International Conference on the Theory and Applications of Cryptographic Techniques (EUROCRYPT), pages 169-186, 2007. Google Scholar
  12. David A Huffman. A method for the construction of minimum-redundancy codes. Proceedings of the IRE, 40(9):1098-1101, 1952. Google Scholar
  13. Russell Impagliazzo. A personal view of average-case complexity. In Proceedings of the Tenth Annual Structure in Complexity Theory Conference, pages 134-147. IEEE Computer Society, 1995. Google Scholar
  14. Russell Impagliazzo and Michael Luby. One-way functions are essential for complexity based cryptography. In Annual Symposium on Foundations of Computer Science (FOCS), pages 230-235, 1989. Google Scholar
  15. Claude Shannon. Communication theory of secrecy systems. Bell System Technical Journal, pages 656-715, 1949. Google Scholar
  16. Claude Elwood Shannon. A mathematical theory of communication. The Bell system technical journal, 27(3):379-423, 1948. Google Scholar
  17. Wojciech Szpankowski and Sergio Verdú. Minimum expected length of fixed-to-variable lossless compression without prefix constraints. IEEE Transactions on Information Theory, 57(7):4017-4025, 2011. Google Scholar
  18. Luca Trevisan, Salil Vadhan, and David Zuckerman. Compression of samplable sources. Computational Complexity, 14(3):186-227, 2005. Google Scholar
  19. Salil Vadhan and Colin Jia Zheng. Characterizing pseudoentropy and simplifying pseudorandom generator constructions. In Annual ACM Symposium on Theory of Computing (STOC), pages 817-836, 2012. Google Scholar
  20. Hoeteck Wee. On pseudoentropy versus compressibility. In Annual IEEE Conference on Computational Complexity (COMPLEXITY), pages 29-41, 2004. Google Scholar
  21. Andrew C. Yao. Theory and applications of trapdoor functions. In Annual Symposium on Foundations of Computer Science (FOCS), pages 80-91, 1982. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact