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How to Use Nondeterminism in Cryptography

Authors Marshall Ball , Peter Crawford-Kahrl

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
  • Security and privacy → Cryptography
Keywords
  • limited nondeterminism
  • cryptography
  • computational complexity
  • hardness amplification
  • pseudorandom generators
  • hardcore bits

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Abstract

Nondeterministic reductions have yielded powerful results in the theory of computational complexity, yet are effectively useless in a cryptographic context. The reason for this is simple, a nondeterministic polynomial time adversary can trivially break almost any cryptographic primitive by simply guessing the "key." 
In order to use this powerful nondeterministic tool kit in the cryptographic context, we initiate the study of cryptography against adversaries with limited nondeterminism: polynomial time nondeterministic algorithms that are restricted to just a few bits of nondeterminism. We demonstrate that limited nondeterministic security is sufficient to prove two foundational results that have eluded our grasp for decades: dream hardness amplification, and extracting ω(log n) hardcore bits.

Cite As Get BibTex

Marshall Ball and Peter Crawford-Kahrl. How to Use Nondeterminism in Cryptography. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.15

Author Details

Marshall Ball
  • New York University, NY, USA
Peter Crawford-Kahrl
  • New York University, NY, USA

Funding

  • Ball, Marshall: This work was supported in part by the National Science Foundation CAREER Award #2443735. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors(s) and do not necessarily reflect the views of the National Science Foundation.

Acknowledgements

The first author would like to thank Benny Applebaum, Iftach Haitner, and Ronen Shaltiel for enlightening discussions on this topic.

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