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On White-Box Learning and Public-Key Encryption

Authors Yanyi Liu, Noam Mazor, Rafael Pass

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  • Theory of computation → Computational complexity and cryptography
Keywords
  • Public-Key Encryption
  • White-Box Learning

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Abstract

We consider a generalization of the Learning With Error problem, referred to as the white-box learning problem: You are given the code of a sampler that with high probability produces samples of the form y,f(y) + ε where ε is small, and f is computable in polynomial-size, and the computational task consist of outputting a polynomial-size circuit C that with probability, say, 1/3 over a new sample y' according to the same distributions, approximates f(y') (i.e., |C(y')-f(y')| is small). This problem can be thought of as a generalizing of the Learning with Error Problem (LWE) from linear functions f to polynomial-size computable functions.
We demonstrate that worst-case hardness of the white-box learning problem, conditioned on the instances satisfying a notion of computational shallowness (a concept from the study of Kolmogorov complexity) not only suffices to get public-key encryption, but is also necessary; as such, this yields the first problem whose worst-case hardness characterizes the existence of public-key encryption. Additionally, our results highlights to what extent LWE "overshoots" the task of public-key encryption.
We complement these results by noting that worst-case hardness of the same problem, but restricting the learner to only get black-box access to the sampler, characterizes one-way functions.

Cite As Get BibTex

Yanyi Liu, Noam Mazor, and Rafael Pass. On White-Box Learning and Public-Key Encryption. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 73:1-73:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.73

Author Details

Yanyi Liu
  • Cornell Tech, New York, NY, USA
Noam Mazor
  • Tel Aviv University, Israel
Rafael Pass
  • Cornell Tech, New York, NY, USA
  • Technion, Haifa, Israel
  • Tel Aviv University, Israel

Funding

  • Liu, Yanyi: Research partly supported by NSF CNS-2149305.
  • Mazor, Noam: Research partly supported by NSF CNS-2149305, AFOSR Award FA9550-23-1-0312 and AFOSR Award FA9550-23-1-0387 and ISF Award 2338/23.
  • Pass, Rafael: Supported in part by NSF Award CNS 2149305, AFOSR Award FA9550-23-1-0387, AFOSR Award FA9550-23-1-0312 and AFOSR Award FA9550-24-1-0267 and ISF Award 2338/23. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Government, or the AFOSR.

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