Paper 2021/637

Doubly-Affine Extractors, and their Applications

Yevgeniy Dodis and Kevin Yeo

Abstract

In this work we challenge the common misconception that information-theoretic (IT) privacy is too impractical to be used in the real-world: we propose to build simple and $\textit{reusable}$ IT-encryption solutions whose only efficiency penalty (compared to computationally-secure schemes) comes from a large secret key size, which is often a rather minor inconvenience, as storage is cheap. In particular, our solutions are $\textit{stateless}$ and $\textit{locally computable at the optimal rate}$, meaning that honest parties do not maintain state and read only (optimally) small portions of their large keys with every use. Moreover, we also propose a novel architecture for outsourcing the storage of these long keys to a network of semi-trusted servers, trading the need to store large secrets with the assumption that it is hard to simultaneously compromise too many publicly accessible ad-hoc servers. Our architecture supports $\textit{everlasting privacy}$ and $\textit{post-application security}$ of the derived one-time keys, resolving two major limitations of a related model for outsourcing key storage, called bounded storage model. Both of these results come from nearly optimal constructions of so called $\textit{doubly-affine extractors}$: locally-computable, seeded extractors $\textbf{Ext}$(X,S) which are linear functions of X (for any fixed seed S), and protect against bounded affine leakage on X. This holds unconditionally, even if (a) affine leakage may $\textit{adaptively depend}$ on the extracted key R = $\textbf{Ext}$(X, S); and (b) the seed S is only $\textit{computationally}$ secure. Neither of properties are possible with general-leakage extractors.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. MAJOR revision.ITC 2021
Keywords
extractorsinformation-theoretic privacyeverlasting privacy
Contact author(s)
dodis @ cs nyu edu
kwlyeo @ google com
History
2021-05-17: received
Short URL
https://ia.cr/2021/637
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2021/637,
      author = {Yevgeniy Dodis and Kevin Yeo},
      title = {Doubly-Affine Extractors, and their Applications},
      howpublished = {Cryptology ePrint Archive, Paper 2021/637},
      year = {2021},
      note = {\url{https://eprint.iacr.org/2021/637}},
      url = {https://eprint.iacr.org/2021/637}
}
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