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Code Offset in the Exponent

Authors Luke Demarest , Benjamin Fuller , Alexander Russell

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Author Details

Luke Demarest
  • University of Connecticut, Storrs, CT, USA
Benjamin Fuller
  • University of Connecticut, Storrs, CT, USA
Alexander Russell
  • University of Connecticut, Storrs, CT, USA

Funding

  • Demarest, Luke: Funded in part by NSF Grants No. 1849904 and 1547399.
  • Fuller, Benjamin: Funded in part by NSF Grants No. 1849904 and 1547399. This research is based upon work supported in part by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via Contract No. 2019-19020700008. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.
  • Russell, Alexander: This material is based upon work supported by the National Science Foundation under Grant No. 1801487.

Acknowledgements

The authors give special thanks to reviewer comments and feedback. The authors thank James Bartusek, Ryann Cartor, Fermi Ma, and Mark Zhandry and their helpful discussions of their work.

Cite As Get BibTex

Luke Demarest, Benjamin Fuller, and Alexander Russell. Code Offset in the Exponent. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 15:1-15:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ITC.2021.15

Abstract

Fuzzy extractors derive stable keys from noisy sources. They are a fundamental tool for key derivation from biometric sources. This work introduces a new construction, code offset in the exponent. This construction is the first reusable fuzzy extractor that simultaneously supports structured, low entropy distributions with correlated symbols and confidence information. These properties are specifically motivated by the most pertinent applications - key derivation from biometrics and physical unclonable functions - which typically demonstrate low entropy with additional statistical correlations and benefit from extractors that can leverage confidence information for efficiency.
Code offset in the exponent is a group encoding of the code offset construction (Juels and Wattenberg, CCS 1999). A random codeword of a linear error-correcting code is used as a one-time pad for a sampled value from the noisy source. Rather than encoding this directly, code offset in the exponent encodes by exponentiation of a generator in a cryptographically strong group. We introduce and characterize a condition on noisy sources that directly translates to security of our construction in the generic group model. Our condition requires the inner product between the source distribution and all vectors in the null space of the code to be unpredictable.

Subject Classification

ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
  • Security and privacy → Biometrics
Keywords
  • fuzzy extractors
  • code offset
  • learning with errors
  • error-correction
  • generic group model

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