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Group Structure in Correlations and Its Applications in Cryptography

Authors Guru-Vamsi Policharla, Manoj Prabhakaran, Rajeev Raghunath, Parjanya Vyas

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Author Details

Guru-Vamsi Policharla
  • Indian Institute of Technology, Bombay, Mumbai, India
Manoj Prabhakaran
  • Indian Institute of Technology, Bombay, Mumbai, India
Rajeev Raghunath
  • Indian Institute of Technology, Bombay, Mumbai, India
Parjanya Vyas
  • Indian Institute of Technology, Bombay, Mumbai, India

Funding

  • Prabhakaran, Manoj: Manoj Prabhakaran was supported by the Joint Indo-Israel Project DST/INT/ISR/P-16/2017 and a Ramanujan Fellowship by the Dept. of Science and Technology, India.

Acknowledgements

We thank Yuval Ishai and various anonymous reviewers for helpful comments and pointers.

Cite AsGet BibTex

Guru-Vamsi Policharla, Manoj Prabhakaran, Rajeev Raghunath, and Parjanya Vyas. Group Structure in Correlations and Its Applications in Cryptography. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 1:1-1:23, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ITC.2021.1

Abstract

Correlated random variables are a key tool in cryptographic applications like secure multi-party computation. We investigate the power of a class of correlations that we term group correlations: A group correlation is a uniform distribution over pairs (x,y) ∈ G² such that x+y ∈ S, where G is a (possibly non-abelian) group and S is a subset of G. We also introduce bi-affine correlation{s}, and show how they relate to group correlations. We present several structural results, new protocols and applications of these correlations. The new applications include a completeness result for black box group computation, perfectly secure protocols for evaluating a broad class of black box "mixed-groups" circuits with bi-affine homomorphisms, and new information-theoretic results. Finally, we uncover a striking structure underlying OLE: In particular, we show that OLE over 𝔽_{2ⁿ}, is isomorphic to a group correlation over ℤ_4^n.

Subject Classification

ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
Keywords
  • Group correlations
  • bi-affine correlations
  • secure computation

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