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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITC.2021.1
URN: urn:nbn:de:0030-drops-143208
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14320/
Policharla, Guru-Vamsi ;
Prabhakaran, Manoj ;
Raghunath, Rajeev ;
Vyas, Parjanya
Group Structure in Correlations and Its Applications in Cryptography
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 ?_{2ⁿ}, is isomorphic to a group correlation over ℤ_4^n.
BibTeX - Entry
@InProceedings{policharla_et_al:LIPIcs.ITC.2021.1,
author = {Policharla, Guru-Vamsi and Prabhakaran, Manoj and Raghunath, Rajeev and Vyas, Parjanya},
title = {{Group Structure in Correlations and Its Applications in Cryptography}},
booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
pages = {1:1--1:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-197-9},
ISSN = {1868-8969},
year = {2021},
volume = {199},
editor = {Tessaro, Stefano},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14320},
URN = {urn:nbn:de:0030-drops-143208},
doi = {10.4230/LIPIcs.ITC.2021.1},
annote = {Keywords: Group correlations, bi-affine correlations, secure computation}
}
Keywords: |
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Group correlations, bi-affine correlations, secure computation |
Collection: |
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2nd Conference on Information-Theoretic Cryptography (ITC 2021) |
Issue Date: |
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2021 |
Date of publication: |
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19.07.2021 |