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DOI: 10.4230/LIPIcs.FSTTCS.2018.41
URN: urn:nbn:de:0030-drops-99400
URL: http://drops.dagstuhl.de/opus/volltexte/2018/9940/
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Bauer, Balthazar ; Vihrovs, Jevgenijs ; Wee, Hoeteck

On the Inner Product Predicate and a Generalization of Matching Vector Families

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Abstract

Motivated by cryptographic applications such as predicate encryption, we consider the problem of representing an arbitrary predicate as the inner product predicate on two vectors. Concretely, fix a Boolean function P and some modulus q. We are interested in encoding x to x_vector and y to y_vector so that P(x,y) = 1 <=> <x_vector,y_vector> = 0 mod q, where the vectors should be as short as possible. This problem can also be viewed as a generalization of matching vector families, which corresponds to the equality predicate. Matching vector families have been used in the constructions of Ramsey graphs, private information retrieval (PIR) protocols, and more recently, secret sharing. Our main result is a simple lower bound that allows us to show that known encodings for many predicates considered in the cryptographic literature such as greater than and threshold are essentially optimal for prime modulus q. Using this approach, we also prove lower bounds on encodings for composite q, and then show tight upper bounds for such predicates as greater than, index and disjointness.

BibTeX - Entry

@InProceedings{bauer_et_al:LIPIcs:2018:9940,
  author =	{Balthazar Bauer and Jevgenijs Vihrovs and Hoeteck Wee},
  title =	{{On the Inner Product Predicate and a Generalization of Matching Vector Families}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software  Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{41:1--41:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Sumit Ganguly and Paritosh Pandya},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9940},
  URN =		{urn:nbn:de:0030-drops-99400},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.41},
  annote =	{Keywords: Predicate Encryption, Inner Product Encoding, Matching Vector Families}
}

Keywords: Predicate Encryption, Inner Product Encoding, Matching Vector Families
Seminar: 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)
Issue Date: 2018
Date of publication: 23.11.2018


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