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Paper: Secure Sketch for Multi-Sets

Authors:
Ee-Chien Chang
Vadym Fedyukovych
Qiming Li
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URL: http://eprint.iacr.org/2006/090
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Abstract: Given the original set $X$ where $|X|=s$, a sketch $P$ is computed from $X$ and made public. From another set $Y$ where $|Y| = s$ and $P$, we can reconstruct $X$ if $|X\cap Y|\ge |s-t|$, where $t<s$ is some threshold. The sketch $P$ is secure if it does not reveal much information about $X$. A few constructions have been proposed, but they cannot handle multi-sets, that is, sets that may contain duplicate elements. We observe that the techniques in the set reconciliation protocol proposed by Minsky et al. (ISIT 2001) can be applied and give a secure sketch that supports multi-sets. If $X$ is a subset of an universe with $n$ elements, the running time of the encoding and decoding algorithms will be polynomial w.r.t. $s$ and $\log n$, and the entropy loss due to the sketch is less than $2t(1+\log n)$.
BibTeX
@misc{eprint-2006-21583,
  title={Secure Sketch for Multi-Sets},
  booktitle={IACR Eprint archive},
  keywords={Secure sketch, set difference, multi-set, error-tolerant cryptography},
  url={http://eprint.iacr.org/2006/090},
  note={ liqiming@gmail.com 13222 received 8 Mar 2006, last revised 15 Mar 2006},
  author={Ee-Chien Chang and Vadym Fedyukovych and Qiming Li},
  year=2006
}