Paper 2015/998

All or Nothing at All

Paolo D'Arco, Navid Nasr Esfahani, and Douglas R. Stinson

Abstract

We continue a study of unconditionally secure all-or-nothing transforms (AONT) begun in \cite{St}. An AONT is a bijective mapping that constructs $s$ outputs from $s$ inputs. We consider the security of $t$ inputs, when $s-t$ outputs are known. Previous work concerned the case $t=1$; here we consider the problem for general $t$, focussing on the case $t=2$. We investigate constructions of binary matrices for which the desired properties hold with the maximum probability. Upper bounds on these probabilities are obtained via a quadratic programming approach, while lower bounds can be obtained from combinatorial constructions based on symmetric BIBDs and cyclotomy. We also report some results on exhaustive searches and random constructions for small values of $s$.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint.
Keywords
combinatorial cryptography
Contact author(s)
dstinson @ uwaterloo ca
History
2015-10-15: revised
2015-10-14: received
See all versions
Short URL
https://ia.cr/2015/998
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2015/998,
      author = {Paolo D'Arco and Navid Nasr Esfahani and Douglas R.  Stinson},
      title = {All or Nothing at All},
      howpublished = {Cryptology ePrint Archive, Paper 2015/998},
      year = {2015},
      note = {\url{https://eprint.iacr.org/2015/998}},
      url = {https://eprint.iacr.org/2015/998}
}
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