Geodesic
All or nothing at all
The electronic journal of combinatorics, Tome 23 (2016) no. 4

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Zbl arXiv
We continue a study of unconditionally secure all-or-nothing transforms (AONT) begun by Stinson (2001). 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 $s$.
DOI : 10.37236/6370
Classification : 05B05
Mots-clés : block designs, cyclotomy, all-or-nothing transform 
Paolo D'Arco; Navid Nasr Esfahani; Douglas R. Stinson. All or nothing at all. The electronic journal of combinatorics, Tome 23 (2016) no. 4. doi: 10.37236/6370
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     author = {Paolo D'Arco and Navid Nasr Esfahani and Douglas R. Stinson},
     title = {All or nothing at all},
     journal = {The electronic journal of combinatorics},
     year = {2016},
     volume = {23},
     number = {4},
     doi = {10.37236/6370},
     zbl = {1351.05036},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/6370/}
}
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