All or Nothing at All

  • Paolo D'Arco
  • Navid Nasr Esfahani
  • Douglas R. Stinson
Keywords: Block designs, Cyclotomy, All-or-nothing transform

Abstract

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 desiredĀ  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 onĀ  exhaustive searches and random constructions for small values of $s$.
Published
2016-10-05
Article Number
P4.10