Cryptology ePrint Archive: Report 2015/998

All or Nothing at All

Paolo D'Arco and 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 $s$.

Category / Keywords: foundations / combinatorial cryptography

Date: received 13 Oct 2015, last revised 14 Oct 2015

Contact author: dstinson at uwaterloo ca

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Version: 20151015:000735 (All versions of this report)

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