{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:49Z","timestamp":1753893829125,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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\u00a0 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\u00a0 exhaustive searches and random constructions for small values of $s$.<\/jats:p>","DOI":"10.37236\/6370","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:12:29Z","timestamp":1578687149000},"source":"Crossref","is-referenced-by-count":6,"title":["All or Nothing at All"],"prefix":"10.37236","volume":"23","author":[{"given":"Paolo","family":"D'Arco","sequence":"first","affiliation":[]},{"given":"Navid Nasr","family":"Esfahani","sequence":"additional","affiliation":[]},{"given":"Douglas R.","family":"Stinson","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,10,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p10\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i4p10\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:11:47Z","timestamp":1579237907000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i4p10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,5]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/6370","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,10,5]]},"article-number":"P4.10"}}