Orthogonal arrays and ordered threshold schemes

E. Dawson Infonnation Security Research Centre Queensland University of Technology GPO Box 2434 Brisbane Queensland 400 1 Australia E.S.~ahmocKlian Department of ~athematical Sciences Sharif University of Technology PO Box 11365 9415 Tehran Iran Alan Rahilly Centre for Combinatorics Department of ~athematics University of Queensland Brisbane Queensland 4072 Australia Perfect threshold schemes whose blocks are ordered are introduced. For a given number of shadows v, participants wand threshold t, let ~(t, w, v) be the maximum number of keys possible for an ordered perfect threshold scheme. We show that ~(t, w, v) = v if and only if there exists an orthogonal array (vt , w + 1, v, t). The implementability of perfect ordered threshold schemes is considered. In certain cases they are implementable without problems of storage or undue difficulties in decoding. Australasian Journal of Combinatorics !!( 1993 L pp. 27-44