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  • 1
    Electronic Resource
    Electronic Resource
    Mutually Trusted Authority-Free Secret Sharing Schemes (1997)
    Springer
    Journal of cryptology 10 (1997), S. 261-289 
    Details
    ISSN: 1432-1378
    Keywords: Key words. Secret sharing schemes.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract. Traditional secret sharing schemes involve the use of a mutually trusted authority to assist in the generation and distribution of shares that will allow a secret to be protected among a set of participants. In contrast, this paper addresses the problem of establishing secret sharing schemes for a given access structure without the use of a mutually trusted authority. A general protocol is discussed and several implementations of this protocol are presented. Several efficiency measures are proposed and we consider how to refine the general protocol in order to improve the efficiency with respect to each of the proposed measures. Special attention is given to mutually trusted authority-free threshold schemes. Constructions are presented for such threshold schemes that are shown to be optimal with respect to each of the proposed efficiency measures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001459900031
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  • 2
    Electronic Resource
    Electronic Resource
    Ideal secret sharing schemes with multiple secrets (1996)
    Springer
    Journal of cryptology 9 (1996), S. 233-250 
    Details
    ISSN: 1432-1378
    Keywords: Ideal secret sharing schemes ; Multiple secrets ; Matroids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider secret sharing schemes which, through an initial issuing of shares to a group of participants, permit a number of different secrets to be protected. Each secret is associated with a (potentially different) access structure and a particular secret can be reconstructed by any group of participants from its associated access structure without the need for further broadcast information. We consider ideal secret sharing schemes in this more general environment. In particular, we classify the collections of access structures that can be combined in such an ideal secret sharing scheme and we provide a general method of construction for such schemes. We also explore the extent to which the results that connect ideal secret sharing schemes to matroids can be appropriately generalized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00189262
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  • 3
    Electronic Resource
    Electronic Resource
    A new hyperoval inPG(2, 32) (1992)
    Springer
    Journal of geometry 44 (1992), S. 117-139 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new hyperoval is constructed in the Desarguesian projective planePG(2, 32). It has a full collineation stabiliser of order 3. It is also shown, with the aid of a computer, that the collineation stabiliser of any further new hyperoval is either trivial or has order 2 with the generator fixing no point on the hyperoval.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01228288
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  • 4
    Electronic Resource
    Electronic Resource
    Unitals and inversive planes (1997)
    Springer
    Journal of geometry 58 (1997), S. 43-52 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show that if U is a Buekenhout-Metz unital (with respect to a point P) in any translation plane of order q 2 with kernel containing GF(q), then U has an associated 2-(q2,q+1,q) design which is the point-residual of an inversive plane, generalizing results of Wilbrink, Baker and Ebert. Further, our proof gives a natural, geometric isomorphism between the resulting inversive plane and the (egglike) inversive plane arising from the ovoid involved in the construction of the Buekenhout-Metz unital. We apply our results to investigate some parallel classes and partitions of the set of blocks of any Buekenhout-Metz unital.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01222925
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  • 5
    Electronic Resource
    Electronic Resource
    Ovoids ofPG(3, 16) are elliptic quadrics (1990)
    Springer
    Journal of geometry 38 (1990), S. 95-106 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is proved, with the aid of a computer, that in PG(3,16) the only ovoids are the elliptic quadrics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01222898
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  • 6
    Electronic Resource
    Electronic Resource
    Unitals which meet Baer subplanes in 1 moduloq points (2000)
    Springer
    Journal of geometry 68 (2000), S. 16-22 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove that a parabolic unitalU in a translation plane π of orderq 2 with kernel containing GF(q) is a Buekenhout-Metz unital if and only if certain Baer subplanes containing the translation line of π meetU in 1 moduloq points. As a corollary we show that a unital 16-03 in PG(2,q 2) is classical if and only if it meets each Baer subplane of PG(2,q 2) in 1 moduloq points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01221057
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  • 7
    Electronic Resource
    Electronic Resource
    Projective spread sets (1990)
    Springer
    Journal of geometry 37 (1990), S. 55-76 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper the notion of a spread set for at-spread ofPG(2t+1,q) is generalised and it is shown that certaint-spreads ofPG(n, q) correspond to these generalised spread sets. Then a projective spread set is defined and it is shown that anyt-spread ofPG(n, q) corresponds to a projective spread set. Connections between the spread set and the projective spread set of at-spread are discussed, in particular in the case of at-spread ofPG(2t + 1,q) the spread set and the projective spread set are equivalent, giving a new and straightforward construction of a spread set. The methods developed are used to show, with the aid of a computer, that the 1-packing ofPG(7,2) constructed by Baker is regulus-free.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230359
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  • 8
    Electronic Resource
    Electronic Resource
    Ovoids ofPG(3, 16) are elliptic quadrics, II (1992)
    Springer
    Journal of geometry 44 (1992), S. 140-159 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In a previous paper [8] the authors have shown that every ovoid ofPG(3, 16) is an elliptic quadric. The arguments used a computer and also depended on the computer-aided classification of hyperovals ofPG(2, 16) (see [3]). Recently (see [9]) the classification of hyperovals ofPG(2,16) has been obtained without the use of a computer. The present paper completes a computer-free proof that every ovoid ofPG(3,16) is an elliptic quadric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01228289
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  • 9
    Electronic Resource
    Electronic Resource
    Classification of ovoids inPG(3, 32) (1994)
    Springer
    Journal of geometry 50 (1994), S. 143-150 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A classification of the ovoids inPG(3, 32) is completed with the aid of a computer. The ovoids are examined in terms of which ovals can possibly appear as secant plane sections. A weak necessary condition for two ovals to appear together as plane sections of an ovoid surprisingly turns out to be sufficient to demonstrate that the only possible secant plane sections are translation ovals. A known result regarding ovoids with such plane sections then identifies the ovoids as either elliptic quadrics or Tits ovoids.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01222671
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  • 10
    Electronic Resource
    Electronic Resource
    Arcs fixed byA 5 andA 6 (1996)
    Springer
    Journal of geometry 55 (1996), S. 123-138 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The complete list of thek-arcsK inPG(n, q) fixed by a projective group isomorphic toA 5 orA 6, which acts primitively on the points ofK, is presented. This leads to new classes of 10-arcs inPG(n, q), 3 ≤n ≤5. Our results also show that the non-classical 10-arc inPG(4, 9), discovered by D.G. Glynn [3], belongs to an infinite class of 10-arcs inPG(4, 3h),h ≥2, fixed by a projective group isomorphic toA 6.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01223038
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