Generalised dual arcs and Veronesean surfaces, with applications to cryptography
 Author
 Andreas Klein (UGent) , Jeroen Schillewaert (UGent) and Leo Storme (UGent)
 Organization
 Abstract
 We start by defining generalised dual arcs, the motivation for defining them comes from cryptography, since they can serve as a tool to construct authentication codes and secret sharing schemes. We extend the characterisation of the tangent planes of the Veronesean surface V2(4) in PG(5,q), q odd, described in [J.W.P. Hirschfeld, J.A. Thas, General Galois Geometries, Oxford Math. Monogr., Clarendon Press/Oxford Univ. Press, New York, 1991], as a set of q(2) + q + 1 planes in PG(5, q), such that every two intersect in a point and every three are skew. We show that a set of q 2 + q planes generating PG(5, q), q odd, and satisfying the above properties can be extended to a set of q2 + q + I planes still satisfying all conditions. This result is a natural generalisation of the fact that a qarc in PG(2, q), q odd, can always be extended to a (q + 1)arc. This extension result is then used to study a regular generalised dual arc with parameters (9, 5, 2, 0) in PG(9, q), q odd, where we obtain an algebraic characterisation of such an object as being the image of a cubic Veronesean.
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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU592357
 MLA
 Klein, Andreas, Jeroen Schillewaert, and Leo Storme. “Generalised Dual Arcs and Veronesean Surfaces, with Applications to Cryptography.” Journal of combinatorial theory, series A 116.3 (2009): 684–698. Print.
 APA
 Klein, A., Schillewaert, J., & Storme, L. (2009). Generalised dual arcs and Veronesean surfaces, with applications to cryptography. Journal of combinatorial theory, series A, 116(3), 684–698.
 Chicago authordate
 Klein, Andreas, Jeroen Schillewaert, and Leo Storme. 2009. “Generalised Dual Arcs and Veronesean Surfaces, with Applications to Cryptography.” Journal of Combinatorial Theory, Series A 116 (3): 684–698.
 Chicago authordate (all authors)
 Klein, Andreas, Jeroen Schillewaert, and Leo Storme. 2009. “Generalised Dual Arcs and Veronesean Surfaces, with Applications to Cryptography.” Journal of Combinatorial Theory, Series A 116 (3): 684–698.
 Vancouver
 1.Klein A, Schillewaert J, Storme L. Generalised dual arcs and Veronesean surfaces, with applications to cryptography. Journal of combinatorial theory, series A. 2009;116(3):684–98.
 IEEE
 [1]A. Klein, J. Schillewaert, and L. Storme, “Generalised dual arcs and Veronesean surfaces, with applications to cryptography,” Journal of combinatorial theory, series A, vol. 116, no. 3, pp. 684–698, 2009.
@article{592357, abstract = {We start by defining generalised dual arcs, the motivation for defining them comes from cryptography, since they can serve as a tool to construct authentication codes and secret sharing schemes. We extend the characterisation of the tangent planes of the Veronesean surface V2(4) in PG(5,q), q odd, described in [J.W.P. Hirschfeld, J.A. Thas, General Galois Geometries, Oxford Math. Monogr., Clarendon Press/Oxford Univ. Press, New York, 1991], as a set of q(2) + q + 1 planes in PG(5, q), such that every two intersect in a point and every three are skew. We show that a set of q 2 + q planes generating PG(5, q), q odd, and satisfying the above properties can be extended to a set of q2 + q + I planes still satisfying all conditions. This result is a natural generalisation of the fact that a qarc in PG(2, q), q odd, can always be extended to a (q + 1)arc. This extension result is then used to study a regular generalised dual arc with parameters (9, 5, 2, 0) in PG(9, q), q odd, where we obtain an algebraic characterisation of such an object as being the image of a cubic Veronesean.}, author = {Klein, Andreas and Schillewaert, Jeroen and Storme, Leo}, issn = {00973165}, journal = {Journal of combinatorial theory, series A}, language = {eng}, number = {3}, pages = {684698}, title = {Generalised dual arcs and Veronesean surfaces, with applications to cryptography}, url = {http://dx.doi.org/10.1016/j.jcta.2008.11.001}, volume = {116}, year = {2009}, }
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