Hadamard matrices, designs and their secret-sharing schemes

  • Authors:

  • Christos Koukouvinos;Dimitris E. Simos;Zlatko Varbanov

  • Affiliations:

  • Department of Mathematics, National Technical University of Athens, Athens, Greece;Department of Mathematics, National Technical University of Athens, Athens, Greece;Department of Information Technologies, University of Veliko Tarnovo, Bulgaria

  • Venue:
  • CAI'11 Proceedings of the 4th international conference on Algebraic informatics
  • Year:
  • 2011

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Abstract

In this paper, we give some methods to generate new secret-sharing schemes from Hadamard matrices derived through orthogonal 3-designs. A close connection of Hadamard designs and secret-sharing schemes is shown. In addition, we survey some of the most prolific construction methods for Hadamard matrices thus providing the necessary structures to describe a two-part secret-sharing scheme based on Hadamard designs. Furthermore, we exhibit how some algebraic aspects of secret-sharing cryptography are interpreted in terms of combinatorial design theory, such as the access structure and the security of the secret-sharing schemes.