A General Formula of the (t, n)-Threshold Visual Secret Sharing Scheme

  • Authors:
  • Hiroki Koga

  • Affiliations:
  • -

  • Venue:
  • ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
  • Year:
  • 2002

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Abstract

This paper provides a new method for construction of the generating (or basis) matrices of the (t, n)-threshold visual secret sharing scheme ((t, n)-VSSS) for any n 驴 2 and 2 驴 t 驴 n. We show that there exists a bijection between a set of generating matrices of the (t, n)- VSSS and a set of homogeneous polynomials of degree n satisfying a certain property. We also show that the set of homogeneous polynomials is identified with a set of lattice points in a linear space of dimension n - t + 1 with explicitly expressed bases. These results yields a general formula of the generating matrices of the (t, n)-VSSS. The formula is not only theoretically of interest but also enables us to obtain efficient generating matrices that have been unknown.