ON CONSTRUCTURES OF IDEAL PERFECT ALMOST-THRESHOLD SECRET SHARING SCHEMES
The article deals with issues related to information security, namely, of the secret sharing schemes and delegation rights of participants. The problem of implementing complex access structures is discuss, including the use of elliptic curves. As an ideal secret sharing scheme correspond to matroids, the study of access structure is presented as a dual version of the axiomatization of matroids with anticycles, i.e. zero-sets. By a geometric interpretation of these axioms is submitted with a number of designs of almost-threshold secret sharing schemes and their associated matroids. It is proved that an infinite series of realized matroids M on m-dimensional projective and affine space over GF(q) with the same power cycles. The cycles of the matroid defined as additions zero-sets. As the zero-sets are taken hyperspaces of M. Thus, an infinite class of almost-threshold ideal perfect secret sharing schemes and matroids is constructed, using combinatorial methods of finite geometries. The implementation of perfect ideal threshold secret sharing schemes are shown on an elliptic curve, on which third-degree polynomial is used to generate the check matrix of code over GF(q) as, a linear secret sharing schemes. An example of the implementation of this scheme with the help of elliptic curves over GF(3) is presented.