Problems of almost threshold secret sharing schemes

The article deals with questions of information security, secret sharing schemes. The problem of structure access realization by elliptic curves is discussed. It is shown that one can realize secret sharing schemes with infinite set of participants, and the everywhere density of rational points is an analogue of perfectness. The problem of unreplacible participants is considered. It is proved that the binary almost threshold matroids without unreplacible participants are only matroids on Reed–Muller codes of first order.