Algorithms for multi-secret hierarchical sharing schemes of shamir type

In this paper there are presented algorithms for multilevel hierarchical threshold secret sharing schemes based on the interpolation of Hermite type, which use either traditional Shamir’s keys or polynomial and orthogonal polynomial keys. These algorithms enable to compute the probability of authenticity of shares during the process of recovering the keys. In addition, two models of secret sharing are considered, which enlarge their security against attacks and decrease their rate of computations by applying FFT-algorithm.