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Numerical models of hierarchical threshold secret sharing and broadcasting with encryption

Kapusta J., Smarzewski R.

Journal of Applied Computer Science

2018

Vol. 26, nr 2

57--72

In the paper there are presented two new models of encrypted hierarchical secret sharing schemes based on barycentric Hermite formula. Moreover an application of the second scheme to design a novel broadcast encryption protocol is proposed. The protocol allows to send a decoding key to any user via broadcast channel and revoke some users without the necessity of updating encrypted private keys of the other users of the system. To ensure the safety of user private keys the protocol uses one-way functions that fulfill special conditions.

Fast multidimensional Bernstein-Lagrange algorithms

Kapusta J., Smarzewski R.

Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

2012

Vol. 12, no. 2

7--18

In this paper we present two fast algorithms for the Bézier curves and surfaces of an arbitrary dimension. The first algorithm evaluates the Bernstein-Bézier curves and surfaces at a set of specific points by using the fast Bernstein-Lagrange transformation. The second algorithm is an inversion of the first one. Both algorithms reduce the initial problem to computation of some discrete Fourier transformations in the case of geometrical subdivisions of the d-dimensional cube. Their orders of computational complexity are proportional to those of corresponding d-dimensional FFT-algorithm, i.e. to O (N logN) + O (dN), where N denotes the order of the Bernstein-Bézier curves.