Secret-sharing schemes and orthogonal systems of k-ary operations

We suggest a general method of the construction of secret-sharing schemes based on orthogonal systems of partial (in particular, everywhere determined) k-ary operations which generalizes some known methods of the construction of such schemes by a nite elds and point the orthogonal systems of k-ary operations respecting to these known schemes. The di erent transformations of orthogonal systems of k-ary operations are reformulated and applied to orthogonal systems of polynomial k-ary operations over nite elds, in particular, to orthogonal systems corresponding to some known schemes.