On explicit constructions for solving the problem "A secret sharing"

"A secret sharing" problem was suggested to the participants of the second round competition in cryptography NSUCRYPT0-2015. The problem is to construct a subset M С f^ satisfying the following conditions: 1) any u G M can be represented as u = x фy ф z, where x, y, z are different elements of M = f^ \ M; 2) x ф y ф z G M for all different x, y, z G M. The paper presents some approaches to solving this problem. In particular, for even n, an explicit construction of the required set M on the basis of a cubic parabola is proposed.

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