  Various notions of non-malleable secret sharing schemes have been considered.
In this paper, we review the existing work on non-malleable secret sharing and
suggest a novel game-based definition. We provide a new construction of an
unconditionally secure non-malleable threshold scheme with respect to a
specified relation. To do so, we introduce a new type of algebraic manipulation
detection (AMD) code and construct examples of new variations of external
difference families, which are of independent combinatorial interest.
