Abstract
In a t out of n threshold scheme, any subset of t or more participants can compute the secret key k, while subsets of t - 1 or less participants cannot compute k. Some schemes are designed for specific algebraic structures, for example finite fields.Whereas other schemes can be used with any finite abelian group. In [24], the definition of group independent sharing schemes was introduced. In this paper, we develop bounds for group independent t out of n threshold schemes. The bounds will be lower bounds which discuss how many subshares are required to achieve a group independent linear threshold scheme. In particular, we will show that our bounds for the n - 1 out of n threshold schemes are tight for infinitely many n.
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