… about the secret. We refer to schemes with such uniform access structures as uniform secret
sharing… We first derive a tight lower bound for share entropy and then present an optimal …

… Our main result is to determine the optimal information ratio of the uniform access functions.
… of linear secret sharing schemes with optimal information ratio for the rational uniform access …

… study secret-sharing schemes for uniform access structures. An access structure is k-uniform
if … By counting arguments, our construction is optimal (up to polynomial factors). Previously, …

… [31] provides an optimal solution since each party gets a share whose … share size (in bits)
of linear d-uniform secret sharing. This immediately implies a similar lower bound on the share …

… We start the analysis by sampling a partition Π with uniform distribution. We first focus on a
single block i, and denote by Yj,i the indicator random variable that is equal to 1 if and only if …

… is uniformly tight by designing a secret sharing scheme that achieves the optimal decoding
… We construct another secret sharing scheme that achieves the optimal decoding bandwidth …

… and then samples a uniformly random univariate polynomial of … is amended with t uniformly
random and independent elements … that is generally sought after for secret sharing schemes. …

… Let the secret be uniformly taken from S (we call S uniformly distributed). Then there exists a
… to papers in which perfect secret sharing schemes attaining the optimal information rate are …

… SO offers a better encoding complexity and latency than the one with optimal SO, as we will
se later in … and uniformly at random from Fq. Then the polynomial PjpXq is constructed as …

… Thus, our results imply the existence of linear secret-sharing schemes for uniform … k-uniform
access structure with n parties can be realized by a linear secret-sharing scheme with share …