10 problems

Let $M$ be an $n\times m$ $t$-disjunct matrix with constant column weight $b$. Set … and assume that $p$ is an integer. A Steiner system $\mathfrak{S}(n,b,p)$ is a family of $b$-su…

A locally leakage-resilient linear threshold secret sharing scheme has reconstruction threshold $t$ among its parameters. Bounded-threshold conjecture. There exist locally leakage-…

Let $C$ be an MDS code over a prime field $\mathbb{F}_p$, and let the Massey scheme be the secret-sharing scheme defined by $C$. A scheme is one-bit local leakage resilient if it r…

Let $n$ be the number of players, let $\alpha>0$ be a constant, and consider Shamir's secret sharing scheme with threshold $k=\alpha n$. A scheme is 1-bit local leakage resilient i…

Let $n\geq 3$ shares be generated from an input, using the sparse polynomial secret-sharing construction described above. For $n=2$, the total leakage is minimized when all shares…

Let $\mathcal A$ be an access structure. It is ideal if it can be realized by an ideal entropic polymatroid, equivalently by an ideal distribution scheme. Let $\mathcal A^\bot$ den…

Let $P$ be a participant set, let $\mathcal A\subset 2^P$ be an access structure, and let $\mathcal A^\bot$ denote its dual access structure. Let $\sigma(\mathcal A)$ denote the en…

Secret-sharing intuition conjecture. The intuitive assignment of values to the shared-information nodes in the partial information lattice for perfect secret sharing schemes should…

Let a graph-based secret-sharing scheme assign shares to the vertices of a graph, and let its complexity (or information ratio) be the maximal amount of information that the vertic…

Let $L^d_k$ be the finite lattice cube with exactly $k$ vertices along each of its $d$ dimensions, and consider perfect secret sharing schemes for its access structure. The average…