0582343 20250317091637.620240205235959.9 85183938750 001173957400001 10.1016/j.disc.2024.113909 18 s. P cav_un_epca*02564980012-365X347Elsevier cryptography multipartite secret sharing entropy method linear secret sharing submodular optimization cav_un_auth*0398469 Csirmaz Laszlo UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR HU Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101161 Matúš František UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0462766 Padró C. ES http://library.utia.cas.cz/separaty/2024/MTR/csirmaz-0582343.pdf https://www.sciencedirect.com/science/article/pii/S0012365X24000402?via%3Dihub Bipartite secret sharing schemes have a bipartite access structure in which the set of participants is divided into two parts and all participants in the same part play an equivalent role. Such a bipartite scheme can be described by a staircase: the collection of its minimal points. The complexity of a scheme is the maximal share size relative to the secret size, and the kappa-complexity of an access structure is the best lower bound provided by the entropy method. An access structure is kappa-ideal if it has kappa-complexity 1. Motivated by the abundance of open problems in this area, the main results can be summarized as follows. First, a new characterization of kappa-ideal multipartite access structures is given which offers a straightforward and simple approach to describe ideal bipartite and tripartite access structures. Second, the kappa-complexity is determined for a range of bipartite access structures, including those determined by two points, staircases with equal widths and heights, and staircases with all heights 1. Third, matching linear schemes are presented for some non-ideal cases, including staircases where all heights are 1 and all widths are equal. Finally, finding the Shannon complexity of a bipartite access structure can be considered as a discrete submodular optimization problem. An interesting and intriguing continuous version is defined which might give further insight to the large-scale behavior of these optimization problems. WOS BA 10000 10100 10101 2025 3 RVO:67985556 https://hdl.handle.net/11104/0350584 S 113909 C MATHEMATICS 0.9 0.3 16.8 0.01052 0.619 9077 92 0.884 19.82 1.04 1247 Q1 0.700 424 Q2 67.6 0.72 Q2 67.6 2024 85183938750 SCOPUS PUBMED 001173957400001 WOS cav_un_epca*0256498 Discrete Mathematics Roč. 347 č. 5 2024 0012-365X 1872-681X Elsevier