Abstract
In this paper, information rates of perfect secret sharing schemes are studied, in particular schemes based on connected graphs on six vertices. We discuss a method to derive information-theoretical upper bounds on the optimal information rate and the optimal average information rate. Stinson [19] proved the general result that, for any graphG having maximum degreed, there exists a perfect secret sharing scheme realizingG with (average) information rate at least 2/(d+1). For alld≥3 and ɛ>0, we construct graphs having maximum degreed such that the optimal (average) information rate is at most 2/(d+1−ɛ).
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Communicated by: D. Jungnickel
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Van Dijk, M. On the information rate of perfect secret sharing schemes. Des Codes Crypt 6, 143–169 (1995). https://doi.org/10.1007/BF01398012
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DOI: https://doi.org/10.1007/BF01398012