In Distributed Secret Sharing schemes, secrets are encoded with shares distributed over multiple nodes of a network. Each involved party has access to a subset of the nodes and thus to a subset of the shares and is able to reconstruct a specific secret. Usually, these schemes are evaluated by measuring the required storage overhead, as well as the encoding and decoding complexities. In this paper, we provide new Distributed (multi) Secret Sharing Protocols for $(k,n)$-threshold access structures that improve on previous results, characterized by nearly-optimal storage overhead, achieving both storage optimality and a better encoding/decoding complexity. The protocols are also simpler than previous ones and allow for easier encoding.
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