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• W2898897019 abstract "Consider the following secret-sharing problem. Your goal is to distribute a long file s between n servers such that $$(d-1)$$ -subsets cannot recover the file, $$(d+1)$$ -subsets can recover the file, and d-subsets should be able to recover s if and only if they appear in some predefined list L. How small can the information ratio (i.e., the number of bits stored on a server per each bit of the secret) be? We advocate the study of such d-uniform access structures as a useful scaled-down version of general access structures. Our main result shows that, for constant d, any d-uniform access structure admits a secret sharing scheme with a constant asymptotic information ratio of $$c_d$$ that does not grow with the number of servers n. This result is based on a new construction of d-party Conditional Disclosure of Secrets (CDS) for arbitrary predicates over n-size domain in which each party communicates at most four bits per secret bit. In both settings, previous results achieved a non-constant information ratio that grows asymptotically with n, even for the simpler (and widely studied) special case of $$d=2$$ . Moreover, our multiparty CDS construction yields the first example of an access structure whose amortized information ratio is constant, whereas its best-known non-amortized information ratio is sub-exponential, thus providing a unique evidence for the potential power of amortization in the context of secret sharing. Our main result applies to exponentially long secrets, and so it should be mainly viewed as a barrier against amortizable lower-bound techniques. We also show that in some natural simple cases (e.g., low-degree predicates), amortization kicks in even for quasi-polynomially long secrets. Finally, we prove some limited lower-bounds, point out some limitations of existing lower-bound techniques, and describe some applications to the setting of private simultaneous messages." @default.
• W2898897019 created "2018-11-09" @default.
• W2898897019 creator A5057984954 @default.
• W2898897019 creator A5086684679 @default.
• W2898897019 date "2018-01-01" @default.
• W2898897019 modified "2023-09-24" @default.
• W2898897019 title "On the Power of Amortization in Secret Sharing: d-Uniform Secret Sharing and CDS with Constant Information Rate" @default.
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• W2898897019 doi "https://doi.org/10.1007/978-3-030-03807-6_12" @default.
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