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Non-interactive and information-theoretic secure verifiable secret sharing. (English) Zbl 0763.94015
Advances in cryptology, Proc. Conf., CRYPTO ’91, Santa Barbara/CA (USA) 1991, Lect. Notes Comput. Sci. 576, 129-140 (1992).
Summary: [For the entire collection see Zbl 0753.00024.]
It is shown how to distribute a secret to \(n\) persons such that each person can verify that he has received correct information about the secret without talking with other persons. Any \(k\) of these persons can later find the secret \((1\leq k\leq n)\), whereas fewer than \(k\) persons get no (Shannon) information about the secret. The information rate of the scheme is \({1\over 2}\) and the distribution as well as the verification requires approximately \(2k\) modular multiplications pr. bit of the secret. It is also shown how a number of persons can choose a secret “in the well” and distribute it verifiably among themselves.

94A60 Cryptography