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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.

##### MSC:
 94A60 Cryptography
##### Keywords:
secure verifiable secret sharing; Shannon information