Some democratic secret sharing schemes (Q1893162)

For constructing a secret sharing scheme a single person or institution trusted by all participants is needed in the classical case. This so- called dealer is responsible for selecting the secret, coining the shares, and their distribution. As for some applications an all-party trustee knowing the secret may be undesirable, secret sharing schemes without a dealer received some attention in the past, e.g. by \textit{I. Ingemarsson} and \textit{G. J. Simmons} [Lect. Notes Comput. Sci. 473, 266- 282 (1991)], who call this type of scheme ``democratic''. A democratic secret sharing scheme is established by the participants on their own with the secret randomly chosen and the integrity of the scheme verifiable for all. From an information theoretic view, but also for reasons of practicability, it is always interesting to ask for short keys, here shares, aiming at a high information rate. The author presents new constructions for democratic secret sharing schemes which are as good as possible in this respect. The amount of information to be kept secret by each participant is not larger than in the corresponding original schemes with a dealer --- overcoming the main disadvantage of former proposals how to share a secret democratically.