*21:17*[Pub][ePrint] Infinite Secret Sharing -- Examples, by Alexander Dibert and Laszlo Csirmaz

The motivation for extending secret sharing schemes to cases when either the

set of players is infinite or the domain from which the secret and/or the

shares are drawn is infinite or both, is similar to the case when switching

to abstract probability spaces from classical combinatorial probability. It

might shed new light on old problems, could connect seemingly unrelated

problems, and unify diverse phenomena.

Definitions equivalent in the finitary case could be very much different

when switching to infinity, signifying their difference. The standard

requirement that qualified subsets should be able to determine the secret

has different interpretations in spite of the fact that, by assumption, all

participants have infinite computing power. The requirement that unqualified

subsets should have no, or limited information on the secret suggests that

we also need some probability distribution. In the infinite case events with

zero probability are not necessarily impossible, and we should decide

whether bad events with zero probability are allowed or not.

In this paper, rather than giving precise definitions, we enlist an abundance

of hopefully interesting infinite secret sharing schemes. These

schemes touch quite diverse areas of mathematics such as projective

geometry, stochastic processes and Hilbert spaces. Nevertheless our main

tools are from probability theory. The examples discussed here serve as

foundation and illustration to the more theory oriented companion paper ``Probabilistic Infinite Secret Sharing.\'\'