1. A computer-implemented method for distributing a secret, the method comprising: creating a share of a plurality of shares of the secret, the share containing a point on a K-dimensional secret hyperplane that embeds the secret, wherein K is the number of shares to reconstruct the secret; constructing sub-shares from the share, the sub-share defining a set of secondary K-dimensional hyperplanes that intersect at the point contained in the share; and distributing the sub-shares to a plurality of cooperating entities for secret sharing.