A method and system calculates shares and sub-shares of a secret for distribution among cooperating entities. In one embodiment, the method creates shares of the secret, with each share containing a point on a K-dimensional secret hyperplane that embeds the secret, where K is the number of shares to reconstruct the secret. The method further constructs sub-shares for the shares. The sub-shares of a share define a set of secondary K-dimensional hyperplanes that intersect at the point contained in the share. The sub-shares are distributed to a plurality of cooperating entities for secret sharing.