George Blakley invented a secret sharing scheme in 1979. Each secret share is a plane, and the secret is the point at which three shares intersect. ...

Two nonparallel lines in the same plane intersect at exactly one point. Three "nonparallel" planes in space intersect at exactly one point. More generally, any n n-dimensional hyperplanes intersect at a specific point. The secret may be encoded as any single coordinate of the point of intersection. The other coordinates must be random. Each player is given enough information to define a hyperplane; the secret is recovered by calculating the planes' point of intersection.

Blakley's scheme is less space-efficient than Shamir's; while Shamir's shares are each only as large as the original secret, Blakley's shares are t times larger, where t is the threshold number of players. Blakley's scheme can be tightened by adding restrictions on which planes are usable as shares. The resulting scheme is identical to Shamir's polynomial system.