### Question 105. What is Blakley's Secret Sharing Scheme?

Blakley's secret sharing scheme [Bla79]
is geometric in nature. The secret is a point in an *m*-dimensional
space. *n* shares are constructed with each share defining a hyperplane
in this space. By finding the intersection of any *m* of these planes,
the secret (or point of intersection) can be obtained. This scheme is not
perfect, as the person with a share of the secret knows that the secret
is a point on his hyperplane. Nevertheless, this scheme can be modified
to achieve perfect security [Sim92].

Figure 10. Blakley's scheme

A special case of Blakley's scheme is shown in Figure 10. This is based
on the scenario where two shares are required to recover the secret. A
two-dimensional plane is used as only two shares are required to recover
the secret. The secret is a point in the plane. Each share is a line that
passes through the point. If any two of the shares are put together, the
point of intersection, which is the secret, can be easily derived.