Blakley Secret Sharing
If you want to find out about other secret sharing methods using Shamir’s Secret Shares and with Chinese Remainder Theory, click here.
With secret sharing, we distribute n secret shares and then define that t of these shares can rebuild a secret. The value of t is known as the threshold. In this article I will use the example here. Blakley wrote about the method in 1979 [1]:
In Blakley’s method, we define a secret x, and then construct a number of hyperplanes. For example, we could define each share with a unique hyperplane of the form:
z = a x + b y + c (mod p)We first define the secret value of x, and then select values of a, b and c for the secrets. If we have three secret shares, we would have:
a1 x + b1 y — z = -c1 (mod p)
a2 x + b2 y — z = -c2 (mod p)
a3 x + b3 y — z = -c3 (mod p)
and to recover the secret, we need to find x. Now we can have a matrix form of:
If we take this example:
z = 4 x + 19 y + 68 (mod 73)
z = 52 x + 27 y + 10 (mod 73)
z = 36 x +65 y + 18 (mod 73)
