Two matrices for Blakley´s secret sharing scheme

The secret sharing scheme was invented by Adi Shamir and George Blakley independently in 1979. In a (k, n)-threshold linear secret sharing scheme, any k-out-of-n participants could recover the shared secret, and any less than k participants could not recover the secret. Shamir´s secret sharing scheme is more popular than Blakley´s even though the former is more complex than the latter. The reason is that Blakley´s scheme lacks determined, general and suitable matrices. In this paper, we present two matrices that can be used for Blakley´s secret sharing system. Compared with the Vandermonde matrix used by Shamir´s scheme, the elements in these matrices increase slowly. Furthermore, we formulate the optimal matrix problem and find the lower bound of the minimal maximized element for k=2 and upper bound of the minimal maximized element of matrix for given k.