MDS Ideal Secret Sharing Scheme from AG-codes on Elliptic Curves

For a secret sharing scheme, two parameters dmin and dcheat are defined in [12] and [13]. These two parameters measure the errorcorrecting capability and the secret-recovering capability of the secret sharing scheme against cheaters. Some general properties of the parameters have been studied in [12],[9] and [13]. The MDS secretsharing scheme was defined in [13] and it was proved that MDS perfect secret sharing scheme can be constructed for any monotone access structure. The famous Shamir (k, n) threshold secret sharing scheme is the MDS with dmin = dcheat = n − k + 1. In [3] we proposed the linear secret sharing scheme from algebraic-geometric codes. In this paper the linear secret sharing scheme from AG-codes on elliptic curves is studied and it is shown that many of them are MDS linear secret sharing scheme.