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

摘要

For a secret sharing scheme, two parameters $d_{min}$ and $d_{cheat}$ aredefined in [12] and [13]. These two parameters measure the error-correctingcapability and the secret-recovering capability of the secret sharing schemeagainst cheaters. Some general properties of the parameters have been studiedin [12,[9] and [13]. The MDS secret-sharing scheme was defined in [12] and itis proved that MDS perfect secret sharing scheme can be constructed for anymonotone access structure. The famous Shamir $(k,n)$ threshold secret sharingscheme is the MDS with $d_{min}=d_{cheat}=n-k+1$. In [3] we proposed the linearsecret sharing scheme from algebraic-geometric codes. In this paper the linearsecret sharing scheme from AG-codes on elliptic curves is studied and it isshown that many of them are MDS linear secret sharing scheme.