MDS Ideal Secret Sharing Scheme from AG-codes on Elliptic Curves
<|reference_start|>MDS Ideal Secret Sharing Scheme from AG-codes on Elliptic Curves: For a secret sharing scheme, two parameters $d_{min}$ and $d_{cheat}$ are defined in [12] and [13]. These two parameters measure the error-correcting 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 secret-sharing scheme was defined in [12] and it is 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 $d_{min}=d_{cheat}=n-k+1$. 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.<|reference_end|>
@article{chen2006mds,
    title={MDS Ideal Secret Sharing Scheme from AG-codes on Elliptic Curves},
    author={Hao Chen},
    journal={arXiv preprint arXiv:cs/0608055},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0608055},
    primaryClass={cs.CR}
}