Ideal Threshold Schemes from MDS Codes

We observe that MDS codes have interesting properties that can be used to construct ideal threshold schemes. These schemes permit the combiner to detect cheating, identify cheaters and recover the correct secret. The construction is later generalised so the resulting secret sharing is resistant against the Tompa-Woll cheating.

[1]  Ehud D. Karnin,et al.  On secret sharing systems , 1983, IEEE Trans. Inf. Theory.

[2]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[3]  Ernest F. Brickell,et al.  On the classification of ideal secret sharing schemes , 1989, Journal of Cryptology.

[4]  Steven Roman,et al.  Coding and information theory , 1992 .

[5]  Mitsuru Ito,et al.  Secret sharing scheme realizing general access structure , 1989 .

[6]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[7]  R. J. McEliece,et al.  On sharing secrets and Reed-Solomon codes , 1981, CACM.

[8]  G. R. BLAKLEY Safeguarding cryptographic keys , 1979, 1979 International Workshop on Managing Requirements Knowledge (MARK).