Constructions of some secret sharing schemes based on linear codes

Abstract

There are perfect and ideal threshold secret sharing schemes, for example, Shamir’s secret sharing  scheme. For the case of general secret sharing schemes with an arbitrary access structure, it is possible to construct a perfect scheme for any access structure (for example, the Ito – Saito – Nishizeki scheme, the Benaloh – Leichter scheme), but in general, such a scheme will not be an ideal secret sharing scheme. In the paper, for some classes of access structures, the construction of perfect and ideal secret sharing schemes based on linear codes is given. We also give a construction of perfect verifiable secret sharing schemes for any access structure for which there is a line code that implements this structure.

Keywords

• cryptography
• linear code
• secret sharing scheme
• access structure